PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information.PDF generated at: Wed, 18 May 2011 11:53:42 UTC

Physics A2

ContentsArticles

A-level Physics 1A-level Physics/Forces, Fields and Energy 2A-level Physics/Forces, Fields and Energy/Further dynamics 3A-level Physics/Forces, Fields and Energy/Work and energy 4A-level Physics/Forces, Fields and Energy/Motion in a circle 5A-level Physics/Forces, Fields and Energy/Oscillations 8A-level Physics/Forces, Fields and Energy/Gravitational fields 11A-level Physics/Forces, Fields and Energy/Electric fields 14A-level Physics/Forces, Fields and Energy/Capacitors 18A-level Physics/Forces, Fields and Energy/Electromagnetism 23A-level Physics/Forces, Fields and Energy/Electromagnetic induction 24A-level Physics/Forces, Fields and Energy/Thermal physics 25A-level Physics/Forces, Fields and Energy/The nuclear atom 29A-level Physics/Forces, Fields and Energy/Radioactivity 32A-level Physics/Cosmology 37A-level Physics/Cosmology/Models of the known universe 37A-level Physics/Cosmology/Stars and Galaxies 43A-level Physics/Cosmology/Structure of the universe 49A-level Physics/Cosmology/Information from stellar observation 49A-level Physics/Cosmology/How the universe may evolve 51A-level Physics/Cosmology/Relativity 51A-level Physics/Health Physics 54A-level Physics/Health Physics/Body Mechanics 54A-level Physics/Health Physics/Medical Imaging 54A-level Physics/Nuclear and Particle Physics 54A-level Physics/Nuclear and Particle Physics/The Nucleus 55A-level Physics/The SI System of Units 56A-level Physics/Equation Sheet 59A-level Physics/Glossary of Terms 60AQA A-Level Physics 65AQA A-Level Physics/Atomic structure 66AQA A-Level Physics/Particles and Anti-particles 69AQA A-Level Physics/Particles and Anti-particles/Constituents of the particle 71AQA A-Level Physics/Particles and Anti-particles/Forces 72

AQA A-Level Physics/Past paper questions 72

ReferencesArticle Sources and Contributors 73Image Sources, Licenses and Contributors 74

Article LicensesLicense 75

A-level Physics 1

A-level PhysicsThis A-level physics book is designed to follow the OCR GCE Physics A specification [1]. For the OCR B'Advancing Physics' specification, see A-level Physics (Advancing Physics). You can use this book as a revisionguide, or as another explanation of concepts that you may not fully understand. At A2 level, in the second year ofstudy, you must take the two core A2 modules along with one of the option modules.Before you begin this course, it is recommended that you understand some of the basic concepts covered in GCSEScience, and have an understanding of the SI unit system (Appendix A).If you find any mistakes, errors, broken links, or if you are able to make the content easier to understand, please donot hesitate to edit and expand on existing content.

Modules

AS Modules• Force(s) and Motion• /Electrons, Waves and Photons/• /Wave Properties/

A2 Core Modules• /Forces, Fields and Energy/• /Unifying Concepts in Physics/

A2 Option ModulesYou are only required to complete one of the optional modules.• /Cosmology/• /Health Physics/• /Materials/• /Nuclear and Particle Physics/• /Telecommunications/

AppendicesAppendix A

• /The SI System of Units/Appendix B

• /Equation Sheet/Appendix C

• /Glossary of Terms/

A-level Physics 2

References[1] http:/ / www. ocr. org. uk/ download/ kd/ ocr_9587_kd_gce_spec. pdf

A-level Physics/Forces, Fields and EnergyForces, Fields and Energy is the main module of the A2 year. You will need to know everything from the previous3 modules from last year. There is a lot to learn this year, but here is where things start to get really interesting!

Contents• Further dynamics• Work and energy• Motion in a circle• Oscillations• Gravitational fields• Electric fields• Capacitors• Electromagnetism• Electromagnetic induction• Thermal physics• The nuclear atom• Radioactivity• Appendix of Formulae

A-level Physics/Forces, Fields and Energy/Further dynamics 3

A-level Physics/Forces, Fields andEnergy/Further dynamicsFrom last year, you should remember kinematics and dynamics, the branch of physics that relates to the motion ofobjects. We will now expand on this and have a look at what happens when two objects collide, the concept ofmomentum, and we will take a closer look at Newton's three laws of motion.

MomentumIf you have seen collisions involving two objects, you may have noticed that the velocity of one object seems to bepassed to the other object. You may also have noticed that heavier objects seem to pass more velocity on to smallerobjects, whereas smaller objects seem to pass less velocity to more massive ones.What is in fact happening is that momentum is being conserved. Momentum is the product of an objects mass andvelocity, or . This means that, after a collision, an object that is heavier will have a lower velocity than alighter object in its place, and vice versa. Momentum is conserved for all collisions. The principle of theconservation of momentum states that:

Within a closed system, the total momentum in any specified direction remains constant.

Momentum is a vector quantity and has the units or (Newton-seconds) in the SI system.

CollisionsSince momentum is conserved, the momentum before a collision is equal to the momentum after a collision. You canuse this fact to solve problems involving collisions.Before Afterm1u1 + m2u2 = m1v1 + m2v2For instance, a ball is moving at 3m/s with mass 3kg. It hits another ball with mass 1kg moving at 2m/s; the two ballscollide and the second ball rebounds at 4m/s. Find the velocity at which ball 1 is moving:Before Afterm1u1 + m2u2 = m1v1 + m2v23x3 + 2x1 = 3v + 1x411 = 3v + 411-4 = 3v7 = 3v7/3 = vSo the velocity at which ball 1 is moving after the collision is 2.3m/s (7/3)m/s 1

A-level Physics/Forces, Fields and Energy/Further dynamics 4

Newton's laws of motion

Newton's first law of motionAn object will remain at rest or in a state of uniform motion unless it is acted on by an external resultant force.

Newton's second law of motionOriginally, you learnt this to be:For an object with constant mass, its acceleration is proportional to the force producing the acceleration, and is in the

direction of the force.However, since you now know that a force changes the rate of change of momentum of an object, we can use a moreaccurate interpretation of Newton's second law:

The rate of change in momentum of an object is proportional to the force that produces it, and takes place in thedirection of the force.

Newton's third law of motionWhen two bodies interact, the forces they exert on each other are equal and opposite.

A-level Physics/Forces, Fields and Energy/Workand energyDoing Work:

A force can increase the kinetic energy or gravitational potential energy of an object. The force moves through adistance, and we say that it does work. The amount of work done tells us the amount of energy transferred by theforce.work done (J) = energy transferred (J)To calculate the amount of work done W, we need to know two quantities:- The magnitude of the force F, - The distance d moved by the force, in the direction of the force,Thenwork done = force x distance moved in the direction of the force.W = F x Dwork done by tension = T x Dwork done against friction = -F x Dwork done by gravity = -mg x h

A-level Physics/Forces, Fields and Energy/Work and energy 5

Energy:

James Joule is the man, where the term 'the joule' comes from. His principle of conservation of energy states that:While energy may be converted from one form to another, the total amount of energy in a closed system is alwaysconstant.There are two main different types of energy; kinetic and potential. Kinetic energy (EK) is moving energy andpotential energy (EP)is the energy that could be transferred to moving energy. The formula for these are:

Kinetic Energy:

Potential Energy: The relationship between work done and energy is:Work done = Energy transferred

A-level Physics/Forces, Fields and Energy/Motionin a circleMotion in a circle is a very interesting concept, and not very complicated either. There are many lines (in the nonliteral sense) that can be drawn between circular motion and linear motion. In fact, as you progress, you will findcircular motion much more convinient that linear motion, because of some basic properties, most importantly, thatthe angular motion, of a body is the same for all particles, though their velocities may change. However, this will bedealt in rotational mechanics, not here. Before reading this section, ensure that you have a thorough understanding oflinear motion, vectors and differentiation.

Angular VariablesSimilar to the variables, found in linear motion, representing the position vector, displacement, velocityand acceleration respectively, we have a few terms in angular motion.The first variable is , which is the angle subtended at the centre of the circle. This can be compared with theposition vector of linear motion. It is measured in radians, or rads.The second variable is angular velocity, . Like velocity is the change in your position vector, or yourdisplacement by time, t, is the change in angle per unit time. It is measured in radians per second, rads/s. Also, itis not your displaced angle. If you cover 360 &deg, and full circle, in one second, it does not mean that your angularvelocity is zero, but 2 &pi radians per second. Mathematically we have, The third variable is angular acceleration, . It is the change in angular velocity by time. It is measured in radiansper second, . Mathematically, Notice that these quantities are not dependent on radius. All angular terms depend only on the axis of rotation, or thecentre of the circle, a fact that makes circular motion useful.

A-level Physics/Forces, Fields and Energy/Motion in a circle 6

Axial VectorsIt should be noted that these vectors are not normal vectors, but are axial vectors. Axial vectors are vectors along theaxis. Rather that along the direction of motion, these angular variables are along the axis, in an upward direction ordownward direction.This concept is quite difficult to visulalise. Imagine a rod, which is your axis of rotation, passing through a disc. Ifyou try and spin the disc, the axis will start to rotate. As such, your axis does not possess a real velocity. It does notmove at all.Now if you put a small ring on the rod. It should be in contact, but not too tightly attached. If you spin the rod, thering will start to move up, or down. This is due to a physical phenomenon, but for this purpose, ignore the dynamicsof its motion, only consider that it is moving up, or down. Also notice, that generally, when you rotate it inanticlockwise direction, it moves up . By this experiment, you can visualise how the axial vector operates.By convention, an anticlockwise rotation the direction of the axial vector is taken as the positive upward vector onthe axis, and vice versa for clockwise rotation. Another point to not is that though axial vectors can be resolved, tosimulate a body rotating in two axes, it more often than not complicates the situation. There are also several technicalcomplications if your two axes of rotation are not passing through the same point. This is a very complicatedsituation, and will not be discussed.

Using Angular VariablesHere are a few examples showing the usage of the angular variables we have just learnt.

Example 1Suppose a body is rotating, such that it subtends an angle of 1200 &deg at the centre every minute. Find its angularvelocity in S.I. units.We know that angular velocity is the angle covered per unit time. Since it covers 1200 degrees per minute, withuniform angular velocity, we can say that it covers 20 degrees in one second. 20 degrees is radians. So we get

rad/s.

Example 2If a body's angular displacement increases by per second, find its, angular velocity, and acceleration at some time,t.It is clear that the angular velocity is not constant from this. The average angular velocity in the first second is rads/s, in the second second, rads/s, and in the third second rads/ sec. You can observe that the angularvelocity is the time, t into radians per second. So, rads/s.We can also see that the angular acceleration is constant, and equal to radians per second square. So, .

Equations of MotionWe now move onto a few equations, bearing striking resemblance to those of linear motion. The second examplegiven above, is much better solved with these equations. All these equations are applicable only under constantangular acceleration.1. This equation gives a relation between your angular velocity and time. is the angular

velocity initially.

2. This equation gives a relation between your angular displacement and time. is the

initial angular displacement.

A-level Physics/Forces, Fields and Energy/Motion in a circle 7

3. This equation gives a relation between your angular velocity and angular displacement.Remember that the &omega is not a vector.

Example 3If a body spins about an axis, accelerating at a rate of 4 rad/s^2, find1. the angular displacement after 5 seconds, and angular velocity at that time2. the angular displacement when it attains an angular velocity of 12 rad/s1. The time has been given. In the first part, we need a relation between &theta and time. This is the second

equation. So, we have the equation identified, . We also know the values of

. Substituting, radians The second part requires us

to establish a relation between &omega and time. This is the first equation. rads/s <\li>

2. There are two methods to solve this equation. One is to find time through the first equation, and substitute it inthe second, the other is to directly use the third equation. or Substituting in equation 2, In the other method,

or

3. One might ask why the first method was even considered. This is because, if the angular4. velocity5. was given, not your6. speed7. , the third equation would require us to first find the speed, i.e. magnitude, of the &omega, and we would proceed

further. This too is not a serious impediment, and could be carried out. But if the angular velocity were asked, thethird equation would not give us that. These are important things to be kept in mind, even if they are not appliedoften.

Angular Unit VectorsFor the sake of convenience, two different vectors are used in circular motion, radial vectors and tangential vectors.Rather than our usual and vectors used for components in the x-axis and y-axis, the radial vector, gives theoutward component along the radial line. The tangential vector, gives the component along the tangent,anticlockwise being positive.If the angle subtended at the centre is known, then it becomes quite easy to convert these vectors into normal x-axisand y-axis vectors, by trigonometry.

A-level Physics/Forces, Fields and Energy/Oscillations 8

A-level Physics/Forces, Fields andEnergy/OscillationsIf you observe the motion of a pendulum, a child on a swing, or a speaker cone playing a low frequency sound, youwill notice that in each case, there is movement backwards and forwards of the same distance from a center point, orin other words, a vibration. These objects that vibrate are said to oscillate.

Observing oscillations

Free oscillationsWhen an object is in free oscillation, it vibrates at its natural frequency. For example, if you strike a tuning fork, itwill begin to vibrate for some time after you struck it, or if you hit a pendulum, it will always oscillate at the samefrequency no matter how hard you hit it. All oscillating objects have a natural frequency, at which they will vibrateat once they have been moved from the equilbrium position.

Forced oscillationsImagine a building in an earthquake. The ground is moving side to side, and the building (assuming that it is strongenough to not be completely destroyed by the forces) will be moving side to side with the ground. In this case, thisoscillation is not the buildings natural frequency, but it is being forced to vibrate with the ground. This is a forcedoscillation.

