SPARKING INQUIRY THROUGH SCIENCE AND MATH...SPARKING INQUIRY THROUGH SCIENCE AND MATH 11A Perimeter Inspirations Grade 11: A Deeper Understandingof Energy Contents About Perimeter

S P A R K I N G I N Q U I R Y T H R O U G H

S C I E N C E A N D M AT H

11APerimeter Inspirations

Grade 1 1 : A Deeper Understanding of Energy

Contents

About Perimeter 2

Introduction 3

Using This Resource in Your Classroom 3

Teacher Background 4

Activity 1: The Conservation and Transformation of Energy 9

Activity 2: Innovative Technologies 17

Activity 3: Nuclear Transformations 22

Activity 4: Ionizing Radiation 29

Activity 5: Mass-Energy Equivalence 36

Activity 6: Where Do the Elements Come From? 42

Activity 7: Conservation Laws and Dark Energy 51

Answers 58

Appendix A: Light Bulb Comparison Cards 64

Appendix B: Table of Isotopes—Simplified 65

Appendix C: Ionizing Radiation Cards 66

Appendix D: Equivalent Dose Table 68

Appendix E: Radiation Scenario Cards 69

Appendix F: Star Cards 70

Appendix G: News Flash— What’s Happening to Our Universe? 71

Appendix H: Fact Cards— What’s Happening to Our Universe? 72

Assessment 73

Self-Assessment 74

Glossary 75

Credits 76

About Perimeter

Perimeter InstitutePerimeter Institute is the world’s largest research hub devoted to theoretical physics. The independent Institute was founded in 1999 to foster breakthroughs in the fundamental understanding of our universe, from the smallest particles to the entire cosmos. Research at Perimeter is motivated by the understanding that fundamental science advances human knowledge and catalyzes innovation and that today’s theoretical physics is tomorrow’s technology. Located in the Region of Waterloo, the not-for-profit Institute is a unique public–private endeavour, including the Governments of Ontario and Canada, that enables cutting-edge research, trains the next generation of scientific pioneers, and shares the power of physics through award-winning educational outreach and public engagement.

Perimeter InspirationsThis series of in-class educational resources is designed to help teachers inspire students by sharing the mystery and power of science and math through inquiry-based, Ontario curriculum–linked activities. Activities integrate global competencies—critical thinking and problem solving; innovation, creativity, and entrepreneurship; self-directed learning; collaboration; communication; citizenship—all of which equip students to make meaningful contributions to society as they learn, grow, and mature.

Perimeter Inspirations is the product of extensive collaboration between experienced teachers and Perimeter Institute’s Educational Outreach staff. This resource has been designed with both the expert and the novice teacher in mind and has been thoroughly tested in classrooms. The digital resource features student activity sheets and a variety of assessment tools in a modifiable format to suit the particular needs of each student.

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A Deeper Understanding of Energy

Introduction

There is an invisible quantity embedded in everything around you. It exists in the food you eat, in the electronics you use, and in every atom in your body. What’s more, it pervades every action and movement you make. This ubiquitous quantity is energy. Understanding how energy flows between, transforms within, and is stored in objects allows scientists to predict the future and understand the past. It’s rocket science; it’s nuclear physics; it’s environmental sustainability. It may even hold the key to understanding what will ultimately happen to all the stars, planets, and galaxies of the universe.

Share the power of representing and understanding energy with your students using these seven hands-on lessons, which explore the topics of mass-energy equivalence, the origin of elements, nuclear radiation, and the enigmatic concept of dark energy.

The resource provides classroom activities to help teachers deliver the Energy and Society strand of Grade 11 Physics (SPH3U). Scientific investigation skills, career exploration, and financial literacy are integrated into the lessons. Specific suggestions have been made

for adapting the activities for a wide range of student learning needs. The resource package also includes a short, dynamic video, closely tied to the lessons. It takes students on a journey from learning how to think about and represent energy, into the very heart of all atoms, and then out to the dynamic evolution of the entire universe.

All activities offer hands-on experiences for students. Each activity includes background information for teachers, assessment material, and specific teaching tips, which will help make energy understandable and relatable and provide a rich and engaging experience for students. The resource culminates with an activity on dark energy, which pushes students to apply their knowledge and creativity to an open problem and to the very nature of science itself.

Developed in a year-long project involving high school teachers and students, physics researchers, Perimeter Educational Outreach staff, and media professionals, the module shares the power of science and empowers students to fully engage in the process of scientific discovery.

Using This Resource in Your Classroom

Flow of ActivitiesThis resource consists of a video and seven activities that explore work and energy. The focus is conceptual understanding, and the resource should be supplemented with related topics and mathematical lessons. Activity 1 introduces students to energy flow diagrams and work-energy bar charts. Activity 2 builds on these skills by examining energy transformations in simple devices. Activity 3 explores energy in nuclear transformations, such as alpha and beta decay. Activity 4 introduces the concept of ionizing radiation and has students examine a variety of potential sources of ionizing radiation in their lives. Activity 5 uses a hands-on activity to introduce binding energy and mass-energy equivalence. Activity 6 guides students through the process that builds elements inside a star. The final activity and video take students on a journey through the evolution of conservation laws and introduces them to dark energy as the latest addition to our model of the universe.

Each activity uses the tools introduced at the start, so beginning with Activity 1 is recommended. Activities 3, 4, and 5 discuss similar concepts from different perspectives. There are many connections between them, but each can be used independently.

Structure of ActivitiesEach of the module’s activities can be completed in approximately one hour and includes two parts for students:

1. Student Activity: a sequence of hands-on activities and related discussion questions

2. Consolidate Your Learning: an assessment for/of learning (formative/summative) designed to help students cement the content covered in the activity

The activities are supported by modifiable handouts. You are encouraged to adapt these to meet the needs of individual students or your particular class.

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Promoting Effective Group WorkThe student activities have been designed with small groups of students in mind. Sharing group work expectations with students will keep groups on task and lead to better participation and deeper learning. Two critical components for effective group work are as follows:

1. Individual accountability: Ensure that each student has an important, specific role to play (e.g., experimenter, recorder), so that they are responsible for their own learning. With this approach, students who might

resist active participation will feel motivated to fulfill their roles and offer meaningful contributions to the group.

2. Positive teamwork: By fostering a positive and supportive classroom environment, students will encourage and challenge each other in constructive ways. Guide students to set a clear and meaningful goal for the group activity, or provide students with a goal. Ensure each student has a different role, and emphasize the significance of each role in achieving the group’s goal.

Teacher Background

The information below is designed to provide a brief overview of energy concepts and related pedagogy. The content is related to the activities in this module but may go beyond the Grade 11 curriculum to provide a deeper framework and help build connections with the Grade 12 curriculum.

What is energy?Energy is an accounting tool that allows physicists to make accurate predictions on how a closed system will behave. In an open system, work accounts for any changes in the amount of energy in that system (as does heat for thermodynamic processes). Energy is energy, whether it’s being stored gravitationally, kinetically, or in an object’s mass, just as money is money, whether it’s being stored as Canadian dollars, American dollars, or Japanese yen. Different energy stores can transform into each other (for example, mass energy into kinetic energy, or elastic energy into gravitational energy).

Is energy really conserved?Not all interactions need to conserve energy in Newtonian mechanics (e.g., friction). However, empirical evidence for the idea of energy conservation for the fundamental interactions has been growing since the 17th century, making conservation of energy a foundational principle we use when modelling everyday phenomena. In the early 20th century, mathematician Emmy Noether strengthened the theoretical support for conservation laws (including energy) by proving a theorem that connected the symmetries of a system to corresponding conservation laws. In particular, she

proved (with assumptions) that energy conservation follows if physics is symmetric under time translations (physics does not depend on when it’s applied). Einstein’s theory of general relativity relates gravity to energy, but the theory makes sense only if energy really is conserved, strengthening the case further at a fundamental level.

Why is energy difficult for students?Energy is an abstract concept that is difficult to visualize. For physics teachers, this is not a problem; we analyze an energy scenario algebraically. (We consider initial and final amounts of energy, determine how much energy is transformed from one type to another, and account for any work that has been done on or by the system along the way.) To students, however, this is a significant leap in learning about energy. In algebraic analysis, two decisions are made that are not obvious. As teachers, we often implicitly make these decisions without explicitly modelling how.

Defining the System: The first of these decisions is how to define the system and the environment. Consider throwing a ball into the air and the ball reaching a maximum height. The kinetic energy of the ball is stored as gravitational energy, between the ball and Earth’s gravitational field. However, an equally valid way to think of it is as the kinetic energy of the ball continually decreasing due to the negative work done by Earth on the ball via the external downward force of gravity. The difference in these analyses is how we define the system and the environment. Consider how confusing this is for a student trying to make sense of these two valid interpretations, without the idea of a system being explicitly mentioned.

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How Energy Is Transformed: The second implicit decision is how one type of energy is transformed within a system, or flows in from, or out to, the environment. Does kinetic energy become multiple forms of energy within the system? Is the energy of the system conserved during this process? These are significant questions for students, often taken for granted when energy analysis is only algebraic.

Using Multiple Representations for Energy AnalysisTwo energy representations are used throughout this module: energy flow diagrams and work-energy bar charts. Why are representations necessary? The same question could be asked for force analysis, but because force diagrams (free-body diagrams) have been taught in classrooms for decades, it isn’t. Physics education research1 shows that student difficulties in understanding the system, work, and external and internal energy transformations can be alleviated with concrete representations of energy ( just as force diagrams do for force analysis). Explanations, advantages, and examples of these representations follow. These representations are best used in conjunction with each other. Use an energy flow diagram first to qualitatively structure transformations within the system and/or flows into and out of the environment. Then quantitatively represent these processes with a work-energy bar chart.

What is an energy flow diagram?An energy flow diagram is a visual representation of energy flows and transformations where the system and the environment are explicitly defined. Objects within a circle are “the system.” Everything outside the circle is “the environment.”

Again consider throwing a ball upward. In Figure 1(a), the ball is the system and Earth is the environment. In this case, energy is leaving the system, because Earth is doing negative work on the ball (equivalently, here, the ball is doing positive work on Earth). As energy leaves the system, the ball slows and then stops for an instant when it reaches a maximum height. To represent energy flows with the environment, we draw an arrow that crosses over the system’s boundary, with the direction of the arrow representing the direction of energy flow. An

1. See A. Van Heuvelen & X. Zou, “Multiple representations of work–energy processes,” American Journal of Physics, 69, 184 (2001); and B. A. Lindsey, P. R. L. Heron, & P. S. Shaffer, “Student understanding of energy: Difficulties related to systems,” American Journal of Physics, 80, 154–163 (2012).

outward arrow is a decrease in system energy (negative work); an inward arrow is an increase (positive work). There is no significance to an arrow being curved or straight; it merely helps space out labels in the diagram.

In Figure 2(a), the ball and Earth are the system. There is no environment, because it’s not significant in this energy analysis. Though the observation is the same, we depict it differently because our choice of system has changed. In this case, kinetic energy has transformed into gravitational energy. Eventually, all kinetic energy is transformed, and the ball stops for an instant at a maximum height. To represent energy transformations within a system, we draw an arrow within the circle. We label energy with the type of storage mechanism (kinetic, gravitational, elastic, etc.) and a subscript number to indicate a moment in time. For work, there is no number subscript, because it’s a process that occurs over an amount of time (you could indicate this with, a “1:2” subscript, but it gets messy).

Notice that this scenario can have either net work or energy conservation, depending on the choice of system. Visually, this is shown by redrawing the circle in Figure 1(a) to include Earth as part of the system (Figure 2(a)).

Ball

Ek1

Wg

Earth

Ek1 +Wext= Ek2

0

–

+

(a) (b)

Figure 1 (a) An energy flow diagram and (b) a work-energy bar chart for a ball moving upward in the air and slowing down. The system is defined as the ball, and the environment is defined as Earth.

Ball + Earth

Ek1 Eg2

Ek1 + Eg1 +Wext= Ek2 + Eg2

0

–

+

(a) (b)

Figure 2 (a) An energy flow diagram and (b) a work-energy bar chart for a ball moving upward in the air and slowing down. Here, the system is defined as the ball and Earth.

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https://aapt.scitation.org/doi/10.1119/1.1286662




What is a work-energy bar chart?A work-energy bar chart shows the amount of energy in each storage mechanism at different moments in time. The shaded column in the chart, Wext, represents the energy flow into, or out of, the system. A work-energy bar chart is a visual representation of an algebraic energy equation.

Consider the ball scenario again. For Figure 1(b), all the energy stored as kinetic energy flows out of the system (represented by a negative Wext) due to the external force of gravity from the environment. This is represented by the negative work bar, which has the same height as the kinetic energy bar at moment 1. In Figure 2(b), the system has not interacted with the environment (assume negligible air resistance), so Wext is zero; all of the kinetic energy at moment 1 transformed into gravitational energy at moment 2. This is shown by the heights of the Ek1 and Eg2 bars being the same, with the assumption that the zero point for gravitational energy is at the height of the initial throw. The exact heights of the bars are not important as long as the comparisons are clear. Just ensure that the heights of the bars aren’t obviously wrong. For a different zero point, there would be a bar for Eg1 and a bar of a different height for Eg2, with ∆Eg = Ek1. The versatility of this representation can help alleviate students’ confusion between ∆Eg and Eg when they represent energy algebraically.

What are the advantages of using energy flow diagrams?An energy flow diagram ensures that the system is explicitly defined in the problem-solving process. This scaffolding step is akin to a force diagram in force analysis. We physics teachers can write equations for the components of Newton’s second law without a diagram, but we wouldn’t expect students who are learning forces to be able to do this without scaffolding. Energy flow diagrams also clarify the distinction between energy conservation and work. Depending on how the system has been defined, a process can either conserve energy (a closed system) or exchange energy with the environment (an open system). If a process doesn’t conserve energy, you can always redefine a larger system to include the environment so that energy will be conserved for that process. For more complex processes, an energy flow diagram can help organize the analysis, keeping track of all possible types of energy storage.

What are the advantages of using work-energy bar charts?Creating energy equations that mathematically represent a situation can be challenging. A work-energy bar chart helps scaffold this step by showing graphically how energy transforms between different types and/or flows in from, or out to, the environment from one moment to the next. After defining a system and qualitatively tracking energy with an energy flow diagram, a work-energy bar chart can quantify the energy flows and transformations and visually represent the correct algebraic energy equation before students are required to use it.

What follows are a series of examples that illustrate how energy flow diagrams and work-energy bar charts can be used to help students conceptually understand energy analysis. They use the notation conventions in the table below.

Notation Energy Store

Ek Kinetic

Eg Gravitational

Ee Elastic

Eth Thermal

E0 Mass

Eγ Light

Eint Chemical

Efus Latent heat of fusion

Subscript numbers are used to define moments. A colon indicates a time period defined by the moments preceding and following it. Object-specific quantities are specified with a comma and an initial.

Example 1: A Mechanical SystemA 1500 kg car travelling at 10 m/s runs out of gas while approaching a valley (Figure 3). The driver puts the car in neutral so it will roll. If the car coasts to a height of 5 m up the second hill, estimate how much thermal energy has been created in the car + road + Earth system if interactions with the environment are negligible.

10 m5 m

Figure 3 A visual representation of the situation in Example 1.

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Example 1 Representations

Both representations have been drawn (Figure 4). Because care was taken in drawing the height of bar Eg2 to be half of Eg1, the thermal energy created should be equal to 1–2Eg1 + Ek1. Visually representing where energy is stored makes it natural to determine quantitative relationships between these storage mechanisms.

From the work-energy bar chart (Figure 4(b)), the algebraic equation representing this energy scenario is

Ek1 + Eg1 = Eg2 + Eth2

Here students need to calculate each of these quantities, except for Eth2, which they are solving for.

(Thermal energy created during ∆t1:2: 1.49 × 105 J)

Car + Road +Earth

Eg1 Eg2

Ek1 Eth2

Ek1+Eg1+Eth1+Wext=Ek2+Eg2+Eth2

0

–

+

(a) (b)

Figure 4 (a) An energy flow diagram and (b) a work-energy bar chart for Example 1

Example 2: Heat Transfer and Calorimetry

Three ice cubes with a mass of 18.0 g and a temperature of −10.0°C are dropped into a cup containing 275.0 g of water at 60.0°C (Figure 5). Determine the final temperature of this water + ice system, after thermal equilibrium has been reached.


Water + Ice

Eth1,w

Eth1,i

Eth2,w

Efus,i:w

Eth2,i

Eth1,w+Eth1,i+Wext=Eth2,w+Eth2,1+ Efus,i:w

0

–

+

(a) (b)


Note: The heights of the bars are not to scale because changes in thermal energies tend to be dwarfed by absolute thermal energies. This is a good discussion to have with students when using energy representations that wouldn’t necessarily arise from an exclusively algebraic approach.

From the work-energy bar chart (Figure 6(b)), the algebraic equation representing this energy scenario is

Eth1,w + Eth1,i = Eth2,w + Eth2,i + Efus,i:w

Or −∆Eth,w = ∆Eth,i + Efus,i:w

This is, of course, just the regular Qlost = Qgained relationship for heat transfer of a closed system, where Q is defined as the thermodynamic quantity of heat. Here students need to calculate each of these quantities, using the familiar ∆Eth = mC∆T and Efus = mLfus to solve for the final temperature. Consider how versatile these representations can be in handling more complex scenarios involving an open system or a third substance at a different temperature.

(Temperature at event 2 (thermal equilibrium): 51.1°C)

Example 3: Mass-Energy Equivalence

One of the last nuclear fusion reactions during a supernova for certain stars is one that turns one carbon atom and one helium atom into an oxygen atom and excess energy:

126C + 4

2He → 168O + γ (energy)

The masses of the relevant nuclei in this nuclear reaction are as follows:

mC = 1.994 42 × 10−26 kg, mHe = 0.664 65 × 10−26 kg, and mO = 2.656 70 × 10−26 kg

How much energy, in MeV (1 MeV = 106 eV), is released when 1 mg of carbon combines with the right amount of helium to fuse completely to form oxygen? You may assume the change in total kinetic energy of all nuclei is negligible in this nuclear process.


From the work-energy bar chart (Figure 7(b)), the algebraic equation representing this scenario is

E0,C + E0,He = E0,O + Eγ

Here students can calculate the mass-energy quantities and solve for Eγ. They can then calculate how many reactions occur for 0.001 g of C to figure out how many multiples of Eγ will be released.

(Energy released by 0.001 g of C fusing with He to form O: 6.67 × 1020 MeV)

Figure 5 A visual representation of the situation in Example 2

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C + He + O

E0,CE0,O

E0,He Eγ

E0,C +E0,He+Wext=E0,C + Eγ

0

–

+

(a) (b)


Advanced Example: Rocket with Spring (includes Grade 12 concepts)

A 10.2 kg rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring whose spring constant is 500 N/m (Figure 8). The bottom of the spring is anchored to the ground. The rocket starts from rest with the partially compressed spring supporting its weight.

(i) After engine ignition, determine the rocket’s speed when the spring has stretched 40 cm.

(ii) Compare this speed to the rocket’s speed after travelling 40 cm, had there been no spring.

Advanced Example Representations

(i) First, define events. Then draw an energy flow diagram and work-energy bar chart:

Rocket + Fuel +Spring + Earth

Eint1Ek2

Ee1 Eg2

Ee2

Eint1 + Ee1 +Wext= Ek2 + Ee2 + Eg2

0

–

+

(a) (b)

Figure 9 (a) An energy flow diagram and (b) a work-energy bar chart for the case with a spring

Event 1 is at rest on the spring. Event 2 is when the rocket is 40 cm above its starting position.

The representations (Figure 9) assume that the height of the rocket at event 1 is the position of zero gravitational energy. We’ve also assumed no losses due to friction, though they are easily added if required. From the work-energy bar chart, the algebraic equation representing this energy scenario is

Eint1 + Ee1 = Ek2 + Ee2 + Eg2

Here students need to calculate each of these quantities, except for Ek2, which they are solving for.

(ii) For the case of no spring, set the spring constant to be 0 N/m in the equations, or draw the two representations (Figure 10) to lead to the algebraic equation.

Rocket + Fuel +Earth

Eint1Ek2

Eg2

Eint1 +Wext= Ek2 + Eg2

0

–

+

(a) (b)

Figure 10 (a) An energy flow diagram and (b) a work-energy bar chart for the case with no spring.

In Figure 10(b), the kinetic energy at event 2 increases, while the gravitational energy does not. (The amount of fuel used is likely less because the rocket will be firing for a shorter time period, so the height of the bar in this scenario is lower.) The increase in kinetic energy is actually given by the difference in height of the elastic energies at moments 1 and 2 (accounting for less Eint1) for the case with the spring. In retrospect, this is an obvious physical insight into this scenario, but one that is easily missed by an exclusively algebraic approach.

From the work-energy bar chart, or by setting the spring constant to be 0 N/m, the algebraic equation representing this energy scenario is

Eint1 = Ek2 + Eg2

Again, students need to calculate each of these quantities, except for Ek2, which they are solving for.

(Speeds at event 2: 2.42 m/s (with spring), 3.43 m/s (no spring))

Figure 8 A visual representation of the situation in the Advanced Example

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Activity 1: The Conservation and Transformation of EnergyLesson Plan

IntroductionIn this activity, students explore two conceptual representations for energy transfer and the conservation of energy. The ideas of the system, the environment, and work are developed in parallel. Students analyze a simple example of a falling ball gaining kinetic energy and then extend their ideas to examples of increasing complexity.

Suggested Time: 70–90 minutes

Purpose• To introduce a visual and conceptual model of energy

conservation and transformation

• To develop terminology related to energy, energy transformations, and work

PRIOR KNOWLEDGE & SKILLS

• Students need a basic understanding of kinematics, in particular, objects experiencing both free fall and falling with air resistance.

Materials• 1 tennis ball (or other object that can be dropped

safely) per group

• spring cart with inclined plane and optional motion sensor

• scrap or recycled paper

Teacher Instructions1. Set up an inclined plane at roughly 20°. Put a barrier

at the bottom of the incline. Compress and trigger the spring cart to test that the release and return speeds are approximately the same. You can also use a motion sensor to show this more precisely.

2. Introduce energy to your class, using ideas from the Teacher Background as desired. Then hand out the tennis balls and have students in groups of three or four work through the activity.

3. Circulate in the classroom to ensure that the correct ideas are emerging. For instance, in Part 1, question 7, students may have difficulty connecting a hand stopping a falling ball to an increase in molecular vibrations in both objects. This is an opportunity to guide them through the concept of thermal energy.

4. As a class, at the end of the activity, check and consolidate the representations of energy.

SAFETY ALERT

When choosing objects to drop, reduce the risk. Find objects that are neither too sharp nor too heavy. Use caution in Part 3 while compressing and triggering a spring cart. Compressed springs can expand suddenly and cause injury. Keep spring carts at least 15 cm away from people’s eyes.

Teacher Tips• This activity uses a particular notation convention

where subscript numbers, such as “1” and “2”, define key moments in time. Two key moments placed on either side of a colon (:) define a time interval. So, ∆t1:2 represents the amount of time between moment 1 and moment 2. You may wish to change this notation style to suit your students’ needs.

• This activity will be easier for students if you have already used a systems approach to the analysis of force. Facilitate this by using interaction diagrams when teaching forces: OAPT–Teaching Forces.

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A Deeper Understanding of EnergyA

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http://newsletter.oapt.ca/PER/PER_Forces_1/

INQUIRY T IP

Discussion: Prompt a deeper discussion of the concept of a system by asking what a ball is made of. As students recall that all objects are collections of molecules and atoms (systems made of many individual objects), discuss how both kinematics and force analysis are possible without taking into account the individual details of each molecule or atom.

DIFFERENTIATED SUPPORT

To Assist: Some students may feel hesitant about group work or have difficulty with it. Provide advance warning, include a familiar student to ease comfort, provide open space to work, provide specific tasks, or teach social skills, such as active listening and constructive feedback.

ExtensionExplore gravitational energy further by introducing the concept of a zero point for an interaction. Choose where to set the amount of energy stored in the gravitational field as zero, explaining the reasons for setting that point. This leads to the zero point of binding energy and is a foundational concept that aligns with this energy introduction.

STSE Connections

Changing energy from an abstract concept to a concrete representation is an important step in tackling our culture’s energy problem. Realizing that most energy transformations (Figure 1) result in usable types of energy stores (e.g., kinetic, gravitational, elastic) becoming an unusable energy store (e.g., thermal) is a critical message that is easily missed when students analyze situations only mathematically. To solve the energy problem, society first needs to understand it. To learn more, students can research global annual energy use and estimated remaining energy at sites such as the World Energy Council. They can then represent this information using work-energy bar charts for different time periods, such as 5 or 10 years.

Teacher Background

Conceptual Student Pitfalls for Energy

A lot of confusion around energy is due to the language we use to describe it. Consider the following statements:

“There’s a difference between kinetic and potential energy.”

Energy is energy. There is no fundamental difference between kinetic and potential energy, only that they are storing energy in different mechanisms. Although potential energy is often thought of as the only way to store energy, conceptually, kinetic energy stores energy in the motion of an object. Consider a puck sliding at a constant velocity; the kinetic energy is stored in the motion of the puck. This removes the importance of the term “potential” as a descriptor of stored energy, because all energy is ultimately stored in some kind of mechanism. The important descriptor of energy is then the type of storage mechanism (gravitational, elastic, chemical, kinetic), not the fact that it’s stored.

“An object has potential energy.”

This is a common way to talk about potential energy, but it leads to misconceptions. Potential energy is due to an interaction between an object and a field. The energy is stored in that field due to this interaction. That is, a bowling ball held in the air has gravitational energy because of its position in Earth’s gravitational field. Stating that “an object has potential energy” does not allude to this deeper understanding and instead creates the misconception that an object can have this type of energy storage in isolation. When there is no reference to the field or object participating in the interaction, confusion is added to the idea of a system (see Teacher Background in the Introduction, page 4).

The idea of interaction energy

A more insightful phrase to describe energy arising from an interaction is interaction energy. (Field energy is another option, but fields are not formally introduced until Grade 12.) For instance, an object has gravitational energy due to its interaction with Earth’s gravitational field. This gravitational energy is stored in this gravitational field and changes as the object’s position changes in that field. This approach prepares students who go on to study more advanced physics to correctly interpret the relationship that connects potential energy to a path integral of a conservative force.

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https://www.worldenergy.org/data/resources/

https://www.worldenergy.org/data/resources/

What’s cutting edge about using multiple representations in energy analysis?

Research into teaching physics concepts started in the 1980s. The compelling results of this research help shape best practices today. Although using multiple representations in energy analysis has a long history, it is only recently gaining traction. To learn more about the benefits of using multiple representations, see these papers: “Learning with multiple representations” and “The use of multiple representations and visualizations in student learning of introductory physics.”

What’s cutting edge about energy transformations?

Innovative and efficient energy transformations may allow us to reduce our energy consumption. Cutting-edge research into transforming stored energy has led to some interesting technologies. One example is smart clothing, which takes body heat (thermal energy) and transforms it into electrical energy to charge personal devices. (See “Lightweight, wearable tech efficiently converts body heat to electricity.”)

Find Out More ►To learn more about multiple representations of energy before facilitating this activity, you may wish to visit the following websites:

OAPT—Feel the energy: A unified framework for teaching energy http://newsletter.oapt.ca/PER/PER_Energy/

Physics! Blog!: Energy Bar Charts (LOL Diagrams) https://kellyoshea.blog/2012/03/05/energy-bar-charts-lol-diagrams/

Institute of Physics: Helpful language for energy talk http://practicalphysics.org/helpful-language-energy-talk.html

Figure 1 Rube Goldberg machines are excellent—and unnecessarily complex—examples of energy conservation and transformation.

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https://arxiv.org/abs/1207.0217

https://arxiv.org/abs/1207.0217

http://www.per-central.org/items/detail.cfm?ID=3796



https://news.ncsu.edu/2016/09/wearable-teg-heat-harvesting-2016/

https://news.ncsu.edu/2016/09/wearable-teg-heat-harvesting-2016/

http://newsletter.oapt.ca/PER/PER_Energy/

https://kellyoshea.blog/2012/03/05/energy-bar-charts-lol-diagrams/

https://kellyoshea.blog/2012/03/05/energy-bar-charts-lol-diagrams/

http://practicalphysics.org/helpful-language-energy-talk.html

http://practicalphysics.org/helpful-language-energy-talk.html

Name: _________________________________________ Date: ___________________________________________

Student ActivityThe Conservation and Transformation of Energy

Science BackgroundConsider converting money. You can convert between different currencies, but the value of the money is unchanged. For instance, on a given day, you could have 650 Canadian dollars, or 500 US dollars, or 53 000 Japanese yen. Although these are different amounts, the value is the same. Similarly, energy can transform between different types, but the amount remains the same. In this activity, you will analyze the different ways we can store energy and investigate how energy is transformed into different types of storage.

Part 1: The Idea of Energy

1. Consider dropping a ball straight down from your right hand to your left. Define moment 1, t1, to be the instant the ball is fully released and moment 2, t2, to be the instant the ball first makes contact with your left hand. Describe how the velocity of the ball changes in the time interval ∆t1:2.

2. You may recall that a moving object has energy due to its motion. Energy stored this way is called kinetic energy (Ek). How is the kinetic energy of the ball at t1 different from the kinetic energy of the ball at t2? What could you measure to track this difference for the ball?

3. There is another mechanism of energy storage in this process. It’s an energy store that is decreasing during the time interval ∆t1:2. What other property of the ball decreased between t1 and t2? What name and label would you give this energy store?

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Name: _________________________________________ Date: ___________________________________________

4. Historically, this energy store has been called gravitational potential energy (Eg). It isn’t stored in the motion of the ball. Instead it’s stored in the gravitational interaction between the ball and Earth’s gravitational field. The greater the separation between Earth and the ball, the greater the amount of energy stored. We will call it gravitational energy. Complete the chart on the right to track how the gravitational energy at moments 1 and 2 (Eg1 and Eg2) compares to the kinetic energy at moments 1 and 2 (Ek1 and Ek2). Justify your representation of the bars.

Energy can flow from one object to another. Energy can transfer from one type of storage mechanism to another. These ideas are an important part of analyzing and understanding energy because it is during these flows and transfers that interesting physics happens.

5. At moment 1, we know energy is stored as gravitational energy, Eg1, by the ball in Earth’s gravitational field. What happened before moment 1? Where did this amount of energy come from? (To simplify, you can abbreviate Earth’s gravitational field to Earth.)

6. Grouping objects into a system makes energy analyses easier because energy is often stored in the interactions between objects. For the time interval ∆t1:2, explain why it’s simpler to choose the ball and Earth as the system for analysis rather than including the right hand from before t1.

7. Some time after moment 2, the ball comes to rest in the left hand. This is moment 3, t3. We know at t3 that the energy is no longer stored in the motion of the ball as kinetic energy. Where is this energy stored now? What property of the hand changed between t2 and t3? What about the ball?

The concept that energy cannot be created or destroyed is called “the conservation of energy.” “Cannot be created” means energy can’t appear out of nowhere. “Cannot be destroyed” means energy doesn’t disappear; instead it must go somewhere.

Eg1 Ek1 Eg2 Ek2

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Name: _________________________________________ Date: ___________________________________________

8. Fill in the table.

Examples of Energy Storage

Type of Storage Name of Energy Label Storage Mechanism Measured Property

Motion energy

Kinetic energy Ek

Thermal energy Eth Stored in molecular and atomic motion

Interaction (potential) energy

Gravitational energy Eg Stored in interaction between object and Earth (Earth’s gravitational field)

Elastic energy Ee Macroscopic: stored in stretch or compression of object (shape change)

Microscopic: stored in deformation of intermolecular bonds due to interactions between molecules

Chemical energy Eint Stored in interactions between particles

Part 2: Energy Flow Diagrams

To visualize how energy is stored and flows, use an energy flow diagram. Draw a circle around objects you choose as your system. Objects outside the system are called the environment. Draw arrows to show the transfers. When energy enters or leaves the system,

this change is called work. You can represent work with an arrow entering or leaving the system.

1. An energy flow diagram for the falling-ball example in Part 1 is shown at the right. Explain what is happening at each arrow and label, for example, Wrh → Eg1.

2. Which objects did we define as the system, and which objects did we define as the environment? Is energy flowing into or out of the system? How does the energy stored in the system change from moment to moment?

3. Consider moment 0, t0, a time before t1, where the ball was at rest and level with your left hand. For the time interval ∆t0:3, we could have chosen the right hand to be part of our system. Qualitatively explain how Eg1, Ek2, and Eth3 would change. What other comparisons can you make with the previous energy flow diagram? How do you know if energy has been conserved for this system?

Ball + Earth +Left hand

Right handWrh

Eth3

Eg1

Ek2

Right hand + Ball +Earth + Left hand

Eint0

Eth3

Eg1

Ek2

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Name: _________________________________________ Date: ___________________________________________

Part 3: Ramping UpExamine the system set up by your teacher, which includes the cart, the spring, and Earth. There are three important events: (1) the spring is triggered, (2) the spring is fully expanded, and (3) the cart reaches its highest point on the track.

1. Assume the kinetic frictional interaction between the wheels and the track is negligible. Draw an energy flow diagram between moments 1 and 2 only. Describe any energy transfers or flows.

2. A student states, “I think energy is flowing from the cart to the track between moments 2 and 3.” Do you agree or disagree? What property of the system might support or refute this statement?

3. Draw an energy flow diagram for ∆t2:3. Describe any energy transfers or flows.

A work-energy bar chart shows the amount of energy stored in each mechanism (gravitational, kinetic, elastic, etc.) of the system objects at two different moments in time. The precise height of the bars is not important, as long as the comparisons between the

bars are clear. The shaded column in the chart, Wext, represents the energy flow into, or out of, the system.

4. Draw a work-energy bar chart, like the one you made in Part 1, for the system between moments 1 and 2. Draw a separate work-energy bar chart for time interval ∆t2:3. What is assumed about the amount of gravitational energy at moments 1 and 2?

EFD 1:2

EFD 2:3

Ee1 + Ek1 +Wext= Ee2 + Ek2

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Consolidate Your LearningAnswer the following questions to check your understanding of the conservation and transformation of energy, using energy flow diagrams and work-energy bar charts.

1. Continue your analysis of the cart on the ramp by considering what happens when the cart returns back to the bottom of the incline, just as the spring comes into contact with the barrier. This is moment 4.

(a) Draw an energy flow diagram and a work-energy bar chart between moments 3 and 4.

(b) Using your diagrams, how will the speed of the cart at moment 4 compare to that at moment 2? Explain your prediction using energy flow and energy transfer ideas.

(c) Draw an energy flow diagram between moments 1 and 4.

2. Test your prediction using the cart and ramp setup. Do your observations confirm your predictions? Explain.

3. In Part 1, you considered dropping a ball from your right hand to your left hand. Now, consider dropping an unfolded piece of paper instead. Define a system and the key moments for this situation. Draw an energy flow diagram. Describe what is happening in terms of energy flows and transfers.

EFD 3:4


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EFD 1:4

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Activity 2: Innovative TechnologiesLesson Plan

IntroductionIn this activity, students use energy flow diagrams to explore how energy is transformed in several simple devices. Students then consider the efficiency and economics of new technology. The exploration continues with a discussion of innovative technologies. The culminating design challenge has students design a simple device that transforms readily accessible energy to solve a problem.


Purpose• To demonstrate how energy flow diagrams work in a

variety of situations

• To apply energy transformation concepts to solve a practical problem


• Students need to know about different forms of energy and energy flow diagrams.

• Students should be able to perform electricity cost calculations.

Materials• GravityLight video (optional; to 6:30 point): Storing

energy in Earth’s gravitational field

• eDrink video (optional): Teen invents coffee mug that can charge your cell phone

• Light Bulb Comparison Cards (1 per pair of students; see Appendix A)

• whiteboards (1 per pair of students)

• collection of energy-transforming devices, such as a flashlight, electric fan, hotplate, pulley-driven cart, and toys that transform energy

Teacher Instructions1. Introduce the activity by discussing how humans need

energy and how the current energy situation is an opportunity for innovation. People who understand energy and develop better ways to generate, store, and use energy will create next-generation technologies.