Examples of oscillating systems• A mass that is held up with a spring• A pendulum• A string of a guitar

Describing oscillationsOscillations can be shown on a displacement-time graph, like this:

A-level Physics/Forces, Fields and Energy/Oscillations 9

Notice that the curves are smooth. This is because the object slows down before changing direction, instead ofbouncing back and forth, which is what a graph with straight lines and sharp corners would describe. Movement thathas a displacement-time graph with curved lines like the one above, is called sinusoidal motion.The graph can show us the differences between several oscillating systems. For an oscillating system, the graphshows us:• The displacement at a given point in time,• The amplitude,• The period and,• The frequency

DisplacementThe displacement at a certain point in time is the distance of the object away from the centre point. The displacementis 0 at the centre, at its maximum at one end (usually on the right when right is taken as positive), and at its greatestnegative value on the opposite end (usually left but, again, only when right is taken as positive). Displacement isgiven the symbol s or x.

AmplitudeThe amplitude is the greatest displacement of an oscillating object. It is measured from the center point to one of themaximum points of displacement. The amplitude can increase or decrease with time. Amplitude is represented by thesymbol A

Period and frequencyperiod is the time taken for a single oscillation. the frequency is the number of oscillations per second

Simple harmonic motionA body executes simple harmonic motion if its acceleration is proportional to its displacement from a fixed point,

and is always in the direction of that point.To explore simple harmonic motion (SHM) let's take the example of a spring with a mass in the absence of gravity(interestingly, you get SHM even with gravity present). If this is our ideal spring, the force is kx where k is ameasure of the stiffness of the spring and x is the displacement. The force is toward the origin if that is theequilibrium position of the spring, so we write -kx to remind ourselves of that. Now, Newton's second law becomes

.

This differential equation is easy enough to solve, and the answer is where A and are arbitraryconstants and . It does not really matter how we got the solution, because we are physicists, not

mathematicians. This is the answer we are expecting, so we try it, and lo and behold, it works. If you do not believeme, substitute it in. Moreoever, this is the complete solution, and you will just have to believe me on that because itis slightly more difficult to prove.Without loss of generality, we will take , also called the phase shift, to be zero (if you are concerned about this,we are just defining where t=0 is).Now, a remarkable thing we recognize about the solution is that the frequency (radians per second), isindependent of A. That is, no matter how big the oscillations are, the frequency is the same. A pendulumapproximately undergoes SHM, so this is why they are used in clocks, the amplitude doesn't affect the period! By theway, we have added the subscript zero to omega because we are going to have some other omegas soon.

A-level Physics/Forces, Fields and Energy/Oscillations 10

Some terms to remember are frequency, f (cycles per second) = and the period, T = . These are notso important, but often people will specify the frequency or the period instead of the angular frequency, so they canbe helpful.Now, to get the velocity, differentiate the position, and to get the acceleration, differentiate the velocity. We have,

and .Now, we have avoided saying what A is. It turns out, it depends on the problem, or the initial conditions. We can saythe velocity or position of the oscillator at some t is something and then use the expression for v or a to find A. Youcan do the same thing with the phase if you want, but it is a little tedious and doesn't tell us much.Notice the greatest velocity is at the equilibrium position (x = 0) of the oscillation. We can go one making suchstatements, but they are all extremely obvious if you simply plot out the position, velocity, and acceleration on thesame graph.

DampingAn object that oscillates freely oscillates at its natural frequency. If it loses no energy, it will continue to oscillateforever. Damping is when an oscillating mass loses energy. There are 3 types of damping:1) Light - The amplitude gradually decreases over time2) Critical - The mass would overshoot 0 displacement3) Heavy - The displacement decreases to 0 without any oscillation.The cause of damping is frictional forces, e.g. Car suspensionLet's try to quantify this a bit. Say there is a friction force which is proportional to the velocity (this is a pretty goodapproximation in many cases) with constant of proportionality c. Then, by Newton's second law,

.

This equation is a little trickier to solve than without the friction. I am going to use a very nice trick which you willfind throughout physics, and whenever you have similar equations. Notice that if x is a solution and y is a solution,then ax + by is also a solution, where a and b are constants (real or complex). This property means the equation iscalled "linear." We know that . Assume x is . Then we just take the real part of xand we get our answer because the equation is linear, but exponentials are so much easier to work with than sinesand cosines. The equation of motion becomes

So,

or .

Defining , and remembering

.

Defining , we have the general solution

.All we do is take the real part of this with Euler's identity, and we have,

,where C and are just A and B written a different way. You can find them if you want, but they won't be veryhelpful. Notice that the oscillator oscillates with ever decreasing amplitude, but not at its "natural" frequency, but at adifferent frequency.

A-level Physics/Forces, Fields and Energy/Oscillations 11

It is conceivable that is imaginary, in which case, the entire solution is just a negative exponential! This is calledcritical damping, when it just turns into being an exponential instead of oscillitory motion.

ResonanceA mass resonates, when the driving frequency of oscillations is equal to the natural frequency of the object. (SeeTacoma Narrows Bridge also known as "Galloping Gertie") This means that work is done to keep drive theoscillations.If the driving frequency is less than the natural frequency, the amplitude decreases to a much smaller value.

A-level Physics/Forces, Fields andEnergy/Gravitational fieldsWe have already met gravitational fields, where the gravitational field strength of a planet multiplied by an objectsmass gives us the weight of that object, and that the gravitational field strength, of Earth is equal to theacceleration of free fall at its surface, . We will now consider gravitational fields that are not uniformand how to calculate the value of for any given mass.

Gravity as a field of forceThe effects of the Earth's gravity extend far out into space. For example, the Moon is kept in orbit by the Earth eventhough it is 400,000km away (where gravity is the centripetal force). The Earth has a gravitational field that willattract any object with mass towards the centre of the planet.

Radial Fields

The Earths radial gravitational field isrepresented by the lines.

The Earth has a radial field of gravity, which means that the gravitationalfield is circular and acts from the centre point.

You can see on the diagram that near the Earth's surface the lines are closertogether than higher up. The closeness of the lines represent the relativestrength of the field, so from the diagram, you can tell that the strength of thefield decreases with altitude. Further apart lines represent points where thefield is weaker.The arrows show the direction in which the force on an object will act, whichis towards the centre of the Earth.

A-level Physics/Forces, Fields and Energy/Gravitational fields 12

Uniform fields

The Earth's gravitational field isrepresented by parallel lines on small

scales.

A uniform field, however, has the lines perfectly parallel. The Earth'sgravitational field can be considered to be uniform on the scale of smallthings such as cars, balls, and planes. For small heights at this scale (a fewdozen kilometres), the strength of the field doesn't change enough to benoticeable. Again, the arrows point towards the centre of the Earth, since thatis the way objects fall.

Newton's ideas of gravity

Isaac Newton was trying to find a way to explain why objects fell towards thecentre of the Earth instead of simply staying put. He began to link the falling

of an apple, with the "falling" of the Moon towards the Earth, and came up with his law of gravitation.

He suggested that any two objects with a mass would have a force of attraction between them. This force ofattraction would be proportional to their masses, so that larger masses would have a stronger force of attraction thana smaller mass.The gravitational field of every object is a radial field, since the mass is concentrated at the objects centre, and as youalready know, this is the point at which gravity could be said to act.

As you can see, a quarter of lines of force goes throughthe plane when the distance is doubled.

The strength of a radial field decreases as you move further awayfrom it. As you can see on the diagram on the right, the number offield lines going through the plane quarter when the distance isdoubled, and it will be of the original value if the distance was

tripled.

This is called the inverse square law, and is true for anythingwhich is a point source, such a light from a point or the amount ofradiation emitted.

The inverse square law follows .

Using the above, Newton suggested that the force of attraction was proportional to the two masses as well as thedistance between them:

.

This relationship is the basis of how Newton's law of gravitation is often stated:Any two point masses attract each other with a force that is proportional to each of their masses and inversely

proportional to the square of the distance between them.However, to make this into an equation, we need to add in a constant of proportionality, G:

.

Where G is the gravitational constant, . There is also a minus sign in the equation, which will beexplained in the "electric fields" module, where we will encounter repelling as well as attracting forces.

is also sometimes written as , so that capital M represents a large mass such a

planet, and lower case m represents a small mass such as a ball or an aeroplane.

A-level Physics/Forces, Fields and Energy/Gravitational fields 13

Gravitational field strength

Defining the gravitational field strengthThe gravitational field strength tells us how strong a gravitational field is. You may recall that the gravitational fieldstrength of the Earth near its surface is . This means an object that is near the surface of the earth willaccelerate towards it at . We could then define the gravitational field strength as the acceleration an objectwill experience within that gravitational field.A better definition, however, can be derived from the equation, . Making the subject of this gives us

, or . From this arrangement of the equation, our definition of gravitational field strength now

becomes:The gravitational field strength at a point is the force per unit mass exerted on a mass placed at that point.

This means that the gravitational field strength, is equal to the force experienced by a mass of 1kg in thatgravitational field.

From the new definition, it follows that gravitational field strength is measured in , though it is perfectlyacceptable to use for situations where it is treated as an acceleration (such as the acceleration of an object infree fall).

Finding the field strength of a mass

Since and , they can be combined to give:

(by substituting F for mg)

(by cancelling the lower case 'm's)

You can use this to find the gravitational field strength of a mass at a particular point, r.Note that the gravitational field strength of the Earth near its surface is numerically equal to the acceleration of freefall, .

A-level Physics/Forces, Fields and Energy/Electric fields 14

A-level Physics/Forces, Fields andEnergy/Electric fieldsLike gravitational fields, electric fields are a field of force that act from a distance, where the force here is exerted bya charged object on another charged object. You may already be familiar with the fact that opposite charges attract,and that like charges repel. Here, we will look at ways to calculate field strengths and the magnitude of forcesexerted, in a very similar manner to gravitational fields.

Representing electric fieldsElectric field lines are drawn always pointing from positive to negative, like the flow of current. Just like magneticand gravitational fields, the separation of the lines tell us the relative strength.

Radial fieldsRadial fields are drawn from a centre point. The field is stronger nearer the surface of the object, and weakens as youmove further away. For a positive charge, the arrows point outwards, and for a negative charge, the arrows pointinwards.

The field is directed into a negative pointcharge...

...and it is directed outwards from apositive one.

A-level Physics/Forces, Fields and Energy/Electric fields 15

Uniform fields

Two plates of opposite polarity(from inside a capacitor) and thelines representing the uniform

field between them.

Between two charged plates there is a uniform electric field, which means that itsstrength is constant between each plate. This is represented by parallel lines, directedfrom the positive plate to the negative plate. The field curves outwards slightly onthe edges of the plates, and it is important that you draw it like that.

Multiple charges

When there are several radial and uniform fields close to each other, they have to becombined into one field, since each of their fields interact and change. The mostcommon shapes are shown, and the arrows, as always, point from positive tonegative. You should be able to draw field lines for simple variations on these.

Two point charges of opposite polarity and the linesrepresenting the electric field between them. A point charge and a plate. Notice how the radial field

transitions to a uniform one near the plate.

Coulomb's lawCoulomb's law is very similar to Newton's law of gravitation, except instead of relating the force between twomasses together, it relates the force between two charges, and . Since the two charges are point chargeswhich have radial fields, they follow the inverse square law.Therefore, the relationship can be expressed as:

.

Or, in words:

A-level Physics/Forces, Fields and Energy/Electric fields 16

Any two point charges exert a force on each other that is proportional to the product of their charges and inverselyproportional to the square of the distance between them.

Just like Newton's law, we need to introduce a constant of proportionality to make it into an equation, which in thiscase is k:

.

Where .

Permittivity of free space

is known as the permittivity of free space, and is roughly . It is often useful to just remember that

in free space, however you do also need to know , as you may be given the

permittivity of different mediums.

Signs of chargesNote that for each charge, you must keep the signs intact in the equation. If you were to have two positive, or twonegative charges in the equation, the result would be positive, but if you were to have one negative and one positivecharge, the final answer would be negative. The sign of the answer tells us whether the force between the twocharges is an attraction, or a repulsion, like charges will repel, and opposite charges will attract. This also explainsthe minus sign in Newton's law of gravitation, since the force between two masses is always an attraction.

Electric field strengthJust as gravitational field strength is the force exerted per unit mass, we could define the electric field strength interms of charge:

The electric field strength at a point is the force per unit charge exerted on a positive charge placed at that point.This is just like saying that the electric field strength is the force a charge of +1 coulomb experiences in that electricfield. Therefore, we can find the electric field strength, E, by:

.

From this equation, you can see that the electric field strength is measured in .

Field strength of a uniform fieldYou can make a uniform electric field by charging two plates. Increasing the voltage between them will increase thefield strength, and moving the plates further apart will decrease the field strength. A simple equation for fieldstrength can be made from these two points:

Where V is the voltage between the plates, and d is the distance between them. Note the minus sign in the equation,which has been added since the force that a positive charge will experience in the field is away from the positivelycharged plate.Here you can see that the units of electric field strength is . is equivalent to .

A-level Physics/Forces, Fields and Energy/Electric fields 17

Field strength of a radial fieldSince the electric field strength could be said to be the force exerted on a charge of +1C, we can substitute 1 coulombfor in Coulomb's law. We then get the equation:

, or

This will tell us the field strength of a charge, Q, at a distance, r.

Force on particles

To calculate the force an electron experiences in a uniform field, we can combine with in the

following steps:

For an electron with a charge of -e, this becomes:

, or

This is useful if you are asked to find the force on an electron in a uniform field, most often in a cathode ray tube.

Comparison of electric and gravitational fieldsAs you may have already noticed, electric and gravitational fields are quite similar. You should be aware of thesimilarities and differences between them.

Similarities• For point charges or masses, the variation of force with distance follows the inverse square law.• Both exert a force from a distance, with no contact.• The field strength of both is defined in terms of force per unit of the property of the object that causes the force

(i.e. mass and charge).

Differences• Gravitational fields can only produce forces of attraction, whereas electric fields can produce attraction and

repulsion.• Objects can be shielded from an electric field, but there is no way to shield an object from a gravitational field.