2. Place several energy transformation devices around the room. Try for a variety of energy sources and efficiencies (see Materials).

3. Distribute the Innovative Technologies activity sheets. Then have students work in pairs and use whiteboards to create energy flow diagrams for all the devices.

4. Once students have completed the energy flow diagrams, lead a brief consolidation discussion about the diagrams. Use the discussion to introduce efficiency.

5. Distribute Light Bulb Comparison Cards. Have students perform the ranking activities based on the information provided (initial cost, efficiency, life expectancy, annual cost, and lifetime cost).

6. Once students have completed the ranking activities, lead a brief consolidation discussion of their conclusions. Use this opportunity to consider how efficiency and conservation are part of the solution to our energy challenges. (Another aspect to consider is the development of new technologies.)

7. Select a few devices that generate electricity using unusual transformations, such as a shaking flashlight, a thermocouple, or a windmill. Have students create energy flow diagrams on the student activity sheets. Show the eDrink video (see Materials) if you don’t have access to appropriate examples.

8. Show the GravityLight video (see Materials). This video contains an overview of the flow of energy, an introduction to the GravityLight, and a summary of how the design process involves many iterations.

9. Have students work in groups of two or three to design a device that will use readily available energy to charge a smartphone. Have students share their ideas with other groups.

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https://www.youtube.com/watch?v=wXUkfGezM9U

https://www.youtube.com/watch?v=wXUkfGezM9U

https://www.youtube.com/watch?v=6EPUlwYUqdg

https://www.youtube.com/watch?v=6EPUlwYUqdg

SAFETY ALERT

Use caution when selecting the devices to examine. Consider using devices that are not operational (not plugged in or without a battery). Ensure appropriate warnings and instructions are provided if the devices pose any danger.

Teacher Tips• Energy flow diagrams provide an excellent structure

for discussing efficiency qualitatively because students see that the energy flowing into a device can be diverted into wasted energy.

• Work-energy bar charts can be used to add a quantitative aspect to the efficiency discussion.

INQUIRY T IP

Hands On: Instead of using the Light Bulb Comparison Cards provided, you can bring in actual light bulbs (or students can bring in theirs) for students to test and determine wattage and luminosity. Have students research average lifespans and current prices online.


To Assist: While students are working on the energy flow diagrams, circulate and assist those who might be struggling with language or with the visual aspect of the diagrams.

To Connect: Choose devices all students will be familiar with, such as hotplates, fans, and TVs.

ExtensionChallenge students to build a prototype of their design or to develop a marketing campaign for their product.

STSE Connections

Students will have discussed alternative energy solutions in other courses. How electricity is generated is part of the problem, but many students won’t have considered the roles efficiency and creative thinking play in developing new technologies. Have students research how innovative technologies such as the GravityLight are improving lives in developing countries.

Teacher Background

Why are energy innovations important?

In 2014, global electricity production was almost 24 000 TWh (terawatt-hours), and 65% of this electricity came from fossil fuels. Fossil fuels are non-renewable and are becoming increasingly difficult to find and extract. Combine this challenge with the reality of anthropogenic climate change and it’s clear that the energy sector is ripe for innovation. This innovation could come in the form of new methods of generating electricity, such as fusion; distributing electricity, such as long-distance DC transmission; or using electricity more efficiently, such as LED bulbs.

What’s cutting edge about renewable energy technologies?

One innovative idea for generating electricity is solar paint, which transforms any painted surface into a solar panel. Have students visit this website to learn more: A New “Solar Paint.”

Indigenous communities are often located in remote locations that are not connected to the energy supply infrastructure. To ensure a reliable energy supply, these communities are developing innovative and environmentally sustainable solutions. Have students read this article and reflect on the challenges facing remote indigenous communities.

Find Out More ►To learn more about innovative technologies before facilitating this activity, you may wish to visit the following websites:

CBC Radio-Canada: Innovation, Science & Technology in Canada https://curio.ca/en/collection/canada-150-innovation-science-and-technology-2380/

MIT Technology Review https://www.technologyreview.com/

Indigenous communities embracing clean energy, creating thousands of jobs http://www.cbc.ca/news/politics/first-nations-renewable-energy-projects-1.4348595

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https://futurism.com/a-new-solar-paint-lets-you-transform-your-entire-house-into-a-source-of-clean-energy/

https://www.theglobeandmail.com/news/national/the-push-to-end-energy-poverty-in-indigenous-communities/article33012480/

https://www.theglobeandmail.com/news/national/the-push-to-end-energy-poverty-in-indigenous-communities/article33012480/

https://curio.ca/en/collection/canada-150-innovation-science-and-technology-2380/

https://curio.ca/en/collection/canada-150-innovation-science-and-technology-2380/

https://www.technologyreview.com/

http://www.cbc.ca/news/politics/first-nations-renewable-energy-projects-1.4348595

http://www.cbc.ca/news/politics/first-nations-renewable-energy-projects-1.4348595

Name: _________________________________________ Date: ___________________________________________

Student ActivityInnovative Technologies

Part 1: Energy Transformations

1. Examine the devices provided by your teacher. Discuss the energy transformations used by the device. Use a whiteboard to draw the energy flow diagram for each. Include energy flowing into the system (work done on the system) and energy flowing out of the system (work done by the system). Which device do you think was the most efficient? In other words, which device has the highest ratio of useful energy output to energy input?

Part 2: Efficiency

1. Examine the Light Bulb Comparison Cards. Rank the bulbs based on the following criteria, and list them (high to low) in the space below. Show your calculations for parts (d) and (e).

(a) Initial cost:

(b) Efficiency:

(c) Life expectancy:

(d) Annual cost (4 hours per day, $0.15/kWh):

(e) Total lifetime cost (total cost for 50 000 hours of light):

2. What other factors would you want to consider in choosing the best light bulb?

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Name: _________________________________________ Date: ___________________________________________

Part 3: Innovative Technologies

1. Consider the devices your teacher showed you. Draw the energy flow diagrams for the devices in the space below.

2. Draw the energy flow diagram for the GravityLight.

A Design ChallengeToday’s society depends on electricity, but current energy production relies heavily on sources that are non-renewable, expensive, and polluting. It’s crucial that we develop solutions that reduce the negative effects of energy production.

Brainstorm with your group and design a device that uses available technologies to charge a smartphone. Once you agree on a device, create an energy flow diagram for it, and discuss the questions below. Choose a speaker to share your solution with the class.

1. How is energy being transformed?

2. What are the advantages and disadvantages of your device?

3. What is preventing this technology from being used today?

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Consolidate Your LearningAnswer the following questions to check your understanding of innovative energy technologies.

1. Some consumers are reluctant to purchase energy-efficient technologies because they tend to be more expensive to buy. Are energy-efficient devices more expensive in the long run? Support your answer.

2. Sometimes people say that energy is lost whenever there is a transformation, but we know that energy can never be destroyed. What do they mean by lost? What does it mean for a device to be efficient?

3. What are the traditional sources of energy for generating electricity? What other sources of energy might be overlooked?

4. Our society is facing major challenges regarding energy. Where do you think the greatest opportunities are? Describe how you would develop these opportunities.

5. The laws of physics forbid perpetual motion machines. Search YouTube for a perpetual motion machine and explain what is wrong with the video, either in the analysis of the device or in what’s hidden from the viewer.

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Activity 3: Nuclear TransformationsLesson Plan

IntroductionIn this activity, students investigate the nature of nuclear transformations. They develop a model that uses forces to predict stable and unstable nuclei. Students then explore how alpha and beta decays move the unstable nuclei closer to stable arrangements by lowering the energy of the nuclei.


Purpose• To understand the nature of radioactive decay

• To determine the nuclei produced by various decays


• Students should be aware of the structure of the atom and standard atomic notation (A, Z, N).

• Students should understand relationships between work and energy.

• Students should know about the behaviour of charged particles.

Materials• whiteboards and markers (1 each per group)

• spring-loaded collision cart or equivalent

• radioactive source and Geiger counter (optional)

• periodic table

• Table of Isotopes—Simplified (see Appendix B)

Teacher Instructions1. Have students work in groups of three or four. Ask them

to draw a Bohr-Rutherford diagram of a carbon atom on a whiteboard and discuss the following questions:• How is your drawing not an accurate

representation of the atom?• What holds the nucleus together?• What happens if we add another proton to the

nucleus?

2. Have students discuss their answers as a class. Highlight the issue of the forces that hold the nucleus together. Model the problem with a compressed spring (you can use a collision cart for this). It takes work to compress the plunger, but if you compress it far enough, the plunger gets held by another mechanism. The nature of this mechanism will be examined in this activity.

3. Lead students through a brief discussion to draw out the following ideas:

• The carbon nucleus was formed when nucleons were “crushed” together.

• A force acting over a distance is work done on the nucleons. Energy is stored in the nucleus.

• Anything that has energy wants to be in the lowest energy state possible. Systems will change and release the excess energy to become more stable. (This can be demonstrated by tipping an object over or rolling a marble inside a bowl.)

4. Demonstrate radioactive decay or use a computer simulation, such as Geiger Counter Simulation. There is also an excellent video on Veritasium’s YouTube channel, The Most Radioactive Places on Earth. Ask questions to raise interest in where the energy of radioactivity comes from.

5. Distribute the student activity sheets and Table of Isotopes—Simplified (see Appendix B). Have students work in small groups to develop a model for the strong force using the activity sheet questions.

SAFETY ALERT

Radioactive sources are controlled substances. Check your local regulations about how to handle radioactive sources in the classroom. Don’t let students handle the sources. Use a computer simulation if you are not comfortable working with radioactive sources.

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http://www.kcvs.ca/site/projects/physics_files/radioactive/geiger_counter.swf

https://www.youtube.com/watch?v=TRL7o2kPqw0

Teacher Tip• Using the term nuclear transformation instead of

radioactive decay will help avoid the misconception that beta particles are somehow in the nucleus already. By emphasizing transformations, you’ll lead students to a deeper understanding of radioactivity.

INQUIRY T IPS

Guided Inquiry: Use a large table of isotopes poster or projected image to work through questions 4–9 together.

Problem Solving: Students must learn to take chances and guess at answers. Many significant advances have been made by scientists making well-thought-out guesses.


To Communicate: Consider having students model transformations using visual, dramatic, graphical, or physical representations.

ExtensionDecay chains illustrate how heavy nuclei undergo many successive transformations before reaching a stable isotope. Have students use their tables of isotopes to construct a decay chain.

STSE Connections

Understanding radioactivity is fundamental to issues surrounding nuclear technologies. Have students research a career that uses nuclear technology and share their findings with classmates.

Teacher Background

What’s happening in the nucleus?

Radioactivity is all about energy. The competing forces in the nucleus produce stable and unstable energy configurations. The electrostatic force is familiar to students. Protons have a positive charge, so they exert a repulsive force on one another. The electrostatic force has an infinite range, but the force decreases with the square of the distance, so it tends toward zero at large distances. The strong force may not be familiar to students. The strong force acts on a different kind

of charge called colour. “Colour” was chosen because there are three types of charge that must add up to zero. Colour works well since the three primary colours (red, blue, and green) combine to give white. Protons and neutrons are composite particles made of colour-carrying quarks, so they feel the strong force. Electrons don’t have colour, so they don’t feel the strong force. At very short distances, the strong force is attractive and stronger than the electrostatic force. Beyond a few femtometres, the strong force becomes insignificant.

What is the valley of stability?

Unstable nuclei become more stable through nuclear transformations, such as alpha, beta, and gamma decays. The Table of Isotopes—Simplified in Appendix B relates the number of neutrons (N) to the number of protons (Z). This plot is an essential tool for understanding nuclear transformations because it shows the valley of stability. The valley shows the combinations of protons and neutrons that are stable. Isotopes not on this line will undergo a transformation to move toward the line, just like a marble rolling down the side of a bowl, or a snowboarder in a half-pipe. There is no way to determine when any one nucleus will change; we can only determine a probability that it will. The Table of Isotopes—Simplified gives the most probable transformation, but, in many cases, there is more than one possible pathway for the isotopes to follow.

What’s cutting edge about nuclear transformations?

Nuclear transformations play a crucial role in generating electricity for space probes, such as Voyager and Cassini. Their radioisotope thermoelectric generators use the heat released by transformations to generate electricity for extended periods of time. Researchers are now looking at ways to implement atomic batteries that never need recharging in smartphones.

Find Out More ►To learn more about radioactive decay before facilitating this activity, you may wish to visit the following websites:

Lawrence Berkeley National Laboratory: The ABC’s of Nuclear Science http://www2.lbl.gov/abc/

Australian Radiation Protection and Nuclear Safety Agency https://www.arpansa.gov.au/understanding-radiation/what-is-radiation/ionising-radiation/radioactivity

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http://www2.lbl.gov/abc/

https://www.arpansa.gov.au/understanding-radiation/what-is-radiation/ionising-radiation/radioactivity

https://www.arpansa.gov.au/understanding-radiation/what-is-radiation/ionising-radiation/radioactivity

Name: _________________________________________ Date: ___________________________________________

Student ActivityNuclear Transformations

1. Sketch the nucleus of a helium atom in the space provided.

(a) What forces are acting on the particles (nucleons) in the nucleus?

(b) Draw the forces acting on one proton and one neutron. What do you notice?

2. Electrostatic repulsion between protons is roughly 1036 times stronger than the gravitational attraction. There must be a stronger force to hold the nucleus together. Try to build a model by making some reasonable guesses.

(a) Would the force be attractive or repulsive? Explain.

(b) Would this force act on protons, neutrons, or both? Explain.

(c) Would the force decrease as distance increases, like the electrostatic force, or something different? Support your reasoning.

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Name: _________________________________________ Date: ___________________________________________

3. Physicists proposed an attractive force called the strong force. The strong force acts on protons and neutrons equally, but it does not act on electrons. Also, the strong force acts over only a very short distance (~10−15 m), unlike the electrostatic force. Consider the helium nucleus from question 1.

(a) What happens to the electrostatic and strong forces when you add a proton to the nucleus?

(b) What happens to each of the forces when you add another neutron to the helium nucleus?

(c) Examine a periodic table. What do you notice about the ratio of neutrons to protons as the elements get heavier?

(d) When this helium nucleus was created, a large force was exerted on the protons to push them into the small volume of the nucleus. What does this tell you about the energy of the nucleus?

Natural systems move toward the lowest energy state by changing and releasing energy. You learned previously that atoms will gain or lose electrons to become more stable; that is, they form ions. For a nucleus to be in the lowest energy state, the electrostatic and strong forces must be balanced. If the forces are not balanced, the nucleus will change and move into a lower energy state. You will use a table to determine whether a particular configuration is stable, and how it must change to become stable if it isn’t already.

4. Examine the Table of Isotopes. The staircase running up the centre of the pattern is called the valley of stability. Discuss any questions you have about this graph.

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Name: _________________________________________ Date: ___________________________________________

5. Consider silicon-32. Silicon has 14 protons, so this isotope must have 18 neutrons (A = Z + N). Locate this isotope on the Table of Isotopes.

(a) Where is it relative to the valley of stability?

(b) Does it have too many protons or too many neutrons?

(c) Make a reasonable guess about how silicon-32 can change to become more stable. Explain your idea.

(d) How does the energy of the isotope change when it becomes more stable?

6. Consider nickel-56. Nickel has 28 protons, so this isotope has 28 neutrons (A = Z + N). Locate this isotope on the Table of Isotopes.

(a) Where is it relative to the valley of stability?

(b) Does it have too many protons or too many neutrons?

(c) Why does this make the nucleus unstable?

(d) Make a reasonable guess about how nickel-56 can change to become more stable. Explain your idea.

(e) When the isotope changes to become more stable, what do you think happens to the net electric charge?

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Name: _________________________________________ Date: ___________________________________________

7. In question 5, you considered silicon-32. This isotope has too many neutrons. The easiest way to solve this imbalance is to transform a neutron into a proton. This change is called beta-minus decay (β−).

(a) Reflect on your answers for question 5. Which details were you able to guess? Which details did you miss?

(b) What happens to the identity of silicon when its proton number increases?

(c) Neutrons don’t have a charge. Protons have a positive charge. What other particle might be created in this process to keep the process electrically neutral?

(d) The new nucleus is more stable. Where did the excess energy go?

8. In question 6, you considered nickel-56. This isotope has too many protons. The easiest way to solve this imbalance is to transform a proton into a neutron. This change is called beta-plus decay (β+).

(a) Reflect on your answers for question 6. Which details were you able to guess? Which details did you miss?

(b) When nickel-56 undergoes β+ decay, a positively charged electron (a positron) is detected moving away. Where did the positron get its kinetic energy from?

Notice that the valley of stability ends at Z = 82. Elements with more than 82 protons exist, but there are no stable configurations. The easiest way for a heavy isotope to become more stable is to spit out a small bundle of nucleons called an alpha particle in a process called alpha decay. An alpha particle contains two protons and two neutrons, so it lowers the

mass number by four and the atomic number by two.

9. Radon-210 undergoes alpha decay because the electrostatic force from the 86 protons is so strong.

(a) What does radon-210 transform into after it loses an alpha particle?

(b) The resulting nucleus is more stable than radon-210. Where did the energy go?

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Name: _________________________________________ Date: ___________________________________________

Consolidate Your LearningAnswer the following questions to check your understanding of nuclear transformations.

1. How do the electrostatic force and the strong force differ?

2. Why do nuclei undergo transformations?

3. In nuclear transformations, particles are emitted from the nucleus. Where does the kinetic energy of the particles come from?

4. Determine the type of transformation and the identity of the nucleus produced by each of the following:

(a) carbon-14

(b) carbon-10

(c) uranium-238

5. Radioactive materials can pose significant health risks. What is dangerous about the emitted particles, and how can you reduce exposure?

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Activity 4: Ionizing RadiationLesson Plan

IntroductionIn this activity, students examine the difference between ionizing and non-ionizing radiation, with a focus on alpha, beta, gamma, and X-ray radiation. They explore different uses of ionizing radiation and the risks associated with different doses.

Suggested Time: 70 minutes

Purpose• To introduce ionizing radiation, including alpha, beta,

and gamma rays

• To introduce risks in terms of exposure and dose of ionizing radiation

• To demonstrate the use of ionizing radiation in medicine


• Students should know about the parts of the light spectrum that lie outside the visible range.

• Students must be familiar with ions and ionization.

• Ideally, students should have had an introduction to radioactive decay and how alpha, beta, and gamma radiation is produced.

Materials• video (optional): Types of Radiation

• video (optional): The Most Radioactive Places on Earth

• Ionizing Radiation Cards (1 set of cards per group; see Appendix C)

• Equivalent Dose Table (1 per group; see Appendix D)

• Radiation Scenario Cards (1 set of cards per group; see Appendix E)

Teacher Instructions1. Before class, prepare sets of Ionizing Radiation Cards,

Equivalent Dose Table, and Radiation Scenario Cards (see Appendices C, D, E). You may wish to add an object to Part 1, question 4.

2. Have students form groups of three or four, and hand out the student activity sheets. Have students complete Part 1 and discuss their predictions based on the photos.

3. You may wish to show the video called Types of Radiation before having students start Part 2. Then, hand out sets of Ionizing Radiation Cards and have students complete Part 2.

4. Distribute sets of Radiation Scenario Cards. In groups, each student should read a card, and then the group should discuss the scenarios. Hand out the Equivalent Dose Table and have students complete the rest of Part 3. You may wish to show the second video, The Most Radioactive Places on Earth.

5. Have students complete Part 4 and discuss their results. You may wish to discuss other uses of ionizing radiation in industry.

Teacher Tips• Before completing Part 3, consider whether some

students may find cancer and cancer treatments an emotional topic.

• Encourage students to calculate their own annual radiation dose, using an online calculator tool.

• When students calculate the increased cancer risk due to the equivalent dose for the person on their card, remind them that the exposure calculations are for one year. Have students consider the lifetime increase in cancer risk for the smoker. This provides an opportunity to talk about risk in general. Compare cancer risk to other familiar risks (car accidents, drowning, etc.). The lifetime risk of dying from cancer under normal circumstances is approximately 20%.

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https://www.youtube.com/watch?v=tYmMtSWPQEI

https://www.youtube.com/watch?v=TRL7o2kPqw0

https://www.nrc.gov/about-nrc/radiation/around-us/calculator.html

• Students may be surprised to learn that tanning beds do not use ionizing radiation. While the UV radiation from tanning beds is non-ionizing, it sits very close to ionizing radiation on the spectrum. Tanning and burning have a number of health effects including skin aging, skin cancer, and eye cataracts. Studies have shown that using tanning beds before the age of 30 increases your risk of developing skin cancer by 75%.

• Students may be curious to know the health risks of vaping (e-cigarettes) versus smoking. Exposure to ionizing radiation in vaping is much lower than in smoking. But there are other possible health effects of vaping, and there have been no long-term studies to establish all risks.

INQUIRY T IP

Open Inquiry: Print only the front side of the Ionizing Radiation Cards and have students research a medical application themselves.


To Assist: In Part 3, some students may need assistance with the units and prefixes (e.g., milli). Consider defining these on the board or providing a handout.

ExtensionIn the 1950s, people were particularly concerned about nuclear weapons and the dangers of radiation. The superpowers of comic book superheroes were often the result of radiation exposure. Have students choose a story that portrays radiation or radioactive elements. Students can prepare a blog post, a poster, or a podcast to fact-check the science and debunk the story.

STSE Connections

Earth’s magnetic field and atmosphere protect life on Earth from harmful ionizing radiation from space. Astronauts must be protected from this radiation because it can cause cancer and other degenerative diseases. Have students research this issue and the measures being taken to protect astronauts, beginning with this link: “Why Space Radiation Matters.”

Teacher Background

What is ionizing radiation, and what are the risks for human health?

Ionizing radiation is a type of radiation (particle or light) that has sufficient energy to ionize atoms. Examples include gamma rays and X-rays (light) and alpha and beta rays (particles).

Ionizing radiation can damage or kill cells by ionizing atoms and molecules. This leads to mutations, which can cause cancer. If ingested or inhaled, a source of alpha particles can pose the greatest risk due to the high ionizing ability of the alpha particles. However, alpha particles can penetrate only short distances and are easily stopped by air, so being exposed to them is usually not a concern.

Pregnant women are told to avoid X-rays because of the potential harm to their fetus. This connection was established by Canadian researcher Irene Ayako Uchida (1917–2013), while working at the University of Manitoba in the 1960s.

One of the riskiest activities associated with ionizing radiation is smoking. Not only do tobacco products contain toxic chemicals, they also contain radioactive isotopes (lead-210 and polonium-201), which come from fertilizers used on tobacco fields. These radioactive isotopes are inhaled and accumulate over time in smokers’ lungs, producing alpha and gamma radiation. This radiation damages the lungs and can lead to lung cancer.

How is ionizing radiation used in medicine?

Ionizing radiation has proved useful in medical imaging because of its penetrating power. X-rays, CT scans, and PET scans all use ionizing radiation.

Ionizing radiation is also used to treat some forms of cancer. The ionizing power can kill and damage cancer cells. Sometimes radioactive isotopes are inserted into tumours, as in targeted alpha therapy, and sometimes radiation is aimed at tumours, as in gamma knife therapy.

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https://www.nasa.gov/analogs/nsrl/why-space-radiation-matters

https://www.nasa.gov/analogs/nsrl/why-space-radiation-matters

What’s cutting edge about ionizing radiation?

Ionizing radiation also has applications in industry. It’s used to sterilize medical equipment; locate leaks in pipelines; and measure the thickness of materials such as plastic, aluminum, and paper.

To locate a leak in a pipe, a gamma ray–producing radioisotope is put in the pipe. An above-ground detector detects the gamma rays. If the radiation suddenly increases and then declines, a leak is detected.

To measure the thickness of materials, a source of beta particles is placed on one side of the material and a detector on the other. Changes in the amount of radiation reveal the thickness of the material, allowing production adjustments to be made.

Career Connections

Medical physicists are healthcare professionals (Figure 1) who apply physics to diagnose and treat illness using technologies such as X-rays, ultrasound, lasers, magnetic fields, and nuclear imaging. Rosalyn Yalow (Figure 2) was a pioneering medical physicist who won the 1977 Nobel Prize in Physiology or Medicine for her part in developing the radioimmunoassay (RIA) technique. Have students research this technique and its many applications.

Figure 2 Rosalyn Yalow, 1921–2011

Find Out More ►To learn more about ionizing radiation before facilitating this activity, you may wish to visit the following websites:

World Health Organization: Ionizing Radiation http://www.who.int/ionizing_radiation/about/what_is_ir/en/

How Does a PET Scan Work? https://www.youtube.com/watch?v=GHLBcCv4rqk

How Does a CT Scan Work? https://www.youtube.com/watch?v=l9swbAtRRbg

Figure 1 A medical physicist examines a patient’s scan.

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http://www.who.int/ionizing_radiation/about/what_is_ir/en/

http://www.who.int/ionizing_radiation/about/what_is_ir/en/

https://www.youtube.com/watch?v=GHLBcCv4rqk

https://www.youtube.com/watch?v=l9swbAtRRbg

Name: _________________________________________ Date: ___________________________________________

Student ActivityIonizing Radiation

Part 1: Ionizing RadiationRadiation is a form of energy transmitted by rays of light or beams of particles. High-energy radiation, or ionizing radiation, can ionize atoms or molecules by stripping their electrons.

1. Form groups of three or four. Together, explain why high-energy radiation ionizes atoms, but low-energy radiation does not.

2. Examine the picture of the light spectrum below. Based on your experience with technologies that produce these light rays, such as microwave ovens and X-ray machines, speculate on which are the most energetic and which are the least. Label the diagram with your answer. Which parts of the spectrum might have sufficient energy to ionize atoms?

Short wavelengthLong wavelength

Radio waves Microwaves Infrared UltravioletVisible light

X-rays Gamma rays

103 m 1 m 105 nm 103 nm 1 nm 10-3 nm 10-5 nm

3. High-speed particles can also ionize atoms. These particles include alpha particles, made of two protons and two neutrons, and beta particles, made of electrons. Explain why only fast-moving particles can ionize atoms.

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Name: _________________________________________ Date: ___________________________________________

4. Examine the images below. Predict whether these objects produce non-ionizing radiation, ionizing radiation, or both. (Hint: You may find the light spectrum helpful in some cases.)

Microwave Oven

Ionizing radiation □ Non-ionizing radiation □

Cellphone


Tanning Bed


Computer Screen


Supernova


Ultrasound


Sun


Dental X-ray


Earth


Object of Your Choice


5. How might ionizing radiation be harmful to our health? Is non-ionizing radiation harmful to our health? Why or why not?

Part 2: Alpha, Beta, X-ray, and Gamma RadiationAlpha, beta, X-ray, and gamma radiation are all forms of ionizing radiation. They differ in terms of their mass, charge, penetration distance, and ionizing power.

1. Your teacher will give you a set of Ionizing Radiation Cards. Each group member should obtain a card. Take turns presenting the information on your card to your group.

2. Rank the ionizing radiation types from lowest to highest, according to the following: (a) mass, (b) penetration distance, and (c) ionizing power.

3. Radiation exposure occurs when a person is near a source of radiation. Radiation contamination occurs when a source of radiation is ingested or inhaled. Which type of radiation might present the greatest health risk in each case? Justify your reasoning.

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Name: _________________________________________ Date: ___________________________________________

Part 3: Dose and ExposureThe effect of ionizing radiation on a person depends on how much energy, E, is absorbed; the mass, m, of the affected tissue; and how harmful that radiation is to the tissue (represented by a weighting factor, wR). The equivalent dose, H, accounts for all of these factors and is expressed as

H = E—mwR

The units of equivalent dose are the sievert (1Sv = 1J/kg) or the millisievert.

1. Your teacher will give you a set of Radiation Scenario Cards, which describe the lifestyles of different individuals. Each group member should obtain a card. Take turns reading your card to your group. Predict the order of your cards from highest to lowest annual radiation exposure. Justify your reasoning.

2. Your teacher will provide an equivalent dose table for different radiation sources. Working individually, use the table to estimate the average annual exposure of the person described on your card.

Person: ___________________________ Annual Exposure: _________________

3. Take turns presenting your estimates. Was your group surprised by any of the estimates? Why? Make any necessary adjustments to the ordering of your cards.

4. The risk of cancer from radiation exposure is estimated at 5% per sievert. Calculate the cancer risk due to the radiation exposure experienced by the person on your card. Compare your findings within your group.

Person: ___________________________ Cancer Risk: _________________

Part 4: Uses of Ionizing RadiationIonizing radiation has important uses in medicine, from medical imaging to cancer treatments.

1. Flip over your Ionizing Radiation Card and take turns presenting how this type of radiation is used in medicine.

2. What properties of ionizing radiation make it useful for (a) cancer treatment and (b) medical imaging?

3. Using the Equivalent Dose Table, discuss the risks associated with these techniques and procedures.

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Name: _________________________________________ Date: ___________________________________________

Consolidate Your LearningAnswer the following questions to check your understanding of ionizing radiation.

1. Working individually, fill in the table, summarizing the different types of ionizing radiation.

Radiation Type

Ionizing Power Penetration Distance in Air

Stopped by Possible Uses

Alpha

Beta

X-ray

Gamma ray

2. Your friend has a leg injury and needs an ultrasound. Your friend is concerned about exposure to radiation. What would you tell your friend?

3. Many smoke detectors make use of americium-241, a source of alpha radiation. Alpha radiation ionizes the air, allowing a current to flow between two plates. If smoke is present, the alpha particles ionize the smoke and the current drops, which triggers the smoke alarm. Should you be concerned about a source of alpha radiation in your home? Explain your answer.

4. Based on what you’ve learned about ionizing radiation, reflect on your lifestyle choices. Are there any changes you would make? Why or why not?

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Activity 5: Mass-Energy EquivalenceLesson Plan

IntroductionIn this activity, students explore the profound concepts of nuclear binding energy and mass-energy equivalence. They examine nuclear reactions to see how energy stored within the mass of objects can be converted into other types of energy, and vice versa.


Purpose• To explain the concept of binding energy at a

fundamental physical level

• To develop the idea that mass is an energy store (i.e., mass stores a type of energy called mass energy)

• To develop the concepts of mass-energy equivalence and E0 = mc2


• Students should be familiar with gravitational and thermal energy.

• Students should understand energy flow diagrams and work-energy bar charts.

Materials• clear plastic tubing, 50 cm in length (1 per group)

• marble that fits inside tubing (1 per group)

Teacher Instructions1. Part 1 explores a physical model for binding energy.

Give a piece of plastic tubing and a marble to each group of three or four students. Next, have students complete and discuss Part 1.

2. Part 2 explores the transformation of mass energy into light energy in a nuclear reaction. After students complete the questions, lead a class reflection.

Teacher Tips• Be aware of prior conceptions about mass. Most

students think of mass as the amount of matter in an object. While this model is useful in chemistry, for example, it fails at the subatomic level.

• In Part 1, consider asking students to draw a work-energy bar chart after drawing the energy flow diagram in question 3.

• At the start of Part 2, ask students to discuss the following: “Imagine pushing two items on your desk together so they touch. Does this change their total mass?”

INQUIRY T IP

Discussion: People often say that mass is converted into energy in nuclear reactions. Ask students to discuss if this is a good way to describe what is happening. Have them carefully consider the concept of mass energy and provide solid reasoning to support their opinions.


To Assist: In Part 1, some students may need help understanding the model. Prompt students to identify which parts of the plastic tube and marble model correspond to key features in the proton-neutron system.

ExtensionMass-energy equivalence is fundamental to nuclear power. Have students research a career in the nuclear power industry and share their findings with classmates.

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Indigenous Connections

Uranium is the fuel of choice for nuclear reactors around the world, and Saskatchewan has rich uranium ore deposits. The government and the mining industry want to open up the land for mining, but the local Dene Nation opposes any mining on their territory. Read this article about the conflict and write a reflection expressing your views on the matter.

Teacher Background

What does mass-energy equivalence mean?

The concept of mass-energy equivalence says that mass stores energy (mass energy) and that this energy can transform into, and from, any other type of energy. Einstein’s famous equation, E0 = mc2, quantifies the relationship between an object at rest with mass, m, and the amount of energy, E0, it stores. Since the speed of light, c, is very large, it tells us that even a tiny mass stores vast quantities of energy.

People sometimes say that mass is converted into energy. This overlooks the fact that mass is already stored energy. Einstein said that, for systems at rest, “the mass of a body is a measure of its energy content.” The energy released in nuclear reactions comes from energy already stored in the mass of nuclei.

Taking this mass energy into account, nuclear reactions always conserve energy when we consider closed systems, just like any other physical process. For open systems, the change in energy comes from work or heat, as usual.

The equation E0 = mc2 applies to objects at rest (as denoted by the subscript 0). For moving objects, the full relationship is

E2 = (mc2)2 + (pc)2

where p is the object’s relativistic momentum. When an object is at rest, its momentum is p = 0 and so the equation reduces to E0 = mc2. For massless objects, such as photons, the equation reduces to E = pc.

What is nuclear binding energy?

Start with a nucleus and pull all of its protons and neutrons out, separating them from each other. Surprisingly, the mass of the separated particles is greater than the mass of the nucleus. If the mass difference is Δm, then, by Einstein’s principle of mass-energy equivalence, the energy difference between the two configurations is ΔE = Δmc2. We call ΔE the binding energy of the nucleus because it’s the amount

of energy that is released when all of the particles bind together. For example, when a neutron and a proton fuse into a hydrogen-2 nucleus, they release 3.6 × 10−13 J of energy in the form of light energy. So, hydrogen-2’s binding energy is 3.6 × 10−13 J.

At a fundamental level, we describe binding energy as coming from the strong force between protons and neutrons. Imagine a group of protons and neutrons that are initially far apart from each other and then gradually move closer until they bind into a nucleus. Their interaction (potential) energy due to the strong force gradually decreases as they move to states of lower interaction (potential) energy and, thus, so does their total energy. Since mass is proportional to energy (from E0 = mc2), this means their mass decreases as well. This phenomenon is similar to a rocket in deep space gradually moving closer to Earth at a constant speed until it is gravitationally bound to Earth. As the rocket gets closer, the total energy of the rocket-Earth system decreases because of a decrease in the system’s gravitational energy.

What’s cutting edge about mass-energy equivalence?

Mass-energy equivalence plays a key role in astronomical processes that create gravitational waves. In 2015, an international team of scientists made the first observation of a gravitational wave created by the merger of two black holes. As the black holes moved closer to each other, energy stored in their masses transformed into the energy of the gravitational wave, thus decreasing their combined mass. In the final 0.4 s before the merger, the equivalent of three solar masses worth of energy was transformed. This is equivalent to 5.4 × 1047 J of energy, or 1027 times all of Earth’s annual energy consumption!

Find Out More ►To learn more about mass-energy equivalence before facilitating this activity, you may wish to visit the following websites:

Minute Physics: E = mc2 Is Incomplete https://www.youtube.com/watch?v=NnMIhxWRGNw

PBS Digital Studios: The Real Meaning of E = mc2 https://www.youtube.com/watch?v=Xo232kyTsO0

The Energy That Holds Things Together https://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/the-energy-that-holds-things-together/

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https://theecologist.org/2016/mar/30/sacred-land-unholy-uranium-canadas-mining-industry-conflict-first-nations

https://www.youtube.com/watch?v=NnMIhxWRGNw

https://www.youtube.com/watch?v=Xo232kyTsO0

https://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/the-energy-that-holds-things-together/



Name: _________________________________________ Date: ___________________________________________

Student ActivityMass-Energy Equivalence

Useful Relations1 u = 1 atomic mass unit = 1.660 54 × 10−27 kg E0 = mc2, c = 2.997 92 × 108 m/s

Part 1: Binding EnergyIn this section, you will investigate the energy transformations that occur when you roll a marble inside a bent tube.

1. Bend the tube into a V-shape with one end higher than the other (see diagram). Place the marble at the lower end of the tube (A) and let go. Observe how it moves, and record your observations.

2. Define the system as the marble and Earth. How does the total energy of the system at A, compare to the total energy at B, when the marble finally comes to rest? Explain any difference between the energies.