A-level Physics/Forces, Fields and Energy/Capacitors 18

A-level Physics/Forces, Fields andEnergy/CapacitorsIntroductionWhen two conductive materials are separated by an insulating material, then it will behave as a Capacitor withassociated Capacitance in the units of Farads (Coulombs/Volt).Intuitively, Capacitance can be interpreted as "How much charge can I shove into a material if I apply a certainvoltage?"Capacitors are useful because it can store energy momentarily and dissipate the energy later, and with combinationof a resistor, it is capable of "delaying" a signal.

Definition of Capacitance/CapacitorA capacitor is usually made from two sheets of metal separated by an insulating material (such as air or ceramics). Ifwe apply a voltage between the two sheets, there will be an associated electric field generated, and charges willaccumulate on each side of the plates. We define Capacitance to be where Q is the charge that

accumulates on the plate when voltage V is applied. The unit of capacitance is in Farad or F for short. Capacitanceis proportional to the area of the plates, and inversely proportional to the separation distance and thepermeability of the insulating material. This makes intuitive sense - if we make the plates bigger, we can store morecharge, and if we bring the plates closer, the tendency for the charges to attract increase, thereby increasing theelectric field generated.Now, it does not mean that capacitance is a property that appears only on two sheets of metallic sheet. In fact, anypiece of wire or metal would have small but non-zero associated capacitance with it. Calculating such capacitancesand either exploiting them or taking necessary measures to counteract it is a big deal in engineering electric circuits.

Capacitors connected in Parallel and SeriesLet's find the equivalent capacitance of capacitors in series and in parallel.

Capacitors in parallel

Fig. 3: Capacitors in parallel

Capacitance in two capacitors connected in parallel adds up, i.e.

A-level Physics/Forces, Fields and Energy/Capacitors 19

Not-so-rigorous proof

When two capacitors are connected in parallel, then the terminals of capacitor will have the same voltage. So, if weswap the capacitors in parallel with some equivalent capacitor, it should have the same voltage drop as the either oneof the parallel capacitors had. If we count the charges accumulated on the capacitors in parallel, they add up (If onecapacitor had Q1 charges accumulated and the other Q2 then the equivalent charges accumulated is Q1+Q2). Thatmeans that the charges in the equivalent capacitor is the sum of charges accumulated... which means:

They are all equal, so let's call it "V".So,

Therefore,

:

...We can generalize this for more than 2 capacitors - just add 'em up.

Capacitors in series

Fig. 4: Capacitors in series

Reciprocal of Capacitance adds up for capacitor connected in series., i.e.

(Once again) Not-So-Rigorous Proof

It's the exact opposite of parallel circuit.First, the voltage drop must add up (for example, if two series capacitors C1 and C2 had voltage drop of 3V and 1V,then the equivalent capacitor had better have voltage drop of 4V).What about the charge, however? The charges must remain the same in the equivalent capacitor. To illustrate,suppose two capacitors C1 and C2 are connected in series. Then if charge Q accumulates on one plate of C1, thencharge of -Q would accumulate on the other plate. Conservation of charge dictates that the '-Q' must come fromsomewhere. That 'somewhere' is the top plate of C2.So, the top plate of C2 loses '-Q' charge, which is essentially saying that C2 accumulates charge of 'Q'. Then, theother side of C2 will have a charge '-Q'. So, if we view the system holistically, the magnitude of charge accumulatedon top of C1 is the magnitude of charge on bottom of C2)...Phew, that was mouthful, long and cumbersome, and it sounded more philosophical than scientific. Anyway, whatwe get is the following equations:

They are all equal, so let's call it "Q".So,

A-level Physics/Forces, Fields and Energy/Capacitors 20

Therefore,

Once again, we can generalize this rule for more than 2 capacitors - just add the reciprocals!

Capacitor as an energy storage elementCapacitor, if we will, can be considered as a device that stores energy in the electric field by applying voltage acrossit. If we calculate the energy stored a capacitor (E) of capacitance C when voltage V is applied, we find that

(By the way, the magnetic analogue of this is called the inductor, and it possesses surprisingly similar characteristicwith surprisingly similar equations.)

Not-so-rigorous ProofThe power dissipated for an electric component was defined to be P=v i where v=voltage and i=current. Current ischange of charge over time, or dQ/dt.We have defined C=Q/V, so Q=CV. Since C is constant, i = dQ/dt = C dV/dt.Plug this into the equation for power, and we get:

Because power is rate at which energy is changing, (P=dW/dt), to find work W, we have to integrate with respect totime. This gives us:

Though mathematicians will be infuriated by what I'm about to say now, it usually works for most cases. If weconsider derivatives like a fraction, then we note that the 'dt's will cancel out, giving us:

which gives us:

...which is the work required to store charges in a capacitor with voltage V applied, which is the energy stored in thecapacitor when we apply a voltage V.

A-level Physics/Forces, Fields and Energy/Capacitors 21

Capacitor with a Resistor (RC Circuits)When we have a circuit with resistor and a capacitor, we have what is known as a RC circuit, which appears all thetime in any electric system. It can be used to delay a signal or filter unwanted signals.

DerivationLet's consider a case where a resistor with resistance R is connected in series with a capacitor with capacitance C anda voltage source with voltage . Assume that the Capacitor at time=0 has potential difference If we take Kirchoff's Voltage Law for this circuit, what we will get is the following:

We know that the current flowing through the resistor is same as the current flowing through the capacitor. BecauseQ=CV for capacitor, the current i is . Replacing i, we get:

Add and divide by RC to get:

This is a first order differential equation. Solving this, we get:

If we then differentiate this we get:

And limiting t towards infinity gives:

If we plug this into the differential equation mentioned above, we will get:

Thus, Now, plug in the equation that we've found for V(capacitor) for time=0 to find:

Which gives us . Combined, we get:

We will call which gives us:

A-level Physics/Forces, Fields and Energy/Capacitors 22

Interpretation of the EquationAt t=0, we can see that voltage of the capacitor is equal to its initial condition. We can also notice that as timeapproaches infinity, the exponential term gets smaller and smaller, which gives us voltage of the source. The natureof the function does not allow discontinuity, so that means that the function is slowly making a transition from V(0)to V(source). How fast? Just take the derivative.With this interpretation, RC circuit is a 'circuit that makes a smooth transition from one voltage level to anotherin an exponential fashion.'

Time Constantis what is known as the "Time constant" of the RC circuit. It is a magnitude that indicates how slowly the circuit

voltage is decreasing or increasing. Larger T implies longer transition between the two states.

Practical uses for Time ConstantRC circuits are mainly used to create delays and filters.

Delay

Let's say you were making a switch where the user had to press a button for more than three seconds. Say this devicewas connected to some other machinery that considered anything higher than 4.5V as "ON." Also suppose you had a5V voltage source. With just these information, you will be able to construct a RC circuit with appropriate timeconstant to achieve this effect. If we assume the capacitor is initially discharged (Vc(0)=0V), then it becomes aproblem of mere algebraic manipulation.

Filter

Remember that high RC meant smoother transition. If the voltage source was changing (as in signals that comes infrom a microphone), then what would happen?Well, from waves we know that low sounds have low frequency. Low frequency means that it takes more time tochange from one value to another. The opposite of that is high frequency, which changes its values rapidly. If our RCterm is very high, then the RC circuit won't be able to "catch up" with the rapid transition of the high frequency. Thismeans that the circuit will pass the low frequency signals better than the higher frequency ones.Such use of RC circuit is called a Low-pass Filter and it has important applications in signal processing.

A-level Physics/Forces, Fields and Energy/Electromagnetism 23

A-level Physics/Forces, Fields andEnergy/Electromagnetism

Magnetic Force on a CurrentF = B I L

F is force measured in Newtons (N)B is flux density (the strength of a magnetic field) measured in TeslasI is current measured in amps (A)L is the length of conductor in the magnetic field measured in metresB = F/IL This defines flux density, B.We can measure F using the current balance.If the current cuts across the magnetic field at the angle θ then the component the current across the field is ISineθand therefore -F= B I L sinθ

θ is the angle the current makes with the magnetic field.F (force) is at its maximum when θ = 90 degrees, F = 0 when the current is parallel to the field lines. i.e., θ = 0degrees.Use Fleming's left hand rule for the direction of motion.

Magnet Force on a moving chargeF=BIL= BQL/T= BQVThe SI unit for charge, Q, is coulombs - C.If charge moving at right angles to the fieldF = -Bev for an electron ( e = charge on an electron)Remember that the direction of conventional current is opposite to that of the electron.The magnitude of an electron charge is -1.6x10-19

Orbiting chargesF is always perpendicular to the path of the charged particle, so the particle moves in a circular path.Therefore, centripetal force = mv²/R = BeVRadius of path = R = mv/Be

Quick noteRadius is large for more massive, faster particles Radius is smaller when the magnetic field strength is large

A-level Physics/Forces, Fields and Energy/Electromagnetic induction 24

A-level Physics/Forces, Fields andEnergy/Electromagnetic inductionWe have already investigated that passing a current through a wire in a magnetic field causes a force to be exerted onit. The opposite is also true, and when a force is exerted on a wire a current is induced in the wire. This completelyrevolutionised the world because it meant that electricity could now be relatively cheaply produced.

Inducing an EMF.When a conductor is moved through a magnetic field, an EMF is generated.

Faraday's LawMichael Faraday states in his law that: The magnitude of the emf generated is proportional to the rate of change ofmagnetic flux.Magnetic Flux density is a measure of the strength of a magnetic field and is essentially how dense the field lines ofa magnetic field are within a given area.

Calculating the induced EMFFaraday's law states: Induced EMF is equal to the rate of change of magnetic flux.Magnetic flux = Magnetic field strength x Area = BA.Rate of change implies we consider the variable with respect to time (in seconds)Therefore...Induced EMF = (change in Magnetic Flux Density x Area)/change in Time.OR EMF = BA/tIf we are doing it with a coil, the area becomes the area of one coil multiplied by the number of coils, n = 2πr2nTherefore, Induced EMF = (B2πr2n)/t.If we want to increase the amount of EMF induced, we either...Increase the area 'swept'.Increase the Magnetic Flux Density.Decrease the amount of time taken.The EMF induced is also proportional to the speed of the object going through the Magnetic Flux.Because BA/t can be re-written as...EMF = Magnetic flux density x Width x Speed.This is because speed = distance / time.REMEMBER! - EMF is measured in volts, magnetic flux density is measured in teslas and area is measured inmeters2, time is measured in seconds.So you will have to convert things from mm, cm, km, minutes, etc.

A-level Physics/Forces, Fields and Energy/Electromagnetic induction 25

Faraday's law The magnitude of induced EMF is proportional to the rate of change of magnetic flux linkage:

Lenz's lawLenz's law states that the direction of the induced current is always so as to oppose the change which caused thecurrent. It is just a small addition to Faraday's law:

(Notice the minus sign!)

TransformersA transformer is made up of two or more coils of unmagnetised magnetic material. One coil is the primary coil andis connected to an alternating supply. The other is the secondary coil.

A-level Physics/Forces, Fields andEnergy/Thermal physicsThermal physics deals with the changes that occur in substances when there is a change in temperature.

Internal energyWhen you heat up a material, it may change state. The molecules vibrate with a greater amplitude, and break apartfrom one another. The material has been supplied with energy and you can feel it getting hotter. The increasedkinetic and potential (from their greater separation) energy of the particles is an increase in what we call internalenergy. Internal energy is defined as:The internal energy of a system is the sum of the randomly distributed kinetic and potential energies of its molecules.Therefore, an increase in temperature for a material means an increase in its internal energy.

The thermodynamic temperature scaleThe Celsius scale of temperature depends on the properties of water. 0°C is the freezing point of water, and 100°C isthe boiling point of water. It is a relative scale, because it is relative to the freezing and boiling points of water. Thethermodynamic scale of temperature (represented by the letter T), however, is an absolute scale of temperuture,and does not depend on the properties of any particular substance. It is also directly proportional to the amount ofinternal energy a substance possesses.

A-level Physics/Forces, Fields and Energy/Thermal physics 26

Absolute zeroThis scale of temperature is defined in terms of internal energy, and is measured in kelvins (K). 0K is defined as thetemperature at which a substance will have minimum internal energy, and is the lowest possible temperature. Thistemperature is known as absolute zero.

Converting between K and °CThe divisions of the kelvin scale are identical to the divisions of the Celsius scale, so that an increase of 1°C is equalto an increase of 1K. This makes it simple to convert between the two, and if you know that absolute zero is-273.15°C, you can simply use the formula:

to convert between °C and K.

Heating up substancesWhen you apply heat to a substance, the temperature does not simply increase in a straight line. Some extra energy isrequired to break bonds between particles.

Energy and temperature changesIf we were to heat a block of ice at a steady rate and plot a graph of the temperature against time, we would get thefollowing graph:

This shape is rather surprising. You would expect the line to increase in a straight line, with none of the breaks thatyou can see above. We should consider what is happening to the molecules of the water at each section of the graphto understand why this is so:• AB

The ice is below freezing point, but the temperature is increasing. The molecules are vibrating slowly, butbegin to vibrate more.

• BC

At 273K (0°C) the ice is at melting point. The bonds between molecules are being broken and molecules havegreater potential energy. This is the Latent Heat of Fusion

• CD

A-level Physics/Forces, Fields and Energy/Thermal physics 27

The water now increases in temperature towards boiling point. The molecules vibrate even more and movearound rapidly as their kinetic energy increases.

• DE

At 373K (100°C) the water is now at boiling point. Molecules completely break away from each other andtheir potential energy increases. DE is much larger than BC because ALL bonds need to be broken for a gas toform. (The Latent Heat of Vapourisation.)

• EF

The water is now steam and the molecules are moving around much faster than before. Their kinetic energycontinues to increase as energy is supplied.

At the sections BC and DE, where there is a change of state, the molcules do not increase in kinetic energy, butincrease in potential energy. The heat energy being supplied does not change the temperature at these sections, but isinstead used to break the bonds between molecules.