3. Draw an energy flow diagram for the system during this process.

4. Where does any energy lost from the system go?

5. We say that an object is bound to another object when it does not have enough energy to move away from it. Is the marble bound when it is at rest in the dip of the tube? Explain.

B

A

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Name: _________________________________________ Date: ___________________________________________

6. The binding energy of the system is the difference between its initial energy (at A) and its final energy (at B). How is this binding energy related to the change in gravitational energy of the system?

Part 2: E0 = mc2

In this section, you will use the marble and plastic tube model to think about the energy of a nucleus.

When a proton and a neutron are close to each other, they experience an attractive force called the strong force. If they get too close, the force becomes repulsive. Protons and neutrons can bind together in a nuclear reaction to create a hydrogen-2 nucleus and light energy:

proton + neutron H+ + light energy (γ)21

Light energy

Before After

Proton

Neutron

1. Using the model from Part 1, imagine that

• the marble is a neutron

• there is a proton fixed just past the higher end of the tube as shown below

• the gravitational energy of the marble-Earth system represents the energy due to the strong force (Es) of the neutron and the proton

Consider the total energy of the neutron-proton system when the neutron is at locations A and B.

B

A

Neutron

Proton

Distance from proton

E s

Proton

A

Distance from proton

E s

Neutron

B

At rest, far from the proton (point A) At rest, closer to the proton (point B)

How do the total energies at the two locations compare?

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Name: _________________________________________ Date: ___________________________________________

2. Where does the energy leaving the system go when hydrogen-2 forms?

3. Einstein said that a mass, m, stores an amount of energy, E0, given by his famous equation, E0 = mc2. We call this mass energy. The quantity c is the speed of light. Draw an energy flow diagram and a work-energy bar chart to illustrate the energy transformation that occurs in the hydrogen-2 nuclear reaction shown on the previous page.

E01 +Wext= E02

0

–

+

4. Predict how the mass of hydrogen-2 compares to the combined mass of a proton and a neutron. Explain your prediction.

5. A proton has a mass of 1.0073 u, a neutron has a mass of 1.0087 u, and a hydrogen-2 nucleus has a mass of 2.0136 u. How do the masses of the reactants and the products compare to your prediction?

6. What is the mass energy of the system before this reaction? What about after?

7. Calculate the light energy released by this reaction.

8. The binding energy of hydrogen-2 is the amount of energy released as light energy when the proton and neutron combine. Where does this energy come from in the nuclear reaction?

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Name: _________________________________________ Date: ___________________________________________

Consolidate Your LearningAnswer the following questions to check your understanding of mass-energy equivalence.

1. Negatively charged electrons are bound to positively charged nuclei in stable, neutral compounds. Explain why you need to rub two materials together to generate a static charge.

2. What is the binding energy of a helium (42He) nucleus (m = 4.0013 u)?

3. Light can transform into subatomic particles in the following nuclear reaction:

light energy → electron + positron

Light energy

Before After

Electron

Positron

A positron is a positively charged particle with the same mass as an electron. Draw the energy flow diagram for this process. What information would you need to predict the speeds of the particles assuming that their speeds are equal?

4. A nuclear reactor uses the transformation of mass energy to generate electricity. Calculate the amount of energy released by the following fission process. (You may need to look up masses.)

10n + 235

92U → 92 36Kr + 141

56Ba + 310n

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Activity 6: Where Do the Elements Come From?Lesson Plan

IntroductionIn this activity, students examine the origin of the elements in the periodic table. Students model the nuclear fusion reactions in stars using ball bearings and magnets. By examining a set of objects, they learn how stars produced most of the elements.


Purpose• To introduce the origin of the elements in the

universe and demonstrate how fusion produces elements in the core of stars

• To demonstrate why fusion stops at iron and how neutron capture produces heavier elements


• Students should know that the temperature of a gas is a measure of the average kinetic energy of the atoms relative to the thermometer.

• Students should know that compressing a gas causes it to heat up and increases the pressure.

Materials• animation (optional): A Tour of Cassiopeia A

• video (optional): We are born of supernovas—our spectacular and totally ordinary origin story

• Star Cards (1 set per group; see Appendix F)

• periodic table, as a class poster, handout, or app

• rulers with a lengthwise groove (1 per group)

• small magnets (1 per group)

• metal ball bearings (1 per group)

• squares of cardstock or cue cards, folded in half

• objects or samples showcasing different elements, such as salt, bone, milk, helium balloon, clay pot, glass of water, empty pop bottle (air)

Teacher Instructions1. Before the activity, secure the magnets to the rulers

with tape. Gather objects that showcase different elements produced in stellar cores (nuclei lighter than iron). Edit the table in the student activity sheets to reflect the objects you have chosen. Prepare the Star Cards (see Appendix F).

2. Have students form groups of three or four. Distribute the student activity sheets.

3. Give each group a ruler with attached magnet, a ball bearing, and cardstock. Have students complete Part 1 and discuss the results.

4. Hand out the Star Cards, have students complete questions 1, 2, and 3 of Part 2, and then discuss the results.

5. Set out the items for display. Have students complete Part 2. If desired, have groups compare their responses.

6. Have students complete Part 3. Show the Cassiopeia A animation and/or the video about supernovas.

SAFETY ALERT

Instruct students to keep their fingers away from the magnet. Ball bearings attracted to strong magnets can pinch. Tell students to keep their faces away from the ruler-and-magnet setup to protect their eyes from ball bearings. As an extra precaution, distribute safety goggles.

Teacher Tips• If you did Activity 3: Nuclear Transformations, you

can skip Part 1, questions 1–4. Students will already be familiar with the strong force.

• You could have students draw energy flow diagrams for the experiment in Part 1, questions 2 and 3. Have students draw a work-energy bar chart for Part 1, question 5.

• You may wish to project the image of the periodic table of the elements and their origins (Figure 2, page 45) when discussing Part 3, question 6 (c).

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http://chandra.harvard.edu/photo/2017/casa_life/animations.html

https://aeon.co/videos/we-are-born-of-supernovas-our-spectacular-and-totally-ordinary-origin-story

https://aeon.co/videos/we-are-born-of-supernovas-our-spectacular-and-totally-ordinary-origin-story

INQUIRY T IP

Open Inquiry: Give 5–10 students different objects that have elements produced in stellar cores (see table for example). Give the remaining students a Star Card. Have students with the objects interview the other students to find the stars that produced the elements in the object.


To Challenge: Edit the table in Part 2, question 4, on the student activity sheets to remove the list of elements. Have students first brainstorm the elements that make up the object.

ExtensionDownload Perimeter Institute’s LIGO newsflash activity “Science in the News—What Made That Sound?,” which explores the detection of a neutron star merger, confirming the theory that these mergers create heavy elements. Students will engage in a game-style activity requiring them to work together to solve a mystery. The activity highlights the importance of collaboration in science and shares an exciting, cutting-edge discovery.

Teacher Background

What determines the properties of stars?

Stars have a careful balance between gravitational forces and forces due to gas and radiative pressure called hydrostatic equilibrium. The gravitational forces compress the core, and pressure forces cause it to expand. This leads to a hot, dense core with a cooler, less-dense envelope. The properties of stars are determined by their masses. Higher-mass stars have a larger force of gravity, which compresses the core to a higher density and temperature. This leads to faster fusion rates, a higher luminosity, and a shorter lifetime because they burn through their nuclear fuel more quickly.

The mass of a star has a lower limit of 0.08 MSUN. Below this limit, the core can’t be compressed to a high enough temperature and density for fusion to occur. Objects below this limit are called brown dwarfs. Likewise, there is an upper limit for the mass of a star at around 100 MSUN. Objects above this limit would have radiative pressures that would expel the outer layers.

How are elements created in stars?

Nuclear fusion reactions in stars are the main mechanism for creating elements up to iron. The reactions are temperature sensitive because nuclei require sufficient kinetic energy to overcome their respective electric repulsions to fuse.

Stars spend 90% of their lives fusing hydrogen into helium. If a star is massive enough, once it exhausts its hydrogen fuel, it begins to burn heavier and heavier elements. However, the fusion of the heavier elements requires higher and higher temperatures as the electric repulsion of the nuclei increases. The stars fuse helium into carbon, carbon and helium into oxygen, and two carbon atoms into magnesium. A combination of such processes eventually culminates with iron. The fusion of heavier elements requires higher temperatures (up to 3 × 109 K) and fuels the star for a shorter and shorter time.

Why does nuclear fusion stop at iron?

Fusion can continue until iron is formed. Iron is one of the most stable elements, and thus it does not release energy when fused. Elements lighter than iron release energy when they fuse to a more stable configuration. Elements heavier than iron emit energy by undergoing fission and releasing a nucleon to a more stable nuclear configuration. Also, to fuse iron, temperatures would have to soar so high that the fusing nuclei would actually break apart into helium nuclei.

How are elements heavier than iron produced?

With heavier elements, the number of protons increases, which increases the electric repulsion. It becomes too difficult to add more protons. However, neutrons can be added. These neutrons undergo beta decay, leaving behind a proton, making a heavier element.

In both supernova explosions (Figure 1) and neutron star mergers, there are a lot of neutrons flying around, which allows neutron capture to happen rapidly. This is called the r-process, or rapid neutron capture. Heavy elements can also be produced through the s-process, or slow process, in less massive stars. Here, neutrons are very gradually added to the nucleus, where they undergo beta decay one by one.

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https://resources.perimeterinstitute.ca/products/science-in-the-news-what-made-that-sound

Figure 1 The supernova remnant Cassiopeia A (Cas A), imaged by Chandra X-ray Observatory (top). Iron, silicon, and magnesium in Cas A, imaged by the Chandra X-ray Observatory (bottom left and middle). Radioactive titanium, imaged by the Nuclear Spectroscopic Telescope Array (bottom right).

Which elements are not created by stars?

Hydrogen, helium, and trace amounts of lithium, beryllium, and boron were created during the first three minutes of the Big Bang. Hydrogen and helium make up 74% and 24% of all baryonic matter in the universe by mass, respectively. Baryonic matter includes the elements of the periodic table but does not include dark matter.

Lithium, beryllium, and boron are mainly created when nucleons are expelled from heavier nuclei during collisions with cosmic rays.

Technetium (Tc), promethium (Pm) and the heaviest group of elements (Z > 94) are created by humans and are not stable.

Figure 2 summarizes the origin of the elements on the periodic table.

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Humansynthesis; nostable isotopes

H1

He2

Li3

Be4

B5

C6

N7

O8

F9

Ne10

Na11

Mg12

Al13

Si14

P15

S16

Cl17

Ar18

K19

Ca20

Sc21

Ti22

V23

Cr24

Mn25

Fe26

Co27

Ni28

Cu29

Zn30

Ga31

Ge32

As33

Se34

Br35

Kr36

Rb37

Sr38

Y39

Zr40

Nb41

Mo42

Tc43

Ru44

Rh45

Pd46

Ag47

Cd48

In49

Sn50

Sb51

Te52

I53

Xe54

Cs55

Ba56

La57

Ce58

Pr59

Nd60

Pm61

Sm62

Eu63

Gd64

Tb65

Dy66

Ho67

Er68

Tm69

Yb70

Lu71

Hf72

Ta73

W74

Re75

Os76

Ir77

Pt78

Au79

Hg80

Tl81

Pb82

Bi83

Po84

At85

Rn86

Fr87

Ra88

Ac89

Th90

Pa91

U92

Np93

Pu94

Am95

Cm96

Bk97

Cf98

Es99

Fm100

Md101

No102

Lr103

BigBangfusion

Cosmicrayfission

Dyinglow-massstars

Mergingneutronstars

Explodingmassivestars

Explodingwhitedwarfs

Figure 2 The periodic table of the elements and their origins

What’s cutting edge about stars?

In 2017, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected the first gravitational waves from a neutron star merger. The detection allowed astronomers to quickly point their telescopes toward the event and capture the light from the explosion. Infrared spectra confirmed the theory that such mergers are responsible for over half of the universe’s heavy elements. When neutron stars merge, they release a tremendous number of neutrons, which strike other atoms. This leads to rapid neutron capture (r-process), which forms a host of heavier elements, including gold, platinum, and neodymium. The merger detected by LIGO created at least 10 times Earth’s mass in gold alone.

Indigenous Connections

The fact that we are made of elements forged in stars and recycled on Earth is familiar knowledge to Indigenous peoples. A key concept in Indigenous world views is Interconnectedness—all of nature is related and bound together.

Career Connections

Astrophysicists use physics and chemistry to understand the nature of astronomical objects. Cecilia Payne-Gaposchkin was a groundbreaking astrophysicist who studied the composition of stars. Her 1925 PhD thesis is still considered one of the most brilliant astronomy papers ever written. Have students research the contributions made to astronomy by Cecilia Payne-Gaposchkin and others at the Harvard College Observatory.

Find Out More ►To learn more about the origin of the elements before facilitating this activity, you may wish to visit the following websites:

Nova: How to Make an Element http://www.pbs.org/wgbh/nova/physics/make-an-element.html

The s-Process—Sixty Symbols https://www.youtube.com/watch?v=KlBG_A4Djp4

Veritasium: Neutron Star Merger Gravitational Waves and Gamma Rays https://www.youtube.com/watch?v=EAyk2OsKvtU

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http://www.pbs.org/wgbh/nova/physics/make-an-element.html

http://www.pbs.org/wgbh/nova/physics/make-an-element.html

https://www.youtube.com/watch?v=KlBG_A4Djp4

https://www.youtube.com/watch?v=EAyk2OsKvtU

Name: _________________________________________ Date: ___________________________________________

Student ActivityWhere Do the Elements Come From?

Part 1: Modelling Nuclear Fusion in StarsInside the Sun, hydrogen nuclei collide with each other. These collisions can sometimes lead to fusion, which produces a helium nucleus and releases energy as described by the following reaction equation:

21H + 3

1H → 42He + 1

0n + light energy

1. Examine this sketch of a helium nucleus. Given that like charges repel, speculate why protons in the helium nucleus stay together.

2. Your teacher will provide you with a magnet, a ruler, a ball bearing, and cardstock. Set them up as shown. Gently tap the ball bearing so it begins to roll toward the cardstock. Observe and explain what happens.

3. Roll the ball bearing again, but this time try to make it stick to the magnet through the cardboard. What do you need to do for this to happen?

4. The ball bearing and magnet are an analogy for two fusing hydrogen nuclei. The cardstock is an analogy for the electric repulsive force between them. The magnetic force is an analogy for an attractive, short-range interaction force called the strong force, which holds nucleons together when they get very close (less than 10−15 m apart). Using the model, qualitatively explain the conditions under which nuclear fusion proceeds and helium nuclei form.

Light energy

Fusion

Hydrogen-2+

+

++

Hydrogen-3

Neutron

Heliumnucleus+

+

+

+

Ball bearingRuler

Cardstock

Magnet

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Name: _________________________________________ Date: ___________________________________________

5. A star like our Sun has a tremendous mass of 2 × 1030 kg. This high mass compresses the core to a temperature of 15 million degrees Celsius. Describe what happens to the kinetic energy of the atoms in a gas when the temperature increases. Explain why nuclear fusion reactions occur only when temperatures are sufficiently high.

6. Examine a proton approaching two different nuclei. Explain whether the electric repulsive force between the proton and the nucleus will increase, decrease, or stay the same as the number of nucleons increases. Explain whether the temperature will need to be higher, be lower, or stay the same for fusion to proceed.

Part 2: Making the ElementsHydrogen, helium, and trace amounts of lithium, beryllium, and boron were created during the Big Bang. Almost all other elements are created by stars.

1. Your teacher will provide you with a set of Star Cards, which describe different stars in the universe. Order the Star Cards from lowest to highest core temperature. What do you notice about the elements that each star produces? Complete the following sentence by circling the correct term:

Stars with higher core temperatures can fuse heavier/lighter elements. Explain why.

2. Examine the masses of the stars ordered based on temperature. Complete the sentence by circling the correct term:

More massive stars have higher/lower core temperatures. Explain why.

3. How does a star’s mass determine which elements it can produce?

++ +

+

+

+

+

+

+++

+

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+

+

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++

+

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Name: _________________________________________ Date: ___________________________________________

4. Examine the objects set out by your teacher. Identify the type of stars needed to produce the elements in the objects.

Object Elements Type of Stars

Bone Calcium

Air Oxygen, nitrogen

Water Hydrogen, oxygen

Clay pot Silicon, oxygen

Salt Sodium, chlorine

Pencil lead Carbon

Pie plate Aluminum

5. The human body is made up of 65% oxygen; 18% carbon; 10% hydrogen; 3% nitrogen; and 8% other elements, including calcium, phosphorus, and potassium. Which types of stars created the atoms in your body?

Part 3: Iron Peak and Heavy ElementsStars fuse lighter atoms together to make heavier ones. But not all elements are made in the cores of stars.

1. Compare the elements from Part 2, question 4 to the periodic table. Which elements are produced in stellar cores?

2. Examine the card with the most massive star and the highest core temperature. What is the heaviest element that is produced? How many protons are in the nucleus?

3. Based on what you know about electric repulsion, speculate on why stars don’t fuse elements heavier than this.

4. Examine this sketch of a neutron approaching a nucleus. Describe the electric repulsive force on the neutron.

++ +

++

+

+

++

+

+

++

++

++

++

++

+

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Name: _________________________________________ Date: ___________________________________________

5. Elements heavier than iron are not formed via fusion reactions in stellar cores. Heavier elements can form by slowly adding neutrons to the nucleus. This forms an unstable nucleus, which undergoes beta decay.

10n → 1

1p + 0 –1e + 0

0ν–

Beta Decay

This process of forming elements happens in shells surrounding the cores of intermediate-mass stars late in their lives.

(a) Consider iron-56. How many neutrons need to be added to make cobalt-59?

(b) Outline the steps needed to go from iron to cobalt.

6. To form the heaviest elements, many neutrons must be rapidly captured by the seed nuclei. This requires a high density of free neutrons.

(a) Consider gold-159. How many neutrons must be added to form gold-159 from iron-56?

(b) Why would neutrons need to be rapidly captured to form the heaviest elements?

(c) Consider the types of stars and stellar life cycle events you learned about in previous courses. Speculate where in the universe the energies would be sufficient to lead to high densities of free neutrons.