Specific heat capacitySome materials will heat up quicker than others. For example, metals are good conductors of heat, and provided theyare the same mass and that the energy is supplied at the same rate, copper will increase in temperature quicker thanwater.The specific heat capacity can tell us how much energy is required to increase the temperature of a substance, and isdefined as:

The specific heat capacity of a substance is numerically equal to the amount of energy required to raise thetemperature of 1kg of the substance by 1K (or by 1°C).

This can be written as the equation:

Where is the energy supplied, is the mass of the substance, is the specific heat capacity, and is thechange in temperature

Measuring the specific heat capacityTo find the specific heat capacity of something, we can control all of the possible variables and then use them tocalculate it. From the equation above, we can see that . This means that if we can supply a known

amount of energy to a material of known mass, and measure the change in temperature, we can insert the values intothe equation and obtain the specific heat capacity.To supply a known amount of energy, we can use an electric heater. You may recall that electrical energy can befound by , so by measuring the voltage, the current and the time that the circuit is switched on, we willhave a value for the energy supplied to the material.In the same time period that the circuit is switched on, we must take measurments for the change in temperature. Anordinary mercury thermometer may be used, although it is recommend to use a temperature sensor with a computerto make more precise and accurate measurements.

Once we have taken readings of the temperature and energy at regular intervals of time, we can plot a graph of against . We can calculate the gradient, making sure to use as much of the line in our calculation as possible,and divide it by the mass of the material to obtain the value of the materials specific heat capacity.

A-level Physics/Forces, Fields and Energy/Thermal physics 28

Specific latent heatWhen you heat up a substance so that it changes state, the temperature stays the same during the change. Differentsubstances will require more energy to change state than others. The specific latent heat will tell us how muchenergy a substance requires to change state and is defined as:The specific latent heat of a substance is numerically equal to the energy that must be supplied to change the state of

1kg of the substance without any change in temperature.This can be written as the equation:

Where is the energy supplied, is the mass of the substance, and is the specific latent heat.

The gas lawsThere are four properties of a gas, that are related to each other. These properties are the pressure, the temperature,the volume and the mass of the gas, and these relationships are expressed as the gas laws.

Boyle's lawBoyle's law relates the pressure of a gas to its volume. Specifically, it states that:

The pressure of a fixed mass of gas is inversely proportional to its volume, provided that the temperature remainsconstant.

This can be expressed as or .

You can picture this at the molecular level, if you were to imagine the number of collisions the particles of a gasmake with the container of a particular size, and then imagine the increased number of collisions when the containeris reduced in size but the number of particles remain the same. This is observed as an increase in pressure of the gas.

Charles' lawCharles' law relates the volume of a gas with its temperature on the thermodynamic temperature scale, and that:

The volume of a fixed mass of gas at constant pressure is proportional to its temperature on the thermodynamictemperature scale.

This can be expressed as or .

It is a little more difficult to understand why this is the case, because a gas will always take up the entire volume ofits container. If you think about how a particle behaves when it is heated up, it will vibrate more and cause anincrease in pressure, or harder and faster collisions of the molecules against the container. However, since pressure isto be kept constant in this case, the volume of the container will need to increase. Therefore by increasing thetemperature of the gas, we have increased its volume.

A-level Physics/Forces, Fields and Energy/Thermal physics 29

Pressure lawThe pressure of a fixed mass of gas at constant volume is proportional to its thermodynamic temperature.

This can be expressed as or .

Equation for an Ideal Gas

n is the number of moles of gas,R is the Ideal Gas Constant,T is the ABSOLUTE temperature,p is the Pressure in Pascal,V is the Volume in m3.

Properties of an Ideal Gas1) Its particles should be monatomic2) The particles are infinitely small3) There are no bonds between the particles, hence all the energy is kinetic.

A-level Physics/Forces, Fields and Energy/Thenuclear atomUp until the 19th century, atoms were once thought to be the smallest building blocks of matter, and that mattercould not be broken down any further. We now know that atoms are made up of smaller, sub-atomic, particles. Thishas also helped us to understand the nuclear processes such as fission and fusion.

Structure of the atom

Plum pudding atom

Near the end of the 19th century, it was widely accepted that the atom was neutral as awhole, and had areas of concentrated negative lumps within a larger positive structure.This model of the atom was called the plum pudding model, where the pudding waspositive, and the plums were the negative electrons. This is also called the chocolatechip cookie model.

Discovery of the nucleus

In 1906, Ernest Rutherford was investigating the passage of α particles through gold foil.What he found was that most of the α particles passed straight through the foil, and there was some that weredeflected by an angle of greater than 90°. It was known that α particles were smaller than atoms and had a positivecharge, and from this Rutherford concluded that the atom is mostly empty space and has a positively chargednucleus at the center, which was repelling the α particles. This experiment disproved the plum pudding model, andthe new nuclear model was now the widely accepted model. He also calculated that the nucleus had a diameter ofaround .

Later, the negative "lumps" that originally led to the plum pudding model were found to actually be electrons orbiting the nucleus with a relatively large radius of about , also confirming that an atom is mostly empty

A-level Physics/Forces, Fields and Energy/The nuclear atom 30

space.

Discovery of the protonThe next step was to find out what the nucleus was made up of. The proton was discovered, again by Rutherford, in1919. To find the protons, he placed a source of α radiation inside a cylinder of nitrogen gas. The cylinder had anopening at one end, which was covered by a sheet of aluminium foil. A screen was placed outside the opening, andflashes of light were observed on the screen. The flashes of light were caused by particles hitting the screen, butsince it was known that aluminium foil prevents α particles from passing through, another, smaller, particle musthave been hitting the screen. Rutherford asked two of his research students, Geiger and Marsden, to takemeasurements of the deflection angles of the particles, and he found by calculations that the proton was smaller thanmost nuclei, and had a positive charge which was the same magnitude of an electron. The distribution of thedeflected alpha particles is different for different forces (for example, magnetic, hard sphere etc.). Rutherford wasable to be sure that the nucleus was positively charged.

Discovery of the neutronIn 1932, James Chadwick discovered a particle that was slightly greater in mass than the proton and had no electriccharge, which he called the neutron. He used α radiation from polonium, and directed it towards some beryllium.The beryllium emitted neutrons when it was bombarded with the α radiation, but since they have no charge, theywere hard to detect. Chadwick placed some paraffin wax in the path of the neutrons, and the paraffin wax emittedhigh energy protons (paraffin wax contains a large amount of hydrogen). This showed that there were particleshitting the atoms of the paraffin wax without being slowed down by the positively charged nucleus of the atoms, andthat they collide elastically with atoms.

Evidence of crystal structureA beam of X-rays can be directed at a piece of crystalline material, and the resulting dots on the screen behind it area regularly spaced pattern. The regularly spaced dots are evidence that the atoms in the material have a crystalstructure. If the atoms weren't in a crystal structure, the resulting pattern would be smeared rings.X-rays are used because the wavelength of X-rays are roughly the same as the spacing between atoms, and thereforethe diffraction is greatest. An electron beam can also be used to provide the same evidence.

Evidence of the size of nucleiA beam of high-energy electrons can be used to find the radius of nuclei. High-energy electrons are electrons thathave been accelerated to high velocities, so that their de Broglie wavelength could be changed to match the spacingsof nuclei. The electrons are diffracted around different nuclei and calculations are done to find the radius of a nucleusfrom the angle of diffraction.

Relative sizesThe size of various particles were found from the above experiments as:• radius of proton ≈ radius of neutron ≈ m• radius of nucleus ≈ m to m• radius of atom ≈ m• radius of molecule ≈ m to m

A-level Physics/Forces, Fields and Energy/The nuclear atom 31

Nuclear processes

Nuclear equations

A helium atom

If we look at a helium nucleus, we can see that it has two neutrons and two protons. Itcan be represented like this:

The 4 at the top represents the number of nucleons in the nucleus, and is therefore calledthe nucleon number, and sometimes the mass number. It is sometimes denoted by theletter A.

The 2 at the bottom represents the number of protons, and is therefore called the protonnumber, or atomic number, and is sometimes denoted by the letter Z. To be more precise, however, the protonnumber represents the charge of the nucleus, so that an electron is represented by:

In all nuclear processes, there is always a balance. The number of neutrons and protons are always the same beforeand after a process, and so the nucleon and proton numbers must stay the same. Consider the reaction:

Here 2 hydrogen nuclei fuse to form a helium nucleus. You can add the nucleon numbers together, to give, and you can add the proton numbers together, to give . As you can see, both sides of the

equals sign are balanced.

Nuclear fissionThe splitting up of nucleus into two approximately equal fragments.

Nuclear fusionIt is when smaller nuclei combines to form larger stable nuclei.

IsotopesIsotopes have same number of protons but different number of neutrons.

A-level Physics/Forces, Fields and Energy/Radioactivity 32

A-level Physics/Forces, Fields andEnergy/RadioactivityWhen atoms are unstable, they will try to make themselves stable again. One way that they do this is by giving offmatter and energy known as radiation. A material with unstable atoms is said to be radioactive.

Types of radiationThere are 3 different types of ionising radiation, simply called α (alpha), β (beta) and γ (gamma), each with theirown properties.α-particles

An alpha particle is basically a helium nucleus. The table below shows its properties:

Nature: 2 protons & 2 neutrons (a helium nucleus)

Symbol: α,

Mass: 4 times the mass of a proton (~4u)

Charge: +2e

Speed: (~5% speed of light)

Penetration: Stopped by paper, skin or a few centimeters of air

Affected by electric and magnetic fields?: yes

β-particles

A beta particle is an electron. The table below shows its properties:

Nature: an electron

Symbol: β, e

Mass: 1/1840 the mass of a proton (~0.00055 u)

Charge: -e

Speed: (up to 98% the speed of light)

Penetration: Stopped by 3mm of aluminium or about 1m of air

Affected by electric and magnetic fields?: yes

γ-rays

A gamma ray is an electromagnetic wave with a wavelength of around . The table below shows itsproperties:

A-level Physics/Forces, Fields and Energy/Radioactivity 33

Nature: an electromagnetic wave of very short wavelength

Symbol: γ

Mass: 0

Charge: 0

Speed: (speed of light)

Penetration: Reduced greatly by several centimetres of lead. Rays are absorbed by several meters of concrete

Affected by electric and magnetic fields?: no

Ionisationα, β and γ radiation are all forms of ionising radiation and they affect the matter that they pass through. They cancause atoms to become ionised by colliding into, or passing closely to them. The atoms have their electrons pushedor pulled by the radiation and become ions, hence the name ionisation.α particles

α particles are the most strongly ionising because they have the greatest mass and charge, and have the lowestvelocity. This means that they affect the most amount of atoms and affect each atom stronger than the other types ofradiation.β particles

β particles are the second most strongly ionising because they are lighter, faster and have a smaller charge then αparticles.γ rays

γ rays are the least ionising of the 3, since they have no charge.

Penetration

Radiation can pass through different materials, though each typeof radiation has its own penetration power.α radiation

α radiation can be easily absorbed by a sheet of paper or by humanskin. This is because it is highly ionising and easily gives itskinetic energy to surrounding atoms and therefore cannot penetratefar into matter.β radiation

β radiation is less ionising, which makes it more penetrating thanα radiation. It needs a denser material such as aluminium tocompletely absorb it.γ radiation

γ radiation is the most pentrating and several metres of concrete ora few centimeters of lead are required to completely absorb it.Again, this is related to its strength of ionisation.

A-level Physics/Forces, Fields and Energy/Radioactivity 34

Nuclear equationsJust like other nuclear processes, radiation emissions can be represented by balanced nuclear equations. An alphaparticle has a symbol of He and a beta particle has a symbol of e. These can easily be used in equations whereradiation is emitted. Gamma photons do not have any effect on the equations since they have no mass and no charge.

Electric and magnetic fieldsBecause of their different charges and masses, each type of radiation behaves differently in electric and magneticfields. The behaviour of positive and negative particles moving in electric and magnetic fields have already beendiscussed earlier. Be especially careful using the left hand rule for β particles in a magnetic field because, as youmay recall, the current is in the opposite direction to the movement of an electron. Gamma rays are not affected byeither types of field and will continue in a straight line.

The hazards of ionising radiationRadiation is dangerous and steps must be taken to ensure that we are exposed to as little radiation as possible. Wewill have a look at these dangers and see how we can minimize the damage to ourselves and the environment.

Effects on living organismsSince radiation is ionising, it can alter the atoms that make up our own cells. There are two main ways that our cellscan become damaged by radiation:• Exposure to intense radiation can kill cells, causing tissue damage known as radiation burn. This same principle is

used to kill microbes from food or on medical equipment.• DNA can be altered by an ionisation, causing the cell to no longer function correctly. The radiation may affect the

DNA directly, or break up a water molecule which will then react with the DNA. The cell may divideuncontrollably, forming a tumour. Also, if the radiation affects an egg or sperm cell, there will be mutationspassed on to the next generation.

Alpha particles are the most dangerous to cells, but fortunately our skin is sufficient to prevent them from enteringour bodies .

Handling radioactive materials safelySince radiation is very hazardous, radioactive materials must be handled, stored and disposed of in a safe manner.To handle radioactive materials, they must not come into contact with the skin, and must be handled in a glove boxor with tongs. Care must be taken to not inhale radioactive gas.To store radioactive materials you can use lead-lined containers, since lead absorbs all of the different types ofradiation. This is also true for materials that emit α radiation, since most α emitting materials will also emit γradiation.Radioactive materials can be disposed of by diluting the radioactive substance with a large amount ofnon-radioactive material. They can also be disposed of by containment, which involves storing the radioactivematerial until it has dropped to a safe level of radioactivity.

A-level Physics/Forces, Fields and Energy/Radioactivity 35

Radioactive decayAs radioactive materials emit radiation, the number of stable nuclei increase, and the number of unstable nucleidecrease. The substance is said to decay because it decreases in mass as particles and energy is given off.