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Name: _________________________________________ Date: ___________________________________________

Consolidate Your LearningAnswer the following questions to check your understanding of the origin of the elements.

1. Nuclear fusion reactions are very difficult to achieve on Earth. Explain why.

2. Cosmologist Carl Sagan wrote, “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of starstuff.” What did he mean?

3. If the elements are made inside stars, how did they get out to make Earth and everything on it?

4. Precious metals, such as gold, silver, and platinum, are rare and are some of the heaviest elements found on Earth. Consider the origin of these elements. What makes them rare and heavy?

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Activity 7: Conservation Laws and Dark EnergyLesson Plan

IntroductionIn this activity, students explore conservation laws to discover that dark energy is a logical consequence of the modelling process. Students see how conservation laws studied in previous classes have evolved into more sophisticated models. Dark energy is presented as another rung in the ladder of progress toward a better model of the universe.


Purpose• To examine how scientific models change and

progress with new experimental evidence

• To analyze the observations that lead to dark energy


• Students should be familiar with the conservation of mass and energy.

• Students should know about beta decay.

Materials• Perimeter Institute video: Model Making: Model Breaking

• News Flash—What’s Happening to Our Universe? (1 per student; see Appendix G)

• Fact Cards—What’s Happening to Our Universe? (1 per student; see Appendix H)

• electronic balance

• hotplate

• baking soda

• cart and ramp

• alpha and beta sources (optional)

• Geiger counter (optional)

Teacher Instructions 1. Divide the class into groups of four. Give each

student a copy of News Flash—What’s Happening to Our Universe? (see Appendix G).

2. Give each student one Fact Card (see Appendix H). Allow groups time to collaborate and enter their facts in the summary table.

3. Instruct the class to mingle and exchange the Fact Cards blindly (without seeing what they are getting). After each exchange, have students return to their groups and share their findings. This continues until groups have all 10 facts. It is fine if some groups find all 10 before others.

4. Once a group has gathered all 10 facts, have them work together to make sense of them. The facts are all true, but not all are relevant.

5. The activity stops when one group puts the entire story together. This group shares its story with the class. Classmates can challenge and correct the story if the group has missed something.

6. Once the story has been assembled and the idea of dark energy has been raised, ask students how they feel about scientists “inventing stuff” to explain observations. Steer the discussion toward the interplay of theory and experiment. Show the accompanying video, Model Making: Model Breaking.

7. Distribute the student activity sheets, and have students work together through the questions about their evolving models of mass and energy.

8. Students can perform the calcium chloride and sodium sulfate experiment in question 1 if time and equipment allow, but it was likely covered in an earlier grade.

9. Using an electronic balance sensitive to 0.1 g will allow the change in mass of the baking soda to become evident within a few minutes of heating.

10. The cart-on-a-ramp activity can be done with probeware, but this could be a good opportunity to reinforce equations of motion.

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SAFETY ALERT

Avoid using lead compounds in the conservation of mass demonstration.

Radioactive sources are controlled substances. Check your local regulations about how to handle radioactive sources in the classroom. Don’t let students handle the sources. Use a computer simulation if you are not comfortable working with radioactive sources.

Teacher Tips• Use cardstock for the Fact Cards so they will be

durable and last for many years.

• The beta and alpha decays can be demonstrated using a Geiger counter if your school is equipped and local regulations allow for radioactive sources in the classroom. You could also use a simulation, such as Geiger Counter Simulation.

INQUIRY T IP

Collaboration: The News Flash activity is meant to reflect the collaborative—yet competitive—nature of science. You can adjust the instructions to increase collaboration by allowing students to reveal their facts before arranging the trade. Make it more competitive by offering prizes or restricting the number of key facts.


To Communicate: Consider having students summarize the News Flash using alternative modes: TV news report, haiku, comic strip, or poster.

ExtensionStudents could be invited to research and share alternative theories for dark energy.

STSE Connections

Science is the continuous search for better explanations. Have students reflect on how their understanding of the world has changed since they began studying science.

Teacher Background

Why do we think the universe is expanding?

Einstein’s theory of general relativity predicted that the universe could either expand or contract, so he added an extra term to produce a static universe. Alexander Friedmann showed that Einstein’s static universe was not stable and published his own solution using general relativity that predicted an expanding universe. Friedmann’s ideas gained traction when Edwin Hubble observed the redshift of distant galaxies and concluded that the universe is expanding. Hubble’s law shows that the speed of galaxies increases with their distance (v = H0D). The current value for the Hubble constant (H0) is about 70 (km/s)/Mpc. Astronomers have increased the precision of H0 by looking farther and farther away, and in the 1990s they began to study very bright objects called Type 1a supernovas.

What are Type 1a supernovas, and why are they important?

A Type 1a supernova involves a binary system in which the larger star becomes a white dwarf that slowly consumes its partner. As the white dwarf gains more and more mass, it approaches the Chandrasekhar limit, where it will briefly reignite and then collapse in a supernova. Since the supernova is triggered when the white dwarf reaches a specific mass limit, all Type 1a supernovas are essentially identical. By observing the brightness of Type 1a supernovas, astronomers can infer how far away they are. Redshift reveals the recessional velocity of the supernovas and gives us a way to measure the expansion of the universe. Measurements of Type 1a supernovas revealed that they were fainter than they should be, based on their redshifts. The discrepancy between brightness and redshift can be explained if we allow the universe to expand more while the light was en route; therefore, the expansion of the universe is accelerating.

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http://www.kcvs.ca/site/projects/physics_files/radioactive/geiger_counter.swf

What is dark energy?In general relativity, energy curves spacetime. Curved spacetime is responsible for gravitational force, time dilation, lensing, and more. To explain expansion and acceleration on the universal scale, we don’t need a force, we need curvature. In the current cosmological model (Lambda-CDM), dark energy is the intrinsic energy of space (vacuum energy). This energy is smooth and persistent—it is uniformly distributed and maintains a constant density, even as the universe expands. The density of matter and radiation decreases while the density of dark energy remains constant (~10−10 J/m3). A universe with uniform dark energy density will expand at the same rate everywhere in the universe (Figure 1). As the universe expands, the influence of dark energy becomes more dominant, so the rate of expansion increases. Conservation of energy on the cosmological scale is an open question. Some cosmologists assert that energy is not conserved in general relativity, while others say that dark energy does negative work on the universe, offsetting the energy gained by expansion.

What’s cutting edge about dark energy?

The observations leading to the inference that dark energy exists are fairly new, and many models are being proposed to explain them. Recent analysis of the cosmic microwave background (CMB) indicates that dark energy accounts for about 68% of the mass energy in the universe.

Find Out More ►To learn more about dark energy before facilitating this activity, you may wish to visit the following websites:

Hubblesite: Dark Energy http://hubblesite.org/hubble_discoveries/dark_energy/de-what_is_dark_energy.php

Sean Carroll: Why Does Dark Energy Make the Universe Accelerate? http://www.preposterousuniverse.com/blog/2013/11/16/why-does-dark-energy-make-the-universe-accelerate/

Figure 1 In this artist’s conception, uniformly distributed dark energy, represented by the purple grid, is pushing matter and space apart. Gravity is attractive, but it weakens with distance, so the effects of dark energy dominate as the universe expands.

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http://hubblesite.org/hubble_discoveries/dark_energy/de-what_is_dark_energy.php

http://hubblesite.org/hubble_discoveries/dark_energy/de-what_is_dark_energy.php

http://www.preposterousuniverse.com/blog/2013/11/16/why-does-dark-energy-make-the-universe-accelerate/

http://www.preposterousuniverse.com/blog/2013/11/16/why-does-dark-energy-make-the-universe-accelerate/

Name: _________________________________________ Date: ___________________________________________

Student ActivityConservation Laws and Dark Energy

IntroductionConservation laws are the foundation of all science. Properties that are conserved in a system don’t change unless something happens to the system. For example, charge is conserved when ebonite and fur are rubbed together; ebonite gains electrons, and fur loses them. The total number of electrons stays constant. In this activity, you will review some conservation laws and reflect on how your understanding of them has grown.

1. A sample of calcium chloride is placed in a test tube that sits in a sodium sulfate solution. The flask is sealed and placed on a scale. The mass of the system is 242.6 g. The flask is then inverted so the two solutions mix and react. When the flask is placed back on the scale, what do you expect the mass will be? Explain.

2. Place a sample of baking soda on a scale. Record the mass. Heat the baking soda for a few minutes on a hotplate and then weigh it again. What do you observe?

3. What do you have to infer from question 2 to maintain conservation of mass?

4. Set up a ramp, as instructed.

(a) Measure the height of the cart at the top of the ramp.

(b) Predict the final speed of the cart at the bottom of the ramp.

(c) Measure the time taken and the distance travelled down the ramp.

(d) Calculate the final speed of the cart at the bottom of the ramp.

(e) Compare the result from (d) with your prediction in (b). Explain any differences.

CaSO4 inNaCl solutionNa2SO4

CaCl2

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Name: _________________________________________ Date: ___________________________________________

5. In 1909, Lise Meitner was studying beta decay when she observed that electrons emitted from the same material had a wide range of energies. This observation led to a problem in physics because it challenged the conservation of energy.

(a) Why does it matter that the electrons emitted from identical nuclei had vastly different energies?

(b) Twenty years later, Wolfgang Pauli proposed a new particle called the neutrino to account for the variable energy. What do you think about scientists inventing things to maintain existing laws?

(c) The neutrino is an almost massless neutral particle that travels at nearly the speed of light. It took another 25 years before neutrinos were detected in an experiment. How did confidence in the conservation of energy lead to the discovery of neutrinos?

Kinetic energy (MeV)

Energy Spectrum of Beta Decay Electrons

Inte

nsity

0.0 0.2 0.4 0.6 0.80.1 0.3 0.5 0.7 0.9 1.0 1.1 1.2

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Name: _________________________________________ Date: ___________________________________________

6. Uranium-233 (m = 233.040 u) [1 u = 1.660 54 × 10−27 kg] is a radioactive substance that emits an alpha particle (m = 4.003 u) while changing into thorium-229 (m = 229.032 u).

(a) Alpha particles leave at 1.5 × 106 m/s. What is the kinetic energy of a typical alpha particle?

(b) Is mass conserved in this transformation? Support your answer.

(c) Is kinetic energy conserved? What questions do you have about kinetic energy for this event?

(d) How can we modify the conservation of mass and conservation of energy laws to explain the observation that mass seems to disappear and energy seems to appear in a transformation?

7. Observations of distant Type 1a supernovas indicate that the expansion of the universe is accelerating. Astronomers have proposed something called dark energy to explain this acceleration. Dark energy is the energy of empty space, so as the universe expands, creating more space, there is more energy. How does this challenge your current understanding of conservation laws?

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Name: _________________________________________ Date: ___________________________________________

Consolidate Your LearningAnswer the following questions to check your understanding of concepts relating to conservation laws and dark energy.

1. What are the possible responses when experimental results disagree with conservation laws?

2. What observational evidence is puzzling astronomers?

3. How is dark energy like Pauli’s neutrino model?

4. Dark energy is challenging to describe. Use your knowledge of motion and energy to explain how a new form of energy can account for an accelerating universe.

5. When you think about dark energy, what do you still wonder about? Where can you look for answers?

My question:

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Answers

Activity 1: The Conservation and Transformation of Energy

Part 11. During the time interval ∆t1:2, the velocity of the ball increases

in the downward direction, due to the unbalanced downward force of gravity on the ball from Earth.

2. The kinetic energy of the ball is greater at moment 2 than at moment 1. We can measure the speed of the ball (the magnitude of the velocity) to track this difference.

3. The ball’s height has decreased from moment 1 to moment 2. I would name this “height energy” and give it the label Eh.

4. The kinetic energy bar at moment 2 (Ek2) is the same height as the gravitational energy at moment 1 (Eg1). They are the same height because all of the energy has transferred.

5. Before moment 1, the right hand lifted the ball up to its initial height. This energy came from the food (chemical) energy stored in the muscles/arm.

6. For the time interval ∆t1:2, the only objects that participate in energy flows or transfers are the ball and Earth. The right hand does not change the amount of energy flowing into or out of the system, nor does it cause a transfer from one storage mechanism to another within the system. So the simplest system to choose is the ball and Earth for ∆t1:2.

7. The energy went into heating the left hand and the ball. Some sound was produced, so the air was slightly heated up, as well. We would need to measure the temperature of the interacting objects to keep track of this new type of energy storage (thermal energy).

8. Examples of Energy Storage

Type of Storage

Name of Energy Label Storage Mechanism

Measured Property

Motion energy

Kinetic energy

Ek Stored in the motion of the object

Speed

Thermal energy

Eth Stored in molecular and atomic motion

Temperature

Interaction (potential) energy

Gravitational energy

Eg Stored in interaction between object and Earth (Earth’s gravitational field)

Vertical position

Elastic energy

Ee Macroscopic: stored in stretch or compression of object (shape change)

Microscopic: stored in deformation of intermolecular bonds due to interactions between molecules

Length (stretch or compression)

Chemical energy

Eint Stored in interactions between particles

Number of chemical species

Part 21. Wrh → Eg1: The right hand does work on the system, lifting up

the ball, causing energy to flow into the system as gravitational energy. At moment 1, when the ball reaches its maximum height, all the work done by the right hand is now gravitational energy in the system. Eg1 → Ek2: When the right hand lets go of the ball, the gravitational energy transfers into kinetic energy as the ball loses height and gains speed. At moment 2, the kinetic energy is at its maximum, because the speed is at its maximum. Ek2 → Eth3: The kinetic energy transfers into thermal energy in the ball and in the left hand after the ball collides with the left hand and both objects reverberate. At moment 3, all the kinetic energy has been transferred into thermal energy because the ball is now at rest.

2. The ball, Earth, and the left hand are defined as the system, and the right hand is defined as the environment. Energy is flowing into the system before moment 1. There is no energy flowing out of the system at any time. Before moment 1, the energy stored in the system objects was changing, but after moment 1 the energy stored in the system objects does not change from moment to moment.

3. Eg1, Ek2, and Eth3 would be no different than in the other energy flow diagram. The only change is that work is no longer being done on the system. Instead, energy stored chemically at moment 0 transfers into gravitational energy at moment 1. This is because the right hand is included in the system objects. Energy has been conserved for this system because there is no flow in from, or out to, the environment.

Part 31. See below left diagram. The elastic energy stored in the spring

at moment 1 transfers into kinetic energy at moment 2, stored in the expanding spring and in the cart as it gets pushed up the ramp. (Negligible amounts of energy are transferred into gravitational and thermal energy, which may be represented in some student answers.)

Cart + Spring +Earth

Ee1 Ek2

EFD 1:2


Ek2 Eg3

EFD 2:3

2. I disagree. The kinetic friction is negligible, so a negligible amount of energy is being transferred into thermal energy. We could measure the temperature of the wheels and the surface of the track to refute this idea.

3. See above right diagram. The kinetic energy at moment 2 transfers into gravitational energy at moment 3.

Eg1 Ek1 Eg2 Ek2

0

–

+

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4. The vertical change of the system objects between the spring being compressed and extended is negligible, so assume that the amount of gravitational energy at moment 1 is the same as it is at moment 2.

Ee1 + Ek1 +Wext= Ee2 + Ek2

0

–

+


0

–

+

Consolidate Your Learning1. (a)


Eg3 Ek4

EFD 3:4


0

–

+

(b) The speed of the cart at moment 4 should be the same as the speed of the cart at moment 2, since the bars show the kinetic energies would be the same.

(c)

2. Observations and predictions should agree, but differences between the observations can be accounted for by small amounts of thermal energy transferred during each energy transformation.

3. Define the system as the paper + Earth + air + left hand. The key moments are t1, the instant the paper leaves contact with the right hand; t2, the instant the paper contacts the left hand; and t3, the first instant the paper is at rest after t2. Eg1 is transferred into both Ek2 and Eth2, due to air resistance (the collisions between the air molecules and the surface of the paper). Shortly after, Ek2 combines with Eth2 to become Eth3 due to collisions between the surface of the left hand and the surface of the paper.

Activity 2: Innovative Technologies

Part 11. Answers will vary.

Part 21. (a) LED, CFL, incandescent; (b) LED, CFL, incandescent;

(c) LED, CFL, incandescent; (d) (bulb power)(4 hours/day)(365 days/year)($0.15/kWh); Incandescent = $13.14, CFL = $3.07, LED = $1.86; (e) (# of bulbs used)(cost per bulb) + (bulb power)(50 000 h)($0.15/kWh) Incandescent = $475, CFL = $122.50, LED = $75.75

2. Sample answer: You might consider the colour of the light; some CFLs and LEDs produce a harsh white light. You might also consider the environmental impact of the bulb’s manufacturing and disposal.

Part 31. Sample energy flow diagrams:

Hand + Flashlight

Shaking Flashlight

Ek1

Eelec2

Eγ3

Air + Windmill +Light

Windmill

Ek1

Eelec2

Eγ3

Flame +Thermocouple +

Light

Thermocouple

Eth1

Eelec2

Eγ3

2. GravityLight energy flow diagram:

Earth + Weight +Motor + Light

Eg

Ek Ee

Eγ

Consolidate Your Learning1. Energy-efficient devices are usually more expensive to buy, but

when you include the cost of electricity, they are often cheaper in the long run.

2. During a transformation, some energy ends up being diverted into other forms (usually heat). A device is efficient if most of the input energy ends up in the intended form.


Ee1

Ek2

Eg3

Ek4

EFD 1:4

Paper + Earth + Air + Left hand

Eg1

Eth2

Ek2

Eth3

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3. Traditional sources of electricity are gravitational, such as hydroelectric; chemical, such as fossil fuels; and nuclear. We might overlook geothermal energy or forms of kinetic energy, such as wind and tides.

4. Sample answer: Opportunities exist in generating and distributing electricity, increasing efficiency and conservation, and developing new technologies. I believe the greatest opportunity lies in developing new technologies.

5. Answers will vary depending on the video students choose.

Activity 3: Nuclear Transformations1. (a) Protons will electrostatically repel each

other and gravitationally attract the other nucleons. Neutrons will feel only gravitational attraction. (Students will not know about the strong force yet).

(b) The forces are not balanced.

nFG

pFGFE

2. (a) The force would have to be attractive to counteract the protons’ electrostatic repulsion.