Spontaneous radiation emissionIf we were to observe a single nucleus of an unstable atom, we would eventually see it decay. We won't be able topredict how long it would take for it to decay, and there is no way to tell if it is about to decay or not. It will beundecayed at one moment, and an instant later, it would have decayed. It is a spontaneuous action. This is verystrange to the way things are on the macroscopic level that we are used to, where we can see gradual changes or thebuild up to an event.Also, each atoms nucleus decays independently of any neighbouring atoms, because if you recall the relativedistances and sizes of subatomic particles, there is an enormous amount of empty space between the nucleus and itsorbiting electrons, which means that one nucleus cannot affect another.Since we cannot predict when a nucleus will decay, we have to find an average over a period of time.

The decay constantThe decay constant is the probability that a particular nucleus will decay per unit time, and is denoted by the symbolλ. It can be found for a particular sample by measuring how many nuclei decay for a given length of time. So, if in asample with 10,000 nuclei, 1000 were to decay in an hour, the probability of one particular nucleus decaying withinan hour is 0.1, because only 10% of the nuclei decayed.

The decay constant has the units in the SI system, but , or even may be used. In the exampleabove, the decay constant, λ, is equal to 0.1 .

Activity and count rateThe activity of a radioactive substance is the number of nuclei that decay in a unit of time, or the rate of decay.Activity is measured in decays per second, and one decay per second is called one becquerel.If you know the decay constant of a particular substance, and the number of undecayed nuclei it has, you can find theactivity for that material using the formula:

where A is the activity, λ is the decay constant, and N is the number of undecayed nuclei.As you can see, this would take us back to how we originally found the decay constant, and so you can how the twoare related.When you are obtaining the activity of a sample with an experiment, you will hardly ever detect all of the radiationemitted. Some will be emitted where there are no detectors. The count rate, R, is the measurement from theexperiment, which will be less than the activity of the sample. A can be calculated from R if you know the efficiencyof the measuring device.

A-level Physics/Forces, Fields and Energy/Radioactivity 36

Exponential decayAs a radioactive substance decays, the number of undecayed nuclei will decrease. Since there are less radioactiveparticles in the substance, the rate of radioactive particles emitted will decrease. A graph of the amount of substanceagainst time will show an exponential curve, where the curve continually gets less steep as the rate of decaydecreases.

Calculating decayThe number of undecayed nuclei can be calculated with the following formula:

Where, is the number of undecayed at the start, is the decay constant, is the time in seconds, and , is theexponential function.Similarly, the count rate and activity can be found from the following equations:

Half-lifeThe half life of a substance is the mean length of time it takes for half of its radioactive material to decay. If youlook at the graph, you can see that the time on the horizontal axis for the number of undecayed nuclei to half is thesame as the time for it to decrease from 50% to 25%, and from 25% to 12.5%.

Half life is written as , and is usually measured in seconds, but for materials that are more stable, it is common tostate the half life in hours, days, or even years.If you consider that a substance with a short half life must decay quickly, and therefore must have a high decayconstant, and that a substance with a long half life will have a low decay constant, you can relate the two using theequation:

This is useful if you are only given either the half life or the decay constant and asked to find the other, as you canrearrange the equation to find the unknown value.

A-level Physics/Cosmology 37

A-level Physics/Cosmology

Contents• Models of the known universe• Stars and Galaxies• Structure of the universe• Information from stellar observation• How the universe may evolve• Relativity

A-level Physics/Cosmology/Models of the knownuniverseAs more sophisticated tools have been developed, our understanding of the universe has improved. Some proposedmodels of the universe were proven wrong, and other ideas are still with us today.

Measuring distances in the universeThe distances at the scale of the universe are gigantic, and our everyday metres and even kilometres are too small tobe used. We need to use units that are more appropriate for large distances. Often, other units are convenient to usebecause of the way they are measured.

The light-year

One light-year is defined as the distance light travels in one year. As you know, light travels at ,and so the distance it covers in one year is enormous. One light year is approximately m.

The astronomical unitThe astronomical unit is defined as the average distance between the Earth and the Sun. It originates from the factthat it was possible to measure the distances of the planets, but only in multiples of the distance between the Earthand Sun. It is still useful today for distances within the solar system. It is approximately equal to m.

A-level Physics/Cosmology/Models of the known universe 38

A simplified example of parallax.

The parsecOne parsec is simply the reciprocal of half the angle of parallax of a star, when observed from Earth at two oppositepoints of its orbit. Parallax is the apparent change in position of an object against a fixed background when theposition of the observer changes, like how buildings seem to move faster than background hills when you're in a car.It is convenient to find from the measured angle, and is therefore used mainly for the distances of stars. This conceptis covered in more detail in Stars & Galaxies. One parsec is approximately m, or 3.26 light-years.

Overview of the solar systemOur solar system consists of the Sun, the planets and an asteroid belt. Additionally, there are comets that have highlyelliptical orbits, and return to the solar system at regular intervals.

PlanetsThere are eight planets orbiting the Sun (Pluto being reclassified as a dwarf planet), which is at the centre of the solarsystem. Most planets also have natural satellites, or moons, orbiting them. The table below outlines the main featuresof the planets, relative to the Earth:

Planet Equatordiam.

Mass Orbitalradius (AU)

Orbitalperiod(years)

OrbitalIncline Angle (°)

OrbitalEccentricity

Day(days)

Moons

Mercury 0.382 0.06 0.387 0.241 7.00 0.206 58.6 none

Venus 0.949 0.82 0.72 0.615 3.39 0.0068 -243 none

Earth 1.00 1.00 1.00 1.00 0.00 0.0167 1.00 1

Mars 0.53 0.11 1.52 1.88 1.85 0.0934 1.03 2

Jupiter 11.2 318 5.20 11.86 1.31 0.0484 0.414 63

Saturn 9.41 95 9.54 29.46 2.48 0.0542 0.426 49

Uranus 3.98 14.6 19.22 84.01 0.77 0.0472 -0.718 27

Neptune 3.81 17.2 30.06 164.8 1.77 0.0086 0.671 13

Pluto 0.18 0.002 39.5 248.5 17.1 0.249 -6.4 3

A-level Physics/Cosmology/Models of the known universe 39

Asteroid beltThere is a concentration of small, rocky asteroids between Mars and Jupiter, which is known as the asteroid belt.There are hundreds of thousands of these planetoids orbiting the Sun, and are sometimes called minor planets.

CometsComets are lumps of rock, frozen water, methane and ammonia that orbit the Sun, and are typically only a fewkilometres in diameter. They have very eccentric (elliptical) orbits and therefore vary greatly in their distance fromthe Sun. When they are near the Sun, they have long tails of approximately 1AU, due to the Sun's radiation.

The progress in the understanding of the universeThe accepted model of the Solar System has been subject to great controversy over the decades. In the oldgeocentric model, the Earth was originally placed in the centre of the Solar System, and had the other planets andthe Sun orbiting it. Now, the accepted model places the Sun in the centre, with the Earth and other planets orbitingaround it.

Copernicus

The retrograde motion of Mars

Nicolaus Copernicus found the oldgeocentric model unnecessarilycomplicated. Instead of having the Earth inthe centre of the universe, he decided toplace the Sun in the centre, which we nowcall the heliocentric model. This modelcould very easily explain the movement ofthe planets and the Sun across the sky, andin particular the retrograde motion ofMars, where it would appear to move"backwards" across the sky for severalweeks. This retrograde motion of Mars waspreviously explained by epicycles where itwould "loop-the-loop" around at certainpoints. With Copernicus' new model, it wasexplained that since the Earth was closer tothe Sun than Mars, there will be sectionswhere the Earth will "overtake" Mars, and will make Mars apparently move backwards across the sky.

Opposition to Copernicus

Copernicus' heliocentric model was rejected by most people mainly because of religious beliefs at the time, andalthough it seemed to simplify the motion of the planets, it was less accurate than the geocentric model at fitting theobserved movements of the planets.People also argued that if the Earth was moving, the stars would have a detectable parallax. Copernicus claimed thatthe stars were too far away to detect any parallax, and with more sensitive equipment, he has now been provedcorrect. Another argument against the heliocentric model was that objects all fall towards the Earth, and so it must bethe centre of the universe. This was the intuitive conclusion before Newton revolutionised our ideas about motion.

A-level Physics/Cosmology/Models of the known universe 40

Kepler

An elliptical orbit with the Sun at one ofthe foci

Johannes Kepler improved upon Copernicus' original model by usingelliptical orbits instead of circular ones. He devised three laws of planetarymotion:

Kepler's first law

Kepler found that the planets fit the observed pattern better with theheliocentric model if they travelled in ellipses, not circles, and had the Sun atone of the foci of these ellipses. Therefore Kepler's first law states:

The planets orbit the sun in elliptical orbits with the sun at one focus.

Kepler's second law

Equal areas are covered in equal amountsof time

Now that the planets had elliptical orbits, it would not make sense for them totravel at the same speed at all points of their orbit. The planets would speedup nearer the Sun, and move slower when they were further away from theSun. Kepler observed that the imaginary triangle formed between the planet attwo points in its orbit and the Sun always had the same area provided the twopoints of the planets orbit had the same time difference between them. Fromthis it follows that a planets orbit is faster nearer the Sun than further awayfrom it. Kepler's second law states that:

The line connecting a planet to the sun sweeps out equal areas in equalamounts of time.

The semi-major axis of an ellipse

Kepler's third law

Kepler realised that the distance of a planet from the Sun and its orbital periodwere related by the formula: , where T is the time taken for one orbit,and d is the distance from the Sun, although it is actually the length of thesemi-major axis (which is half of the longest diameter of the elipse).

The square of the orbital period is proportional to the cube of the distance from the Sun.

A-level Physics/Cosmology/Models of the known universe 41

Galileo

The Phases of Venus.

Galileo Galilei was the first person to use a telescope tolook at the night sky. He was able to view many thingsthat weren't visible to the naked eye, such as theimperfectness of the surface of the moon, and the factthat there were many faint stars in the sky. Both ofthese supported Copernicus' ideas.

Galileo and Venus

When Galileo observed Venus with his telescope. henoticed that it went through phases, like the Moon. Healso noticed that when Venus was a crescent, it wasmuch larger than when it was full. This observationwas evidence that Venus was orbiting around the Sunand not Earth.

Galileo and Jupiter's Moons

Galileo also observed four objects orbiting Jupiter, which are now known as the Galilean moons They supported theview that not everything orbits the Earth.

Newton's universal law of gravitationWhen Issac Newton created his universal law of gravitation, he attempted to show that Kepler's observations ofplanetary motion agreed with it. This was significant evidence to show that he was correct.Newton's law of gravitation can be used to give a formula for the planets in the form :The force of gravitational attraction between the Sun and a planet is equal to the centripetal force required to keepthe planet in its orbit:

The period of the planets orbit can be given by:

Where the distance is the circumference of a circle, (note that d is distance from Sun, and is therefore theradius, not the diameter). This gives us:

Which we can re-arrange to make v the subject and substitute into in the centripetal force equation:

Eliminating m, the mass of the planet, and tidying up:

A-level Physics/Cosmology/Models of the known universe 42

And finally, making the subject:

We now have a formula in the form , with as the constant of proportionality, where m is the mass of

the Sun.

The discovery of Neptune

In 1821, Alexis Bouvard published very accurate observations in the orbit of Uranus. However, soon after this, theorbit of Uranus was observed to deviate from the published values. In 1845 John Adams, using Newton's universallaw of gravitation, calculated the orbit of another planet outside of Uranus whose gravity would account for theperturbations in Uranus' orbit. Neptune was discovered in its predicted position a year later. Pluto was discoveredin a similar way, since it was causing further perturbations in the orbits of Uranus and Neptune.

Problems encountered with Newton's theory

Although Newton's theory was very successful in explaining the motion of the planets, and had even been used todiscover unknown planets, there were still some problems with it:• The orbit of Mercury was observed to have a different orbit to the one predicted by the theory. This has now been

resolved by Einstein's general theory of relativity.• If every object in the universe attracts each other, then the entire universe should have collapsed because of the

gravitational attraction. To solve this, Newton came up with the idea that the universe was infinitely large, andthat matter was uniformly spread throughout. This led to its own problems, though, namely Olber's paradox,which states that an infinitely large universe will always have a star on any given line of sight, and so the nightsky should actually be bright. This has been resolved with the observations of an expanding universe by EdwinHubble.

A-level Physics/Cosmology/Stars and Galaxies 43

A-level Physics/Cosmology/Stars and GalaxiesThe universe consists of millions of stars, which are grouped together as galaxies.

NGC 4414, is a typical spiral galaxy.

Stars

Stars, like our Sun, are giant hydrogen fusionreactors, producing huge amounts of energy formillions of years.

The birth of a star

The Omega Nebula contains many young stars, which causes it toshine.

Stars begin their life in interstellar gas clouds, wherethe particles attract each other by gravitational forces.These gas clouds consist mainly of hydrogen andhelium, though more recent stars will contain heavierelements produced from older, and now dead, stars.

The gravitational attraction increases as the massbecomes heavier. A protostar is now formed, which isa local concentration of atoms that are large enough toform a star, and begins to increase in temperature, sincethe lost gravitational potential energy is converted tothermal kinetic energy.

Once the temperature reaches about , the coreis hot enough for hydrogen fusion to occur. The star,over time, stabilizes its temperature, where the rate ofenergy released at its surface matches the rate of energyproduced in its core, and stabilizes its size, where the outward pressure from the thermal reactions matches thegravitational attraction inwards.

The star is now a main sequence star, and will produce energy from hydrogen for many millions of years. Note thatsince more massive stars "burn" hydrogen at a much faster rate, they have much shorter life spans than less massivestars.

A-level Physics/Cosmology/Stars and Galaxies 44

Nuclear Fusion within starsStars consist mainly of hydrogen, which is used for the fusion reactions that produce almost all of their energy. Inthis process four hydrogen nuclei fuse to form a helium nucleus. However, this does not happen directly, andactually happens in stages:• Two protons fuse to form a deuterium nucleus, and releases a neutrino and a positron.

• The deuterium nucleus fuses with another proton, and produces a helium-3 nucleus.

• Two helium-3 nuclei fuse to produce the helium-4 nucleus. Two protons are released.

Energy released

The energy released can be calculated by .

Red giantsOnce most of the hydrogen in the star has run out, the star will be unable to maintain equilibrium. The core of heliumwill contract and hydrogen burning will continue in a shell surrounding the core. Since gravitational potential energyis lost when the core contracts, the thermal kinetic energy will increase. This increase causes the star itself to expand.The star is no longer a main sequence star, but is a red giant.

Helium burning within a red giantSince the temperature of the core of the red giant increases, "helium burning" will occur when the temperaturereaches about 100 million K. Like "hydrogen burning", "helium burning" happens in stages:• Two helium nuclei fuse to form a beryllium nucleus

• Another helium nucleus fuses with the beyllium nucleus to produce a carbon nucleus and a gamma photon.

• Yet another helium nucleus fuses with the carbon nucleus to form an oxygen nucleus and another gamma photon.

Further fusion reaction in red giantsMore massive red giants that are more than 3 times the mass of the Sun can reach higher temperatures and fusion ofheavier elements can occur:• At 600 million K, "carbon burning" occurs, producing neon and magnesium nuclei.• At 1 billion K, "neon burning" occurs, producing oxygen and magnesium nuclei.• At 1.5 billion K, "oxygen burning" occurs, producing silicon nuclei.• At 3 billion K, "silicon burning" occurs, with the production of iron nuclei.After iron, nuclear fusion does not produce any energy, so the thermonuclear reactions cease.

A-level Physics/Cosmology/Stars and Galaxies 45

The death of a starOnce the temperature in the core is too low for the next thermonuclear reaction to begin, the star will becomeunstable. What happens next in the life cycle of a star depends on the Chandrasekhar limit, which is equal to 1.4times the solar mass.

Stars with masses less than the Chandrasekhar limit

NGC 6543, also known as the Cat's Eye Nebula

When the star is unstable, it will shed the outer layers of gas,which results in a planetary nebula (only called that becausethey were once thought to resemble planets). The core itselfwill shrink and become more dense, and reach a density sogreat, that one teaspoonful will have a mass of many tonnes.The core will stop shrinking once the fermi pressure ofelectrons that are packed very closely prevents any furthercollapse. The dense, but dim, star is now a white dwarf.There is no further energy in the core, and the white dwarfwill gradually radiate it all away and cool down.

Stars with masses greater than the Chandrasekhar limit

The Crab Nebula is the remains of a supernova explosion.

For stars that are greater than 1.4 solar masses, theFermi pressure of electrons is too weak to prevent thegravitational collapse. In the space of a few seconds,the electrons are crushed against the protons to formneutrons, and the core now has a very immensepressure, and therefore, a very high temperature.Elements heavier than iron are produced during thiscollapse. When the collapse of the core suddenly halts,it causes an explosion due to the immense outwardpressure. This explosion is called a supernova. Theremaining cloud of dust may eventually form a groupof new stars.

Neutron stars

The core within the supernova remains, and iscomposed entirely of neutrons, since electrons havebeen forced into the nucleus. Their density is so great,

that the Earth at the same density would be only a few hundred meters in diameter. This leftover core is called aneutron star, because of the fact it is made of nothing other than neutrons.

A-level Physics/Cosmology/Stars and Galaxies 46

PulsarsMost stars have their own angular velocity, or rate of spin. When a star decreases in size rapidly, it will spin faster,because angular momentum is conserved. This is similar to the way an ice-skater can spin faster if she holds herarms closer to her body. Often, this is what happens when the core of a supernova shrinks to form a neutron star. Therate of rotation increases massively, and this results in a pulsar. We call it this because on Earth we detect them asregular radio pulses, with periods sometimes in the millisecond range. The regularity and short periods of thesepulses led scientists to believe that aliens were trying to communicate with us, although the pulses are now known tocome from the magnetic field of a spinning neutron star.Like all stars, pulsars have their own magnetic field. As the rate of rotation of a star increases, the magnetic fieldstrength around it also increases. The moving magnetic field creates an intense electric field. This intense electricfield accelerates electrons and creates an intense beam of radiation at both magnetic poles. Because magnetic northand the axis of rotation aren't perfectly lined up, just like on Earth, it's possible for the beam of radiation to passthrough the Earth and reach us, producing the observed pulses of radiation.

Black holes

A black hole cannot be directly observed, instead, we must look forits effects, such as the bending of light from a distant galaxy shown

in this simulated image.

If a neutron star is greater than approximately 3 solarmasses, it will collapse further to an infinitely smallpoint, called a singularity, and will become infinitelydense. The gravitational field strength at a fewkilometres from the singularity is so intense that evenlight cannot escape, and the star is now a black hole(light is affected by gravity despite the fact that photonshave no mass, this is explained by Einstein's generaltheory of relativity). Since nothing can travel fasterthan the speed of light (also explained by relativity),anything that falls into a black hole is lost forever.

Quasars

A quasar is a source of radiation which is veryluminous, brighter than many galaxies. They vary inbrightness with periods of a few days or months andbecause an object cannot change luminosity faster than the time it takes light to travel from one end to the other, theyare thought to be relatively small objects, only a few light-days or light-months in diameter. Quasars have beencalculated from their red shift to be very distant, as far away as 18 billion light-years, and the only explanation forthem is that they are radiation emitted by matter as it falls into a black hole, as the gravitational potential energy ofthe matter is lost.

A-level Physics/Cosmology/Stars and Galaxies 47

Measuring the distance to starsTo measure the distance of stars from Earth, several methods have been devised.

ParallaxWe can measure the angle of parallax a star makes as it appears to move across the background of distant stars whenthe Earth moves from two extreme points in its orbit. We assume that the distant stars are stationary. The diagramshows what is meant by the parallax of a star:

From this angle, we can find the distance in parsecs by:

.

Therefore, the smaller the angle of parallax, the further away the star is from Earth, and when a star has a parallax of1 arc second ( of a degree) we say that it is one parsec away. One parsec is approximately equal to

m, or 3.26 light-years.

A-level Physics/Cosmology/Stars and Galaxies 48

Intensity of lightOnce, it was thought that all stars were exactly the same brightness, but some appeared dimmer than others becausethey were further away. We now know that stars can individually vary in brightness, but the magnitude system is stillused.

Apparent magnitude

The visible stars were separated into 6 classes depending on their perceived brightness. The brightest stars wereclassed as magnitude 1, and the dimmest stars visible with the naked eye were classed magnitude 6. It was thenfound that a difference in magnitude actually represented a ratio of 2.5 in intensity, since the human eye works on alogarithmic scale. That means that a magnitude 1 star was times more intense than a magnitude 6 star.The ratio of intensities of two stars can be found from their apparent magnitude by:

Today, with telescopes, we can measure stars with apparent magnitudes ranging from approximately +25 to -25,where smaller is brighter. We calculate it from the measured value of intensity, using the formula:

where m is the apparent magnitude and I is the intensity.

Absolute magnitude

The apparent magnitude of a star gives us no information of its true intensity, only the intensity of light that reachesus. That means a very distant star could be more intense than a nearer one, but it would appear dimmer from Earth.The absolute magnitude of a star is the apparent magnitude it would have if it was at a distance of 10 parsecs. Theabsolute magnitude is given by the equation:

Where d is the distance of the star in parsecs.

The Milky Way

The Milky Way is a spiral galaxy. The Sun is on the end of one ofthe arms.

The galaxy we are in is called the Milky Way. It is aspiral galaxy and is thin, but lens like, in thickness. Ithas a radius of 30 000 light-years, and is about 2000light-years thick.

A-level Physics/Cosmology/Structure of the universe 49

A-level Physics/Cosmology/Structure of theuniverse

Olbers' ParadoxHeinrich Olbers showed that in an infinite and uniform universe the sky at night would be exceedingly bright,whereas we know perfectly well that this is not the case. This contradiction, that the universe must be infiniteotherwise it would collapse under its own gravitational forces, yet cannot be infinite otherwise the sky would bebright at night - is now known widely as Olbers' Paradox.To be included in this section:• Cosmological Principle• Hubble's Law (and why it can't be used accurately at the moment to estimate the age of the Universe)• Significance of the 3 K microwave radiation that we can detectfrom A level OCR Physics A specification

A-level Physics/Cosmology/Information fromstellar observation

Understand that stars and galaxies are detected by the electromagneticradiation which they emit, whilst planets are detected by reflected sunlightStars, galaxies and planets are all visible to us here on Earth, but the reasons for our ability to see these stellar bodiesdiffer:• Stars and Galaxies - these themselves emit electromagnetic radiation, and can therefore be detected using this

source• Planets - these are not themselves sources of electromagnetic radiation, and are therefore only detectable via the

sunlight which they reflect

Sketch and interpret a graph to illustrate the variation with wavelength of thetransparency of the Earth's atmosphere for the electromagnetic spectrum.The ability of the different types of electromagnetic radiation to penetrate the Earth's atmosphere and therefore bedetected on Earth varies within the spectrum. It can be broken down into three absorption categories: opaque(undetectable on the Earth's surface), partial absorption (some radiation makes it through, some doesn't), andtransparent (radiation easily passes through the Earth's atmosphere).• Opaque - includes: X-rays, Ultraviolet, and Long Wave Radio• Partial Apsorption - includes: Gamma, Infrared, Radar Radio• Transparent - includes: Visible, UHF Radio, Short Wave RadioFollow this link [1] for an example of this graph.

A-level Physics/Cosmology/Information from stellar observation 50

Explain how the composition of stellar atmospheres may be obtained fromstellar spectraWe can find out which chemical elements stars are made of from the radiation we don't receive from them. Toexplain this we need to consider the atoms of the emitting substance. an atoms comprises a very small, massivenucleus surrounded by a much larger volume which is sparsely occupied by electrons. When an atom absorbsenergy, one or more of these electrons may become 'excited', i.e., jump to a higher energy level. if an excitedelectron then returns to its original energy level, energy is released as radiation. The wavelength of the radiationemitted by a particular electrons depends on precisely the amount of energy it releases as it returns to its unexcitedstate. the larger the amount of energy released by an electron, the higher the frequency - and the shorter thewavelength - of the radiation it emitsStellar spectra include: continuous spectra, emissions spectra, and absorption spectra.• Continuous Spectra - radiation of all frequencies within a certain range. When atoms are very close together, as in

a solid or the dense matter of a star, there are so many different interacting forces that the electrons in atoms makejumps of all sizes within a certain range.

• Emissions spectra - a set of individual lines from which individual elements can be identified by their particularlines. When atoms are well separated, as in a gas, each type of atom emits its own distinctive wavelengths ofradiation, which can be separated using a diffraction grating.

• Absorption spectra - the spectrum produced by the radiation from a star, or more specifically, the radiation fromthe atoms in the atmosphere of a star. It is a continuous spectrum with dark lines missing - Fraunhofer lines.These lines are representative of the elements present in the atmosphere of the star. Of the radiation emitted fromthe stars surface, some is absorbed and re-emitted in all direction by atoms in the atmosphere, meaning much lessof this wavelength radiation is travelling in the original direction of travel, and therefore much less is reaching us,producing a dark line, a negative version of the characteristic emission spectrum of the atmospheric element.

These chemical elements can be identified by comparing the dark lines in the aborption spectra with the emissionspectra of the individual elements present in the stars atmosphere.

Understand what is meant by the Doppler EffectDoppler Effect - the change in wavelength of a source due to the relative motion between the source and an observer.

Recall and use Δλ / λ = v / cA source of wavelength λ emitted at speed c takes λ/c seconds to emit one complete wave. If the source is movingaway from the observer at v ms-1, the wavelength observed will have increased by Δλ, therefore:

Δλ / λ = v / c

Understand what is meant by red-shift and by blue-shift and appreciatesimple differences between red-shift and terrestrial Doppler EffectsRed-Shift - the observed increase in wavelength (reduction in frequency) caused by an emitter of radiation and adetector moving away from each otherBlue-Shift - the observed decrease in wavelength (increase in frequency) caused by an emitter of radiation and adetector moving towards each otherTerrestrial Doppler Effects on light are so small that they are barely noticeable, and so are only observed for soundand water waves (for example, the sound of a motorbike). The speeds of recession for planetary Red-Shift are a greatenough proportion of the speed of light, c, to produce noticeable effects on light waves.

A-level Physics/Cosmology/Information from stellar observation 51

"Red-Shift is the Doppler Effect for light."

References[1] http:/ / en. wikivisual. com/ images/ 8/ 83/ Atmospheric_electromagnetic_transmittance_or_opacity. jpg

A-level Physics/Cosmology/How the universe mayevolveThe question of whether the Universe is infinite or not depends crucially on the value of the quantity know as Ω.Such a value, although not determined yet, depends basically on the rate of expansion, or the Hubble Constant, of theUniverse.In simple terms, the quantity Ω is the ratio of the density of the universe (mass per unit volume) to the critical valuewhich determines expansion or collapse. There are three possible outcomes from this value -• Steady State: the Universe will continue to expand up to a point, whereupon the Universe will stay in a constant

state. This would occur if Ω = 1.• Continuous Expansion: The Universe will continue to expand. This will occur if Ω<1. The result of continuous

expansion would be, according to the 1st Law of Thermodynamics, a Universe which would gradually cool downuntil the temperature became 0 Kelvin.

• Regression: The Universe will grow, and then collapse on itself. This will occur if Ω>1. It has been postulatedthat if the Universe were to carry on this course, all matter would recondense into a singularity, and recreateanother big bang.