(b) The force would have to act on both types of nucleons because the forces are not balanced for either particle in question 1.

(c) The force must decrease with distance, or there would be no limit to how big atoms could be. The exact relation is beyond the scope of this resource.

3. (a) When you add a proton, both the electrostatic force and the strong force increase.

(b) When you add a neutron, the strong force increases and the electrostatic force decreases as the protons get farther apart.

(c) Heavier elements have more neutrons than protons, so the ratio increases.

(d) Work is done to form nuclei, so there must be energy stored in them.

4. Sample answers: What is so special about this line? Why isn’t the staircase at Z = N?

5. (a) Si-32 is above the valley of stability. (b) It has too many neutrons. (c) One of the excess neutrons can change into a proton. (d) The energy of the resulting nucleus is lower. The beta

particle carries excess energy away.6. (a) Ni-56 is below the valley of stability. (b) It has too many protons. (c) This is a problem because the protons repel each other and

push the nucleus apart. (d) One of the excess protons can change into a neutron. (e) The positive charge of the proton must be ejected from the

nuclei somehow.7. (a) Student reflections will vary. (b) The proton number determines the element, so Si-32

becomes P-32.

(c) An electron must be produced to keep net charge conserved.

(d) The excess energy has been released as the kinetic energy of the beta particle.

8. (a) Student reflections will vary. (b) The kinetic energy of the positron comes from the change

of energy in the nucleus.9. (a) Radon-210 becomes Po-206. (b) The change of energy in the nucleus transferred into the

kinetic energy of the alpha particle.

Consolidate Your Learning1. The electrostatic force pushes protons apart and does not

interact with neutrons. The strong force pulls protons and neutrons together. At close distance (~1 fm), the strong force is much stronger than the electrostatic force. The electrostatic force acts over a greater distance than the strong force.

2. The competing forces create a situation in which the nucleus is unstable, so the nucleus changes to move into a lower energy state.

3. When the nucleus changes, it moves to lower energy, so that energy must go somewhere. The kinetic energy of the emitted particles comes from the excess energy that was in the nucleus.

4. (a) C-14 → N-14 + β−

(b) C-10 → B-10 + β+

(c) U-238 → Th-234 + α5. The emitted particles carry energy that can damage biological

tissue when the particles strike the tissue. To reduce exposure, you must place protective material between the source and the tissue.

Activity 4: Ionizing Radiation

Part 11. Ionizing an atom or molecule requires energy. The electron

needs energy to escape the atom. Low-energy radiation cannot impart enough energy to the electron for it to escape.

2. Radio waves and microwaves are low energy, and X-rays and gamma rays are high energy. X-rays and gamma rays can ionize atoms.

3. Fast-moving particles have high kinetic energy, which can be transferred to the electron so that the atom can be ionized. Slow-moving particles do not have enough kinetic energy to ionize atoms.

4. Non-ionizing: microwave oven, cellphone, tanning bed, computer screen, ultrasound; ionizing and non-ionizing: Sun, Earth, supernova remnant; ionizing: dental X-ray

5. Ionizing radiation can ionize atoms in cells and cause damage. This damage can cause genetic mutations when the cell tries to reproduce itself. The radiation can also kill cells, and if enough cells die, the organism can die. Non-ionizing radiation can also be harmful. UV and IR radiation can cause burns.

Part 22. (a) Gamma rays, X-rays, beta particles, alpha particles (note

that the order of gamma and X-rays doesn’t matter because they are both massless)

(b) Alpha particles, beta particles, X-rays, gamma rays (c) Gamma rays and X-rays, beta particles, alpha particles

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3. Gamma rays and X-rays are the most penetrating and can travel many kilometres in air. Thus, they present the greatest risk in terms of exposure. Alpha and beta particles are stopped easily and thus can’t do much damage to organisms from the outside. Alpha particles have the highest ionization power. If ingested or inhaled, they can do severe damage to living tissue.

Part 31. Answers will vary.2. Answers may vary depending on what students decide to

include. For example, they may try to estimate the number of X-ray scans the pilot has per year or the number of bananas consumed by Juan. Sample estimates: Anya: 2.7 mSv; Juan: 2.4 mSv; Cleo: 4.6 mSv; Paul: 38.5 mSv

3. Sample answer: Paul, Cleo, Anya, Juan4. Sample answer: Anya = (2.7 × 10−3) × 5 = 0.0013%;

Juan = (2.4 × 10−3) × 5 = 0.0012%; Cleo = (4.6 × 10−3) × 5 = 0.023%; Paul = (38.5 × 10−3) × 5 = 0.18%. (Note that these calculations are for one year only. It is also important to remember that the average incidence of cancer includes exposure to background radiation, 2.4 mSv.)

Part 42. (a) The ionizing power of the radiation makes it useful for

damaging and killing cancer cells in cancer treatments. (b) The penetrating power of X-rays and gamma rays make

them useful for medical imaging.3. Answers will vary, but students will notice that CT scans have

relatively high equivalent doses. (Doctors are starting not to order too many CT scans for an individual patient. Targeted cancer treatments also have high doses, but they are used to treat cancers that are otherwise difficult to treat, such as brain cancer and metastasized cancer.)

Consolidate Your Learning1.

Radiation Type

Ionizing Power

Penetration Distance in Air

Stopped By

Possible Uses

Alpha Very high (5000 ion pairs/mm)

5 cm Paper TAT

Beta High (10 ion pairs/mm)

2 m Aluminum PET scan

X-ray Low (<0.1 ion pairs/mm)

Thousands of m mm of lead

CT scan

Gamma ray

Low (<0.1 ion pairs/mm)

Thousands of m cm of lead

Gamma knife, PET scan

2. Ultrasound isn’t a form of electromagnetic radiation (neither ionizing nor non-ionizing). Ultrasound waves are high-frequency sound waves. There are no known health risks associated with ultrasound procedures.

3. Alpha particles are easily stopped by air and cannot travel more than a few centimetres. As long as the source is in the smoke detector and is not ingested or inhaled, one should not be concerned with an alpha particle source in the smoke detector.

4. Sample answer: Students may reflect on the cancer risk of smoking or the low risk associated with living near a nuclear plant.

Activity 5: Mass-Energy Equivalence

Part 11. The marble rolls down the tube and partway up the other

side before moving back and forth about point B, where it eventually comes to rest.

2. The final total energy is less because the system’s final gravitational energy is less.

3. Sample energy flow diagram:

Eg1Eth2

Eg2

Wth

Marble + Earth

Tube

4. Some energy leaves the system, since both the marble and the tube heat up due to the frictional interaction between them, and the tube is not part of the system.

5. The marble is bound because it does not have enough energy to escape from the dip at B.

6. The binding energy is equal to the amount of energy released into the environment.

Part 21. The neutron-proton system has less total energy at B because

it has less energy due to the strong force (strong energy).2. The energy leaving the system appears as light in the

environment.3. Sample energy flow diagram and work-energy bar chart:

Neutron + Proton

Light

E01 Wγ

E02

E01 +Wext= E02

0

–

+

4. The mass of hydrogen-2 is less than the sum of the masses of a proton and a neutron due to the light energy leaving the system.

5. The initial mass is 1.0073 u + 1.0087 u = 2.0160 u. The final mass is 2.0136 u, which is 0.0024 u less.

6. before = 3.0087 × 10−10 J; after = 3.0051 × 10−10 J7. 3.6 × 10−13 J8. The binding energy comes from mass energy from the proton

and neutron that transforms into light energy.

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Consolidate Your Learning1. Bound electrons do not have enough energy to move away

from the nuclei. Rubbing two materials together gives the electrons enough energy to move from one compound to another.

2. 4.58 × 10−12 J3. Sample energy flow diagram:

Eγ1

Ek2

E02

Light + Electron+ Positron

EFD 1:2

Information needed: amount of initial light energy, mass energies of electron and positron

4. 2.8 × 10−11 J

Activity 6: Where Do the Elements Come From?

Part 11. Students may guess that gravity keeps the protons together.

This is an opportunity to calculate the gravitational force and compare it to the electric repulsive force.

2. Sample answer: The ball bearing rolls toward the cardstock and bounces off.

3. You need to push the ball harder to make it roll faster (higher kinetic energy).

4. Fusion can proceed only if the nuclei have sufficient kinetic energy to overcome the electric repulsion, allowing the nuclei to be within range of the strong force.

5. When the temperature of gas atoms increases, so does their kinetic energy, and they move faster and faster. For fusion to proceed, the nuclei need high kinetic energies and therefore high temperatures.

6. As the number of protons increases, the electric repulsive force increases. This means higher kinetic energy and temperature are required for fusion.

Part 21. Stars with higher core temperatures can fuse heavier elements.

This is because the nuclei have sufficient kinetic energy to overcome the increasing electric repulsion.

2. More massive stars have higher core temperatures. In more massive stars, the force of gravity is higher. This force compresses the core to higher temperatures.

3. The core temperature of a star is linked to its mass. The higher the mass, the higher the force of gravity, and the higher the temperature to which the core can be compressed. The temperature of the core determines which elements can be produced.

4. Sample answer:

Object Elements Type of Stars

Bone Calcium Only the highest-mass stars

Air Oxygen, nitrogen

At least intermediate-mass stars or more massive ones

Water Hydrogen, oxygen

Hydrogen is formed in the early universe, but oxygen forms in at least intermediate-mass stars.

Clay pot Silicon, oxygen

Highest-mass stars for silicon and at least intermediate-mass stars for oxygen

Salt Sodium, chlorine

At least high-mass stars for sodium and highest-mass stars for chlorine

Pencil lead Carbon At least intermediate-mass stars

Pie plate Aluminum Highest-mass stars

5. The highest-mass stars are needed to form elements like calcium. Hydrogen was formed in the early universe, and oxygen and nitrogen can be made by at least intermediate-mass stars.

Part 31. With the exception of hydrogen, the lightest elements in the

upper rows of the periodic table are produced in stellar cores.2. Iron; 263. As the number of protons goes up, the electric repulsion

increases and higher and higher temperatures are needed for fusion. This may have a limit.

4. Neutrons are neutral. There is no electric repulsive force acting on the neutron, so it can be added to the nucleus more easily than a proton.

5. (a) 3 (b) 56

26Fe + 10n → 57

26Fe 5726Fe + 1

0n → 5826Fe

5826Fe + 1

0n → 5926Fe

5926Fe → 59

27Co + 0–1e + 0

0ν–

6. (a) 103 (b) The heavier elements have many more nucleons and

so, many more neutrons need to be added. This needs to happen before beta decay occurs, so it must happen quickly.

(c) Students may recall supernova and neutron stars from grade 9. (Discuss supernova explosions and neutron star mergers.)

Consolidate Your Learning1. For fusion to proceed, the electric repulsion between nuclei

must be overcome. To do this, the nuclei need sufficient kinetic energy or temperature. The temperatures needed are difficult to produce on Earth.

2. Most of the elements in our bodies and around us on Earth were produced in stellar cores.

3. Supernova explosions expel elements out into space. These elements are available to form new stars, solar systems, and planets. The elements on Earth were created by previous generations of stars.

4. The heaviest elements are produced only in rare events, such as supernova explosions and neutron star mergers. The heaviest elements form via rapid neutron capture and require a high density of neutrons.

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Activity 7: Conservation Laws and Dark Energy

News Flash ExplanationRedshift tells us the recessional velocity of the object and gives us a tool to measure the expansion of the universe. Distance estimates based on redshift and Hubble’s constant assume the universe is expanding at a constant rate and is valid at all scales. Distance can also be established by measuring the brightness of objects. Type 1a supernovas are ideal standard candles, so they can be used to explore the expansion of the universe over the last five billion years. We see that objects are fainter than they should be based on the time light has travelled, so we infer that the expansion of the universe has increased. The cosmological constant is the strongest candidate for explaining how the universe is expanding at an increasing rate.

Student Activity1. The mass shouldn’t change. Nothing has been added or

removed from the flask.2. The mass of the baking soda decreased over time because

carbon dioxide was being released.3. We infer that matter has been released in the heating process

(carbon dioxide).4. (a)–(c) answers will vary; (d) v = 2d/t; (e) The two speeds

should be equal. Any differences are due to experimental error or friction.

5. (a) Conservation of energy would say that the electrons should all have the same speed when emitted from the nuclei. The fact that they have a range of speeds indicates that something else is happening.

(b) Sample answer: Hypothesizing the existence of a previously unknown thing is an important part of the scientific process.

(c) Because there was so much evidence in other parts of physics to support the idea of conservation of energy, scientists were willing to spend a lot of time and money building experiments to find the neutrino.

6. (a) 7.5 × 10−15 J (b) Mass is not conserved. The mass before the transformation

is 233.040 u; the total mass after is 233.035 u. (c) Kinetic energy is not conserved. The kinetic energy before

the transformation is 0; the total kinetic energy after is at least 7.5 × 10−15 J (the Th-229 will have a very small amount as well).

(d) The mass that disappeared becomes kinetic energy. Putting mass and energy together into a larger concept called mass-energy equivalence allows us to keep a conservation law, but it is the conservation of mass-energy.

7. Dark energy is a problem for conservation laws because there is a continuously changing amount of energy in the universe and the conservation laws say that energy cannot be created.

Consolidate Your Learning1. You can challenge the data, change the law (expand energy to

include mass), or you can propose new matter that makes the previous laws work (dark matter).

2. Astronomers are puzzled by distant supernovas that are fainter than they should be. This implies that the supernovas have moved farther than expected, so the expansion of the universe must be accelerating.

3. Dark energy is like the neutrino model because the evidence for it is indirect, and there is no immediate way to detect it directly.

4. Using basic physics, acceleration requires a force. A force is a push or a pull. Dark energy is a puzzle because it’s not a force, but it is causing an acceleration.

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Appendix A: Light Bulb Comparison CardsActivity 2

Incandescent

Uses 60 W to produce 800 lumens 1 bulb lasts for 1000 hours

Purchase price: $0.50

Compact Fluorescent (CFL)

Uses 14 W to produce 800 lumens 1 bulb lasts for 10 000 hours


Light-Emitting Diode (LED)

Uses 8.5 W to produce 800 lumens 1 bulb lasts for 25 000 hours


Incandescent

Uses 60 W to produce 800 lumens 1 bulb lasts for 1000 hours


Compact Fluorescent (CFL)

Uses 14 W to produce 800 lumens 1 bulb lasts for 10 000 hours


Light-Emitting Diode (LED)

Uses 8.5 W to produce 800 lumens 1 bulb lasts for 25 000 hours


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A

Appendix B: Table of Isotopes—SimplifiedActivity 3

Number of protons, Z

Type of transformation

Valley of stability

Num

ber o

f neu

tron

s, N

Too

man

y ne

utro

ns

Too m

any p

rotons

14 506 28 82

6

14

28

50

82

126

β+β-αStable nuclide

Source: International Atomic Energy Agency

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B

Appendix C: Ionizing Radiation CardsActivity 4

+

+

Helium Nucleus

α

Alpha Particle–

Electron (or positron)

β

Beta Particle

Ionization Power: 5 000 ion pairs/mm air

Ionization Power: 10 ion pairs/mm air

Mass: 4 u

Range in Air: 5 cm

Mass: 1/2000 u

Range in Air: 2 m

Charge: 2+

Range in Tissue: Does not penetrate

Charge: 1– (or 1+)

Range in Tissue: Several layers of skin

Speed: 10–20% speed of light

Stopped by: Paper

Speed: 25–99% speed of light

Stopped by: Aluminum

Light

γ

Gamma RayLight

Χ

X-ray

Ionization Power: <0.1 ion pairs/mm air

Ionization Power: <0.1 ion pairs/mm air

Mass: 0

Range in Air: Thousands of m

Mass: 0

Range in Air: Thousands of m

Charge: 0

Range in Tissue: Very penetrating

Charge: 0

Range in Tissue: Penetrates tissue but not bone

Speed: Speed of light

Stopped by: Several cm of lead

Speed: Speed of light

Stopped by: Several mm of lead

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PET Scan

Positron emission tomography (PET) is a nuclear imaging technique that uses positrons (beta particles), the anti-particles of electrons. A positron-emitting source, which is designed to be taken up more readily by tumours than by healthy tissue, is injected into the patient. Inside the tumour, the positrons meet with electrons and annihilate, releasing gamma rays, which are mapped by the PET scanner, producing an image.

TAT

Targeted alpha therapy (TAT) is a new type of radio-immunotherapy that uses alpha particles to attack tumour cells. An alpha-emitting isotope is inserted into the tumour. The short range and high ionizing power of alpha particles kill tumour cells but don’t damage surrounding healthy tissue. TAT is in clinical trials for use as a therapy for leukemia and prostate cancer.

Cancer cell

Alpha emitter

CT Scan

Computed tomography (CT) scans the body by taking many X-ray images at different angles. X-rays are directed through the body to a detector on the other side. Depending on whether the beam travels through bone or tissue, it will be blocked by different amounts. The images are used to create cross-sectional slices of bones, blood vessels, and soft tissues in the body, resulting in 3-D images.

Rotating X-ray source

X-ray beam

Motorized table

Gamma Knife

Gamma knife therapy is a type of radiation procedure used to treat brain tumours. It contains 201 cobalt-60 sources, which aim gamma radiation at the patient’s brain. Each beam on its own is too weak to damage healthy brain tissue on the way to the tumour, but the beams converge in the tumour and together destroy cancerous tissue.

Cobalt-60

Helmet

Gammarays

Target

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Appendix D: Equivalent Dose TableActivity 4

Activity Dose (mSv)

Eating a banana 0.0001

Airport security scan 0.0001

Typical dose for living one year near a nuclear plant in Canada 0.001

Dental X-ray 0.005

Sleeping next to someone for one year 0.01

7-hour flight 0.02

Living in a stone, brick, or concrete building for one year 0.07

Chest X-ray 0.1

Increased background radiation for one year at the top of the CN tower due to cosmic rays

0.18

Annual dose for a uranium mine worker 1

Exposure of airline crew during one year of work 2.2

Annual exposure to natural background radiation (radon, cosmic rays, and food) 2.4

Whole-body PET scan 14.0

Chest, abdomen, and pelvis CT scan 21.0

Smoking 1.5 packs of cigarettes a day for one year 36

Average annual dose to astronauts on ISS 150

Dose that may cause radiation sickness 1000

Fatal limit if received over entire body 10 000

Nuclear therapy (targeted) for cancer 10 000–50 000

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D

Appendix E: Radiation Scenario CardsActivity 4

Anya lives in a stone building in downtown Toronto. After school and on weekends, she has a part-time job at the restaurant at the top of the CN Tower. This year her dentist discovered several cavities, so she had to have two dental X-rays.