A-level Physics/Cosmology/Relativity

Time DilationA thought experiment:Imagine two glass train carriages on parallel railway tracks, each with a mirror along their full length facing the othertrain. Each train has an observer on it. The trains are travelling in opposite directions at close to the speed of light.One observer sends a pulse of light at right angles to their direction of travel, towards the other train. This pulse oflight is reflected between the two mirrors over and over again.The first part of the diagram represents what the observer who sent the light sees - the light bouncing backwards andforwards in a straight line. The other observer, however, sees the light moving in a "zig-zag" pattern. This is becausehe is moving away from the light as it is being sent, so after each successive reflection the light has further to travel.Another experiment for time dilation has been carried out with muons, extremely low mass particles which decayvery quickly and virtually disappear. When these particles are accelerated (by particle accelerators), their lifetimesare significantly increased, suggesting that time has been slowed down.

Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories underwhich a clock at a different gravitational potential is found to tick at a different rate than one's own clock.Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity inaccelerated frames of reference. In general relativity, it is considered to be difference in the passage of proper time atdifferent positions as described by a metric tensor of spacetime. The existence of gravitational time dilation was firstconfirmed directly by the Pound-Rebka experiment.

A-level Physics/Cosmology/Relativity 52

DefinitionBackground knowledge the reader may need to learn: What is a gravitational field? What is time dilation? What isspacetime? The reader may also research gravitational redshift or ordinary redshift.Gravitational time dilation can be manifested by the presence of large mass, and the larger the mass, the greater thetime dilation. In more simple terms, it is meant that observers far from massive bodies are distant observers with fastclocks, and observers close to massive bodies are time-dilated observers with slow clocks.It can also be manifested by any other kind of accelerated reference frame such as a dragster or space shuttle.Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitation time dilation as an effect oftheir angular spin.This is supported by General Relativity due to the equivalence principle that states all accelerated reference framespossess a gravitational field. According to General Relativity, inertial mass and gravitational mass are the same. Notall gravitational fields are "curved" or "spherical", some are flat as in the case of an accelerating dragster or spaceshuttle. Any kind of g-load contributes to gravitational time dilation.

• In an accelerated box, the equation with respect to an arbitrary base observer is , where• is the total time dilation at a distant position,• is the acceleration of the box as measured by the base observer, and• is the "vertical" distance between the observers.

• On a rotating disk when the base observer is located at the center of the disk and co-rotating with it (which makestheir view of spacetime non-inertial), the equation is , where

• is the distance from the center of the disk (which is the location of the base observer), and• is the angular velocity of the disk.

(It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation).

A common equation used to determine gravitational time dilation is using the Schwarzschild solution, whichdescribes spacetime in the vicinity of a non-rotating massive object. The Schwarzschild solution for time dilation fora spherically-symmetric object is:

, where

• is the proper time between events A and B for a slow-ticking observer within the gravitational field,• is the proper time between events A and B for a fast-ticking observer distant from the massive object (and

therefore outside of the gravitational field),• is the gravitational constant,• is the mass of the object creating the gravitational field,• is the radial coordinate of the observer (which is analogous to the classical distance from the center of the

object, but is actually a Schwarzschild coordinate), and• is the speed of light.

is the called the Schwarzschild Radius of M. If a mass collapses so that its surface lies at less than thisradial coordinate (or in other words covers an area of less than ), then the object exists within ablack hole.

A-level Physics/Cosmology/Relativity 53

ConsequencesIf a satellite drifting in deep space is sending out laser light at n cycles per second, and an Earth-based observer seesthis signal to be blueshifted, with a higher frequency of n+1 cycles per second, then the only apparent way for thissituation to be sustainable (with signals being registered faster on the receiving equipment than they are being sentby the transmitting equipment, indefinitely) is if the two sets of equipment are operating differently due to theirdifferent gravitational environments.

Important things to stress• According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated

reference frame.• The speed of light in a locale is always equal to c according to the observer who is there. The stationary observer's

perspective corresponds to the local proper time. Every infinitesimal region of space time may have its ownproper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and mattermay be equally affected, since they are made of the same essence (as shown in many tests involving the famousequation ). Such regions are significant whether or not they are occupied by an observer. A time delayis measured for signals that bend near the sun, headed towards Venus, and bounce back to earth along more orless a similar path. There is no violation of the speed of light in this sense, as long as an observer is forced toobserve only the photons which intercept the observing faculties and not the ones that go passing by in the depthsof more (or even less) gravitational time dilation.

If a distant observer is able to track the light in a remote, distant locale which intercepts a time dilatedobserver nearer to a more massive body, (putting aside the fact that a photon cannot be observed withoutinterception with the observer) he sees that both the distant light and that distant time dilated observerhave a slower proper time clock than other light which is coming nearby him, which intercept him, at c,like all other light he really can observe. When the other, distant light intercepts the distant observer, itwill come at c from the distant observer's perspective.

Experimental confirmationGravitational time dilation has been experimentally measured using atomic clocks on aeroplanes. The clocks thattravelled aboard the aeroplanes upon return were slightly fast with respect to clocks on the ground. The effect issignificant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificialsatellites, providing a further experimental confirmation of the effect.Gravitational time dilation has also been confirmed by the Pound-Rebka experiment and by observations of thespectra of the white dwarf Sirius B.

References• Einstein, Albert. "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg.

<http://www.gutenberg.org/etext/5001.>• Einstein, Albert. "The effect of gravity on light" (1911), translated and reprinted in The Principle of Relativity• Nave, C.R. "Gravity and the Photon." Hyperphysics.

<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/blahol.html#c2.>• The Pound-Rebka-Snider Experiments [1]

A-level Physics/Cosmology/Relativity 54

References[1] http:/ / www. wbabin. net/ sfarti/ sfarti11. pdf

A-level Physics/Health Physics

Contents• Body Mechanics• The Eye and Sight• The Ear and Hearing• Medical Imaging• Medical Treatment

A-level Physics/Health Physics/Body MechanicsHealth physics is a constantly expanding new part of the A levels.

A-level Physics/Health Physics/Medical ImagingMedical imaging includes MRI CT and X-ray scanning. It is useful to see the internal structure of the human body.

A-level Physics/Nuclear and Particle Physics

Contents• The Nucleus• Neutrons And Fission• Fusion• Matter and Anitmatter• Fundametal Particles

A-level Physics/Nuclear and Particle Physics/The Nucleus 55

A-level Physics/Nuclear and Particle Physics/TheNucleus

NucleonsProtons and neutrons are the constituents of atomic nuclei. A proton is a positively charged particle which has thesame charge as an electron, but positive. A neutron, on the other hand, is a neutral particle with zero charge. Protonshave a mass of 1.6552e-27 kg and a charge of +1.66e-19 Coulombs, while neutrons have a mass of 1.6725e-27 kg.Protons and neutrons collectively are called NUCLEONS. The number of protons in the nucleus give the atomicnumber, while the sum of the total mass of protons and neutrons gives 99.9% of the mass of the atom, the rest is dueto electrons. On the periodic table, you can see the number of nucleon written as the mass number.

What force holds the atomic nuclei together?For many years people had wondered what held an atom in place and why it doesn't just split apart due to repulsiveelectric forces. At first they thought that it was gravity which held the atoms, protons and neutrons in place. This wasdisproved after they found out gravity was very very weak at nuclear levels. In fact it's a million million millionmillion million million times too small. (10^36)We now know the interaction responsible for binding quarks, anti-quarks, and gluons to make hadrons is calledstrong nuclear force (SNF) or The Strong Interaction. Residual strong force interactions provide the nuclear bindingforce. Simply put, strong force is the force that holds atomic nuclei together against the Coulomb (electrostaticrepulsion) force of repulsion between protons. The strong force acts on any pair of hadrons. It has an extremely shortrange of only a few femtometers. Even so, at a very short range indeed, the SNF becomes repulsive, otherwise theneutrons and protons would be attracted together to the point where they would become a singularity.

The radii of atomic nucleiThe following gives the formula to work out the radii of atomic nuclei.

Where:• r is the radii• A is the number of nucleons• r0 is a constant having value 1.2 fermi to 1.5fermi.

Density of nuclear matter

(since is the volume of nucleus which is considered as sphere of radius r).NUCLEAR

DENSITY is constant throughout the nuclear dimensions.

Calculating electrostatic force

Where:• F is the force

A-level Physics/Nuclear and Particle Physics/The Nucleus 56

• is the permittivity of free space with the value 8.8541878176e-12 F/m c(farad per metre per coulomb)above expression is known as a coulomb law of electrostatics.

Calculating gravitional force

Where:• F is the force• m1 and m2 are product of the two masses;• and r being the distance between them.• G is the value of the gravitational constant, which is

A-level Physics/The SI System of UnitsSI units are used throughout science in many countries of the world. There are seven base units, from which allother units are derived.

Base unitsEvery other unit is either a combination of two or more base units, or a reciprocal of a base unit. With the exceptionof the kilogram, all of the base units are defined as measurable natural phenomena. Also, notice that the kilogram isthe only base unit with a prefix. This is because the gram is too small for most practical applications.

Quantity Name Symbol

Length metre m

Mass kilogram kg

Time second s

Electric Current ampere A

Thermodynamic Temperature kelvin K

Amount of Substance mole mol

Luminous Intensity candela cd

Derived unitsMost of the derived units are the base units divided or multiplied together. Some of them have special names. Youcan see how each unit relates to any other unit, and knowing the base units for a particular derived unit is usefulwhen checking if your working is correct.

Note that "m/s", "m s-1", "m·s-1" and are all equivalent. The negative exponent form is generally preferred, for

example "kg·m-1·s-2" is easier to read than "kg/m/s2".

A-level Physics/The SI System of Units 57

Quantity Name Symbol In terms of other derivedunits

In terms of base units

Area square metre

Volume cubic metre

Speed/Velocity metre per second

Acceleration metre per secondsquared

Density kilogram per cubicmetre

Specific Volume cubic metre perkilogram

Current Density ampere per squaremetre

Magnetic Field Strength ampere per metre

Concentration mole per cubic metre

Frequency hertz Hz

Force newton N

Pressure/Stress pascal Pa

Energy/Work/Quantity of Heat joule J N m

Power/Radiant Flux watt W

Electric Charge/Quantity of Electricity coulomb C s A

Electric Potential/Potential Difference/ElectromotiveForce

volt V

Capacitance Farad F

Electric Resistance Ohm

Electric Conductance siemens S

Magnetic Flux weber Wb V s

Magnetic Flux Density Tesla T

Inductance henry H

Celsius Temperature degree Celsius °C K - 273.15

Luminous Flux lumen lm cd sr

Illuminance lux lx

Activity of a Radionuclide bequerel Bq

A-level Physics/The SI System of Units 58

PrefixesThe SI units can have prefixes to make larger or smaller numbers more manageable. For example, visible light has awavelength of roughly 0.0000005 m, but it is more commonly written as 500 nm. If you must specify a quantity likethis in metres, you should write it in standard form. As given by the table below, 1nm = 1*10-9m. In standard form,the first number must be between 1 and 10. So to put 500nm in standard form, you would divide the 500 by 100 toget 5, then multiply the factor by 100 (so that it's still the same number), getting 5*10-7m. The power of 10 in thisanswer, i.e.,. -7, is called the exponent, or the order of magnitude of the quantity.

Prefix Symbol Factor Common Term

peta P quadrillions

tera T trillions

giga G billions

mega M millions

kilo k thousands

hecto h hundreds

deca da tens

deci d tenths

centi c hundredths

milli m thousandths

micro µ millionths

nano n billionths

pico p trillionths

femto f quadrillionths

Homogenous equationsEquations must always have the same units on both sides, and if they don't, you have probably made a mistake. Onceyou have your answer, you can check that the units are correct by doing the equation again with only the units.

Example 1For example, to find the velocity of a cyclist who moved 100 metres in 20 seconds, you have to use the formula

, so your answer would be 5 .

This question has the units , and should give an answer in . Here, the equation was correct, andmakes sense.Often, however, it isn't that simple. If a car of mass 500kg had an acceleration of 0.2 , you could calculatefrom that the force provided by the engines is 100N. At first glance it would seem the equation is nothomogeneous, since the equation uses the units , which should give an answer in . Ifyou look at the derived units table above, you can see that a newton is in fact equal to , and thereforethe equation is correct.

A-level Physics/The SI System of Units 59

Example 2Using the same example as above, imagine that we are only given the mass of the car and the force exerted by theengines, and have been asked to find the acceleration of the car. Using again, we need to rearrange it for

, and we now have the formula: . By inserting the numbers, we get the answer . You

already know that this is wrong from the example above, but by looking at the units, we can see why this is the case:

. The units are , when we were looking for . The problem is the fact that

was rearranged incorrectly. The correct formula was , and using it will give the correct answer

of 0.2 . The units for the correct formula are .

A-level Physics/Equation SheetEquations, constants, and other useful data that the A-level student of physics is required to memorise.

Forces and Motion

Newtonian MechanicsKinematic Equations

•

•

••

•

•

Force and Momentum

••

•

•

Work and Energy

• (for small heights only)

• (for any height)

•

•

•

A-level Physics/Equation Sheet 60

Where:• = initial velocity• v = final velocity• a = acceleration• s = displacement• t = time• W = work done• m = mass• M = different mass, for equations with 2 masses interacting• P = Power

A-level Physics/Glossary of TermsDefinitions of keywords and terms that you will need to know.

AAbsolute zero

Zero on the thermodynamic temperature scale, or 0 K (kelvin), where a substance has minimum internalenergy, and is the coldest possible temperature. It is equal to -273.15 degrees Celsius.

Absorption spectrumA spectrum of dark lines across the pattern of spectral colours produced when light passes through a gas andthe gas absorbs certain frequencies depending on the elements in the gas.

AccelerationThe (instantaneous) rate of change of velocity in respects to time.

Acceleration of free fall (g)The acceleration of a body falling under gravity (9.81ms-2 on earth).

AmmeterA device used to measure the electric current in a circuit. It is connected in series with the components.

Amount of substanceA SI quantity, measured in moles (mol).