Juan lives with his parents near a nuclear power plant in a brick house. He loves bananas, and eats two or three a day. This year he had to have an ultrasound on his leg.

Cleo wants to be an astro-naut and is taking flying lessons. She flies seven hours a week. She lives in a wood house with her parents and twin sister. In her spare time, Cleo likes to play computer games.

Paul smokes one to two packs of cigarettes a day. This year, he had a chest X-ray. He enjoys chatting with friends on his cellphone.

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Appendix F: Star CardsActivity 6

Low-Mass Stars

Mass: <1 MSUN

Abundance: 88%

Lifetime: 1011 years

Low-mass stars are the most abundant stars in the universe. Their low mass leads to relatively low temperatures in their core (1–3 × 107 K), which means they can only fuse hydrogen into helium. Once hydrogen runs out, the star becomes a white dwarf.

Intermediate-Mass Stars

Mass: 1 MSUN – 8 MSUN

Abundance: 10%

Lifetime: 109–1010 years

Our Sun is an intermediate-mass star. For most of its life, it will fuse hydrogen into helium. Once the hydrogen is gone and the core is helium, it will contract, compressing the core to a temperature of 2 × 108 K. These higher temperatures allow helium to fuse to form carbon. Heavier stars form nitrogen and oxygen. Once this fuel runs out, the star becomes a white dwarf.

High-Mass Stars

Mass: 8 MSUN – 9 MSUN

Abundance: 0.7%

Lifetime: 108 years

In stars more massive than 8 MSUN, once helium is depleted, gravity allows the core to contract, compressing it to a temperature of 109 K. Carbon can now fuse to make magnesium, sodium, and neon. Once this fuel runs out, the star becomes a white dwarf.

Highest-Mass Stars

Mass: >10 MSUN

Abundance: 0.7%

Lifetime: 108 years

The most massive stars fuse even heavier elements. After carbon burning, the core compresses to a temperature of 2 × 109 K, which allows neon and oxygen burning to proceed, making elements between magnesium and sulfur in the periodic table. The final stage is silicon burning at 3 × 109 K, which produces heavier isotopes up to and including iron. At iron, the star ends its life in a tremendous supernova explosion.

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Appendix G: News Flash— What’s Happening to Our Universe?Activity 7

Edwin Hubble demonstrated that the universe was expanding when he measured the redshift of distant galaxies. Scientists working on the High-Z Supernova Team and the Supernova Cosmology Project have found that very distant supernovas are fainter than they should be based on their redshifts. Something was wrong with our model of the universe.

Summary of Facts:

Conclusion

What do these puzzling results tell us about the universe?

Redshift, z

Observed Brightness vs Redshift

Obs

erve

d br

ight

ness

, mB

1415161718192021222324

0.0 0.2 0.4 0.6 0.80.1 0.3 0.5 0.7 0.9

Source: Supernova Cosmology Project

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Appendix H: Fact Cards— What’s Happening to Our Universe?Activity 7

Type 1a supernovas are excellent standard candles (they all have the

same luminosity).

The cosmological constant describes the energy of empty space and can

explain an accelerating universe.

The supernovas being studied are about 5 billion to 8 billion light

years away.

Einstein often referred to the cosmological constant as his

“greatest blunder.”

The distance to nearby supernovas can be determined by measuring their

redshift and using Hubble’s law.

Light from distant objects gets redshifted because the universe is

expanding. A larger redshift implies a greater distance.

Researchers expected the supernovas would be brighter, allowing them to

show that the expansion of the universe was slowing down due to gravity.

The observed brightness of any object depends on the object’s distance. Fainter objects are farther away.

The very distant Type 1a supernovas are not as bright as they should be

based on their redshift.

Hubble’s law, which assumes a constant rate of expansion for the

universe, was based on objects that were less than 1 billion light years away.

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Assessment

Assessing Global CompetenciesThe following rubric highlights the key global competencies to evaluate as students complete an activity. It is not essential to evaluate all the competencies at once. Rather, at certain points during an activity, you may choose to evaluate one or more of the competencies. You may evaluate a small sampling of students for one activity and other groupings of students for subsequent activities.

Global Competencies Activity Rubric

Level 1 Level 2 Level 3 Level 4

Critical Thinking and Problem Solving

- demonstrates limited ability to acquire, process, analyze, and interpret information during completion of the activity

- demonstrates some ability to acquire, process, analyze, and interpret information during completion of the activity

- demonstrates good ability to acquire, process, analyze, and interpret information during completion of the activity

- demonstrates advanced ability to acquire, process, analyze, and interpret information during completion of the activity

Innovation, Creativity, and Entrepreneurship

- demonstrates limited ability to turn ideas into action, lead, take risks, think unconventionally, and test new strategies, techniques, or perspectives

- demonstrates some ability to turn ideas into action, lead, take risks, think unconventionally, and test new strategies, techniques, or perspectives

- demonstrates good ability to turn ideas into action, lead, take risks, think unconventionally, and test new strategies, techniques, or perspectives

- demonstrates advanced ability to turn ideas into action, lead, take risks, think unconventionally, and test new strategies, techniques, or perspectives

Self-Directed Learning

- demonstrates limited awareness of student’s own process of learning, with regard to motivation, perseverance, resilience, and self-regulation

- demonstrates some awareness of student’s own process of learning, with regard to motivation, perseverance, resilience, and self-regulation

- demonstrates good awareness of student’s own process of learning, with regard to motivation, perseverance, resilience, and self-regulation

- demonstrates advanced awareness of student’s own process of learning, with regard to motivation, perseverance, resilience, and self-regulation

Collaboration - rarely provides suggestions and ideas to the group

- rarely listens to and values the suggestions or ideas of others

- rarely assumes shared responsibility for the completion of the activity

- sometimes provides suggestions and ideas to the group

- sometimes listens to and values the suggestions or ideas of others

- sometimes assumes shared responsibility for the completion of the activity

- usually provides suggestions and ideas to the group

- usually listens to and values the suggestions or ideas of others

- usually assumes shared responsibility for the completion of the activity

- always provides suggestions and ideas to the group

- always listens to and values the suggestions or ideas of others

- always assumes shared responsibility for the completion of the activity

Communication - demonstrates limited ability in expressing thinking and understanding using various means: reading and writing, viewing and creating, listening and speaking

- demonstrates limited ability in using a variety of media appropriately, responsibly, safely, and with regard to digital footprint

- demonstrates some ability in expressing thinking and understanding using various means: reading and writing, viewing and creating, listening and speaking

- demonstrates some ability in using a variety of media appropriately, responsibly, safely, and with regard to digital footprint

- demonstrates good ability in expressing thinking and understanding using various means: reading and writing, viewing and creating, listening and speaking

- demonstrates good ability in using a variety of media appropriately, responsibly, safely, and with regard to digital footprint

- demonstrates advanced ability in expressing thinking and understanding using various means: reading and writing, viewing and creating, listening and speaking

- demonstrates advanced ability in using a variety of media appropriately, responsibly, safely, and with regard to digital footprint

Citizenship - demonstrates limited ability in understanding diverse worldviews and perspectives

- demonstrates limited appreciation for the diversity of people and perspectives, and for the value of a more sustainable future for all

- demonstrates some ability in understanding diverse worldviews and perspectives

- demonstrates some appreciation for the diversity of people and perspectives, and for the value of a more sustainable future for all

- demonstrates good ability in understanding diverse worldviews and perspectives

- demonstrates good appreciation for the diversity of people and perspectives, and for the value of a more sustainable future for all

- demonstrates advanced ability in understanding diverse worldviews and perspectives

- demonstrates advanced appreciation for the diversity of people and perspectives, and for the value of a more sustainable future for all

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Self-AssessmentScientific Investigation Skills

After completing an activity, read the following statements. For each statement, if applicable, write the rating that best represents your contribution.

Rating Scale 1. Rarely 2. Sometimes 3. Usually 4. Often

Initiating and Planning___ I formulated questions.

___ I made predictions.

___ I planned experiments to answer my questions and test my predictions.

___ I tested predictions by determining relationships between variables in my activity.

Performing and Recording___ I made observations.

___ I gathered, organized, and recorded information from my activity.

Analyzing and Interpreting___ I analyzed the data or information from the

activity.

___ I identified patterns and relationships to draw conclusions.

Communication___ I was able to communicate with others my ideas,

procedures, results, and conclusions.

___ I communicated verbally, in writing, and with labelled diagrams.

Self-AssessmentScientific Knowledge and Skills

After completing an activity, read the following statements. For each statement, if applicable, write the rating that best represents your contribution.

Rating Scale 1. Rarely 2. Sometimes 3. Usually 4. Often

Knowledge and Understanding___ I gained knowledge from the activity.

___ I learned new terms from the activity.

___ I understand the concepts and the process of science explored in the activity.

Thinking and Investigation___ I identified the problem being investigated and

asked questions to help study the problem.

___ I gathered, recorded, and analyzed data and was able to draw conclusions from the data.

Communication___ I expressed myself verbally, in writing, and with

labelled diagrams.

___ While communicating, I used scientific information and terms learned from completing the activity.

Application___ I applied knowledge and understanding to familiar

problems presented in the activity.

___ I transferred knowledge to unfamiliar situations presented in the activity.

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Glossary

Binding energy: the amount of energy needed to separate two objects; nuclear binding energy is the energy needed to separate the nucleus into its component nucleons (proton and neutrons)

Chandrasekhar limit: the maximum mass of a white dwarf star (1.4 times the mass of the Sun); above this limit the gravitational force overpowers electron degeneracy pressure and triggers a supernova

Cosmic microwave background: early light of the universe that still exists today as very faint microwaves present throughout all of space

Equivalent dose: a measure of the damage to living tissue from radiation exposure; the equivalent dose is the absorbed dose (amount of energy absorbed per unit mass) multiplied by a weighting factor (wR) that takes into account biological effects. For instance, alpha particles have a significantly higher equivalent dose than gamma radiation, even if the absorbed dose is the same.

Environment: an object or collection of objects that interacts with the system but is not explicitly chosen to be part of the system.

Hubble constant: a proportionality constant that relates the distance of a galaxy to its recessional velocity; more-distant galaxies are moving away faster. The Hubble constant is a measure of the expansion of the universe.

Hydrostatic equilibrium: the balance between pressure (radiative and thermal) and gravity in a star

Mass energy: the energy of an object at rest due to its mass; quantified by Einstein’s equation, E0 = mc2, where E0 is the energy, m is the mass of the object, and c is the speed of light

r-process (rapid neutron-capture process): the process by which neutrons are added to nuclei faster than the nuclei can undergo radioactive decay; occurs only in supernovas and neutron star mergers because it requires a high density of free neutrons

Radioactivity: the emission of particles or radiation from an unstable nucleus, leading to the creation of a nucleus of another chemical element or to another energy level

Redshift: a shift in the position of spectral lines of a galaxy to the red end of the spectrum caused by the expansion of space. As the light from the galaxy travels through space, the universe expands over time and stretches the light, causing it to appear redder. More-distant galaxies have higher redshifts.

Strong force: the force that binds nucleons (protons and neutrons) into an atomic nucleus. The strong force is attractive at distances of ~1 × 10−15 m but rapidly declines with distance, leading to the physical size of the nucleus. At distances less than 0.7 × 10−15 m, it is repulsive.

s-process (slow neutron-capture process): the process by which heavier isotopes are formed when neutrons are captured by nuclei that then undergo beta decay to produce heavier elements; occurs in stars that have left the main sequence

System: a chosen object, or collection of objects, whose properties and interactions are relevant to a physical process

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Lead Authors and Educational Consultants

Nathan Chow Royal St. George’s College Toronto, Ontario

Dave Fish Sir John A. Macdonald Secondary School Waterloo Region District School Board

Lead Authors and Scientists

Dr. Kelly Foyle Perimeter Institute for Theoretical Physics Waterloo, Ontario

Dr. Damian Pope Perimeter Institute for Theoretical Physics Waterloo, Ontario

Science Advisor

Dr. Cliff Burgess Perimeter Institute for Theoretical Physics Waterloo, Ontario

Project Manager and Field-Test Coordinator

Jill Bryant Perimeter Institute for Theoretical Physics Waterloo, Ontario

Developmental Editor

Louise MacKenzie Toronto, Ontario

Copy Editor

Julia Cochrane Wolfville, Nova Scotia

Proofreader

Francine Geraci Toronto, Ontario

Designer

Tom W. Dart Toronto, Ontario

Executive Producer

Greg Dick Perimeter Institute for Theoretical Physics Waterloo, Ontario

Associate Producer

Dr. Damian Pope Perimeter Institute for Theoretical Physics Waterloo, Ontario

Advisory Panel

Kevin Donkers Preston High School Waterloo Region District School Board

Olga Michalopoulos (retired) Halton District School Board Burlington, Ontario

Laura Pankratz Western Canada PI Teacher Network Coordinator Edmonton, Alberta

Angela Robinson Perimeter Institute for Theoretical Physics Waterloo, Ontario

Marie Strickland Perimeter Institute for Theoretical Physics Waterloo, Ontario

David Vrolyk Sir John A. Macdonald Secondary School Waterloo Region District School Board

Tonia Williams Perimeter Institute for Theoretical Physics Waterloo, Ontario

Indigenous Reviewer

Laurie Minor Wilfrid Laurier University Waterloo, Ontario

Differentiated Support Reviewer

Jessica Webb Safe and Inclusive Schools Newfoundland and Labrador English School District St. John’s, Newfoundland and Labrador

Safety Reviewer

James Palcik Flinn Scientific Canada Inc. Hamilton, Ontario

Grade 11 Reviewers and Field Testers

Nadia Bechtold Columbia International College Hamilton, Ontario

Stephan Bibla Lawrence Park Collegiate Institute Toronto District School Board

Joseph Brecka Superior Collegiate and Vocational Institute Lakehead District School Board

Sebastiano Buono École secondaire catholique Renaissance MonAvenir Catholic School Board / Conseil scolaire catholique MonAvenir

Jarron Childs Superior Collegiate and Vocational Institute Lakehead District School Board

Ed Dyk (retired) Grand Erie District School Board Paris, Ontario

Teresa Franklin Valour JK–12 School Renfrew County District School Board

Alexis Howell Castlebrooke Secondary School Peel District School Board

Robert Klassen Rockway Mennonite Collegiate Kitchener, Ontario

Timothy Kwiatkowski John Paul II Catholic Secondary School London District Catholic School Board

Melissa Laukkanen Nipigon Red Rock District High School Superior-Greenstone District School Board

Bill Lee Seneca College, King Campus King City, Ontario

Siow-Wang Lee Vaughan Secondary School York Region District School Board

Greg Levack W.F. Herman Academy Greater Essex County District School Board

Syed Riaz Mahmood Yorkdale Adult Learning Centre & Secondary School North York, Ontario

Andrew G. Miller Kirkland Lake District Composite School District School Board Ontario North East

Dr. Tahira Nasreen Middlefield Collegiate Institute York Region District School Board

Katie Nelson Stephen Lewis Secondary School Peel District School Board

Felicia Palage Kitchener-Waterloo Collegiate & Vocational School Waterloo Region District School Board

Ashley McCarl Palmer Waterloo Collegiate Institute Waterloo Region District School Board

Alasdair Paterson White Oaks Secondary School Halton District School Board

Darrell Pratt Kirkland Lake District Composite School District School Board Ontario North East

John K. Rodgers Bruce Peninsula District School Bluewater District School Board

Margaret Scora Monsignor Paul Dwyer Catholic High School Durham Catholic District School Board

Jackie Wong Middlefield Collegiate Institute York Region District School Board

Credits

76


CopyrightPublished by Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5. Copyright © 2018 by Perimeter Institute for Theoretical Physics.

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For permission to use material from this module or product, submit a request online to Perimeter Institute.

The information and activities presented in this module have been carefully edited and reviewed for accuracy and are intended for their instructional value. However, the Publisher makes no representation or warranties of any kind, nor are any representations implied with respect to the material set forth herein, and the Publisher takes no responsibility with respect to such material. The Publisher shall not be liable for any general, special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material.

AcknowledgementsPerimeter Institute gratefully acknowledges educators David Vrolyk, Sheldon Valeda, and Nathan Zehr of Waterloo, Ontario, who permitted in-class testing for lessons in development on December 4, 5, and 7, 2017; February 28, 2018; and April 12, 2018.

Perimeter Institute gratefully acknowledges the thoughtful discussions and inspirational materials of Chris Meyer, shared with author Nathan Chow.

Photo CreditsFront cover left (chalkboard notes) Adobe Stock; middle (MRI) Adobe Stock; right (composite image of the Tycho supernova remnant) X-ray: NASA/CXC/SAO; Infrared: NASA/JPL-Caltech; Optical: MPIA, Calar Alto, O. Krause et al; 1 top, middle top, middle, middle bottom Adobe Stock; bottom NASA/JPL-Caltech/STScI/CXC/SAO; 2 Perimeter Institute; 11 courtesy of Argonne National Laboratory; 31 top United States Information Agency/Creative Commons; bottom Adobe Stock; 33 all but far right Adobe Stock; far right (supernova) NASA, ESA, J. Hester, A. Loll (ASU); 44 NASA/CXC/SAO; 64 Adobe Stock

Illustration Credits5–8, 13–16, 20, 24, 32, 38–41 Allan Moon; 45 CMG Lee based on graphic by Jennifer Johnson/Creative Commons; 46–48 Allan Moon; 53 Adobe Stock; 54, 58–62, 66, 67, 70 Allan Moon

Perimeter Institute has made every effort to ensure that permission for copyrighted material has been obtained. Perimeter Institute welcomes communication from any copyright holder it has not been possible to contact.

Perimeter Institute for Theoretical Physics gratefully acknowledges the support of the Government of Ontario and the Government of Canada.

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