AmpereThe SI unit for electric current.

AmplitudeThe maximum displacement of a wave from its rest/mean position (measured in metres).

AntinodeA point of maximum amplitude along a stationary wave caused by constructive interference.

A-level Physics/Glossary of Terms 61

CCouple

Two equal, opposite and parallel forces which create rotational force.

DDisplacement

A vector quantity, the distance something is from its initial position, in a given directionDensity

Density is the mass of a body per unit volume

EEnergy

The stored ability to do workExtension (x)

The change in length of an object when a force is applied to it

FForce

A force causes a mass to change motion

GGravitational Potential Energy

the energy an object has due to its relative position above the ground. Found by mass x gravity (orgravitational field strength) x height

HHeat

is a form of energy transfer, also known as 'Thermal Energy'.Hookes Law

an approximation that states that the extension of a spring is in direct proportion with the load added to it aslong as this load does not exceed the elastic limit.

A-level Physics/Glossary of Terms 62

JJoule

The SI unit of work done, or energy. One joule is the work done when a force of one newton moves an objectone metre.

KKinetic Energy

The energy an object possesses due to its motion, given by KE = 0.5 x mass x velocity²

NNewton

Unit in which force is measured. Symbol "N". One Newton is the force required to give a mass of 1kg anacceleration of 1ms^-2

PPeriod (T)

The time taken for one complete oscillation. Denoted by 'T'. T=1/fPower

The rate at which work is done.Pressure

The load applied to an object per unit surface area.Potential difference

The work done in moving a unit positive charge from one point to the other. The unit is volt.

RResistivity

Proportional to lengthRadian

A radian is the angle subtended at the centre of the circle when the arc length is equal in length to the radius.

SScalar

A quantity with magnitude but no direction.Speed

A scalar quantity, speed = distance / timeNB s can also mean displacement.Stopping Distance

Stopping distance = Thinking distance + Braking distancethinking distance (distance traveled while reacting) = time taken to react X velocitybraking distance (distance traveled while braking)

A-level Physics/Glossary of Terms 63

TTemperature

A SI quantity, measured in kelvin (K).Tensile forceThe forces being applied onto a material (usually a wire) on two opposite sides in order to stretch it. Both forces'values are the same as the tensile force value.Tensile stress

The tensile force per unit cross-sectional area.Terminal Velocity

maximum velocity a body can travel. When resistive forces = driving force, acceleration = 0, so it cannottravel any faster.

ThermistorAn electrical component that changes its resistance depending on its temperature.

Thinking distanceThe distance travelled from seeing the need to stop to applying the brakes.

Threshold frequencyThe lowest frequency of electromagnetic radiation that will result in the emission of photoelectrons from aspecified metal surface.

ThrustA type of force due to an engine (usually forward force).

Time interval (t)A SI quantity, measured in seconds (s).

Torque / momentMoment = force x perpendicular distance from the pivot to the line of action of the forceTorque = one of the forces x the distance between them

Trasverse WaveA progressive wave that trasfers energy as a result of oscillations/vibrations.

Triangle of forcesIf three forces are acting at a point that can be represented by the sides of a triange, the forces are inequilibrium.

Turning forcesMore than one forces that if unbalanced will cause a rotation.

A-level Physics/Glossary of Terms 64

UUltimate tensile strength

The maximum tensile force that can be applied to an object before it breaks.Ultimate tensile stress

The maximum stress that can be applied to an object before it breaks.Ultraviolet

A form of electromagnetic wave (wavelengths 10-9-3.7x10-7m). It may cause sun tanning. Usually classifiedinto three categeries:UV-A, UV-B and UV-C.

UpthrustA force experienced due to the pressure difference of the fluid at the top and bottom of the immersed portionof the body.

VVector

A quantity with magnitude and direction.Velocity

The (instantaneous) rate of change of displacement with respect to time. Velocity is a vector.Velocity-time graph

A motion graph which shows velocity against time for a given body.Volt (V)

The unit of potential difference (p.d.) or electromotive force (e.m.f.)potential difference=energy/chargeVoltmeter

A device used to measure the potential difference across a component. It is connected in parallel across acomponent.

Volume(V)A physical quantity representing how much 3D space an object occupies, measured in cubic metres(m3)

WWatt(W)

The unit of power.power=energy x time

WaveSeries of vibrations that transfer energy from one place to another.

Wavelength(λ)The smallest distance between one point of a wave and the identical point of the next wave, measured inmetres (m).

Wave-particle dualityThe theory which states that all objects can exhibit both wave and particle properties.

Weight

A-level Physics/Glossary of Terms 65

The gravitational force acting on a body, measured in newtons (N).weight=mass x gravitational forceWork Done

The energy transferred when an object is moved through a distance by a force. Can be calculated bymultiplying the force involved by the distance moved in the direction of the force.

Alternatively, [work done = transfer of energy]. i.e., work is done when energy is transferred from one form toanother.Work function energy (Φ)

The minimum energy that is required for a material to release an electron, measured in joules(J).

XX rays

A form of electromagnetic wave (wavelengths:10-12-10-7m). It is used in X-ray photography.

YYoung's double slit experiment

An experiment to demonstrate the wave nature of light via superposition and interference.Young Modulus

Stress per unit Strain, units: Pascals or N/m2

AQA A-Level Physics

AQA A-Level PhysicsThis book is designed to help students who are studying the AQA Specification A syllabus to understand the topicscovered, as well as explaining the way in which questions are asked in exams and how they differ from otherexamining bodies. Don't worry about the hard-sounding names of things; the concepts in this module are really, veryeasy.

Particles, Radiation and Quantum Phenomena

Particles and antiparticles• /Atomic structure/ • /Particles and Anti-particles/

• Constituents of the particle• Forces• Particle-Antiparticle interactions• Creation and annihilation• Conserving and illustrating interactions

• /Quarks and sub-atomic particles/

AQA A-Level Physics 66

Waves and Particles• The photon • Waves and particles • Mass and energy

Electromagnetic Phenomena• Reflection, refraction and optics • The photoelectric effect

Formulas & Resources• /List of formulas/ • /Past paper questions/

AQA A-Level Physics/Atomic structureThe atom as we know it, was not originally known as it is today. As you may know fromGCSE physics, the way in which an atom is structured consists of a nucleus and electrons.This isn't far from the truth, but there are some differences in the way in which the atom islaid out. To better understand this, we need to look at how the modern structure of the atomwas discovered.

10.1.1 Constituents of the atom -- "What is the atom made of"

Rutherford Scattering

The original model of the atom -- the"plum pudding"

Originally the atom was thought of as a tiny pieceof solid matter. People "knew" that the atom wasthe smallest thing you could have, the word atomcomes from a Greek word meaning indivisible.So if the atom was the smallest thing it seemedperfectly sensible to imagine it as a sort of solidjelly. Rutherford had a different idea, and to test it hehad to make a very thin solid layer. He used gold,because it is easier to roll or hammer out a thinsolid layer of gold than any other material. Hewanted a thin layer because he wondered if theatoms really were solid. To test his idea he fired alpha particles (usuallywritten as -particles) at the foil. These particlesconsist of 2 protons and 2 neutrons, that is they

are helium nuclei. They were quite easy to use because a common type of radio-active decay

AQA A-Level Physics/Atomic structure 67

The original model of the atom at thetop, and the Rutherford one.

emits -particles. When this experiment was firstperformed, by Rutherford's assistants, Geiger andMarsden, in 1909 they found a rather interestingresult. Most of the particle went straight throughthe foil. However, a few of them bounced off.This behaviour could not be explained if theatoms are really a jelly-like solid.If we think about this result and consider it at thelarge scale we can get an idea of what ishappening. Imagine we have a wire fence, andlet's imagine that it is perfectly strong, and we fireballs at it. Let this fence be the nice open net thatwe often get with holes about 75mm square. If wefire a football we are not surprised if it justbounces straight off. The football is much biggerthan the holes in the fence and so the fenceappears to be solid. If we hit golf balls at thefence we'd not be surprised if most went straightthrough it, and the ones that hit right onto a wirebounced back. If we fired slugs from an air pistolwe'd expect even more to go straight through. This sort of thinking gave Rutherford the idea ofthe atom. 1. He suggested that because most of the -particles went straight through the atom must

contain a majority of empty space.2. Some alpha particles scattered off so these must have been repelled by something.3. That something must have a positive charge to repel the positive charge of the -particle

and must be heavier than the -particle to make it bounce the way that it did.This gave Rutherford the idea that the atom was mostly empty space, with a heavy, positivelycharged nucleus with the relatively light, negatively-charged electrons orbiting around it likeplanets around a star. (Of course, in those days the only star that we knew had planets wasour sun.)

The now-known structure

As we know now, the atom contains: 1. Nucleons (Protons and Neutrons bundled together) 2. Electrons Now, the things to remember about atoms are that the The atom is defined by the numberof protons in the nucleus!, so if there's 1 proton in the nucleus, then it's going to behydrogen, because its atomic number (number of protons) is 1. If you want to know what theelement is, then look it up on the periodic table. Now, for some quick facts:1. The number of electrons in an atom is equal to the number of protons, due to the charge of

1 proton pulling in 1 electron (in AS anyway)2. When electrons are removed or added to an atom, it becomes an ion. This is called

Ionisation.

AQA A-Level Physics/Atomic structure 68

3. When there are more or less neutrons in the nucleus, then an atom is an Isotope.4. Isotopes have the same physical and chemical properties, but the nuclei can be either

stable or unstable, for example, C-12 and C-14 both occur in matter but the C-14 isotope isunstable

These are important concepts, as they're the basis of other theories and models that you'lllearn later on in the module. Now, remember these definitions. • Isotopes are atoms of the same element with different masses due to differing

numbers of neutrons in their nucleus.• Ions are atoms which have a number of electrons different to the number of protons,

resulting in a charge.

A X Z 4 He 2

To understand what these mean, you need to know what the top value and the bottom valuemeans.. the top value, • A is the number of protons AND neutrons in the nucleus of the element, known as

nucleon number• Z is the number of protons in the nucleus.. so, therefore...• number of neutrons.Now, with that said, you will need to be able to calculate the masses and charges of theseparticles, and you will need to use their specific values unlike in GCSE. Don't worry, youdon't need to remember them as you will get them in a data sheet at the front of the exampaper. With that said, it wont hurt to remember them!

Particle Charge MassProton Neutron NONE Electron

AQA A-Level Physics/Atomic structure 69

Practice Questions

Don't let the wording phase you, and make sure to read and understand what answer thequestion wants, and what part is just explaining something. To see the answers, lookbelow.• An isotope of Plutonium-210 is a radioactive isotope, which emits alpha radiation.

Calculate: • The number of protons • The number of electrons • The number of neutrons

• The isotope undergoes an ionisation process which removes 2 electrons from the atom.Calculate the overall charge of the atom.

Answers

1. Number of protons= 94, Number of neutrons=116, number of electrons=94 2. (2 x 1.60 x10-19) = 3.2 x10-19

AQA A-Level Physics/Particles and Anti-particles

Albert Einstein -- the man who changed the world, butsadly not his hair stylist

The idea of mass and energy

Einstein's most famous equation is . Although thisequation is quite well known, not many people really understandwhat it means. To truly understand the significance of Einstein'swork, we have to understand a few things about the history ofPhysics.Before Einstein wrote down his equation, our understanding of theworld was based mainly on ideas from the theories of motion andgravitation that were written down by Sir Isaac Newton[1] . Theseideas, along with theories on heat and light that were worked outin 19th century, make up what we call Classical Physics[2] .

Newton's theory was a powerful tool for making predictions aboutthe positions of the planets and the trajectories of cannon balls. InNewton's theory the motion of objects could be measured withreference to a universal reference frame that was the same foreveryone, irrespective of their relative motion. Also, time wasassumed to pass at the same rate for everyone everywhere. Inaddition to this, energy was thought of as something that waspassed from one object to another but the mass of any particular object had nothing to do with its motion or howmuch energy it had.In Einstein's theory the mass of an object is intimately connected with its energy. In fact, mass and energy turn out tobe different ways of looking at the same thing. In Einstein's universe mass can change into energy and energy canchange into mass. Just how much energy we can get from a certain amount of mass is given by Einstein's famousformula .

AQA A-Level Physics/Particles and Anti-particles 70

Paul Dirac -- the father of anti-matter, who predictedantimatter.

The Play Dough Idea

Imagine that something like a car, is made of play dough. Now,when you have play dough you can rip bits off and make otherthings out of it. Now, imagine that when the play dough is madeinto something, it goes hard and you have a solid object, but whenit's soft, it's easy to model into other things. That's kind of like howenergy works when you're talking about particles.Basically, energy and mass are interchangeable, and anything thathas mass has an energy amount, which is larger, associated withthat mass. This broke free of the Newtonian ideas, as he saidobjects at rest have no energy associated with them.

Particles

Now, you may be thinking about why particles are so important.Who cares if something super-small exists and does x, y and z ?Well, lots of people -- and you too will find it important because itdescribes something which is interesting because it's happeningmillions of times around you in a split second!Now, if you remember the original things were the proton, the neutron and the electron, which are what the majorityof all atoms (except anti-hydrogen) are made out of. Now, you think of these being the only particles there are, but,unfortunately, there's lots of other kinds of particles which are smaller and do all kinds of crazy things! In this bit,we've got a lot to go into, but it's all very easy stuff, and if you remember one key rule, you'll be fine.

These concepts were created by humans, and are understood by them.

Anti particlesThese lovely things sound like they're straight out of Star Trek, but they're nowhere near as complicated when youthink about it. They're basically the reverse image of the normal particle, and have similar properties and have asimilar structure, but they're the mirror image.Have you ever head in maths where if you do +1 and add it with -1? Well, that's how it happens with particles andantiparticles. Now.. are you ready to get into the nitty-gritty of the particles? It's not hard, i promise you.

References[1] http:/ / www. newton. ac. uk/ newtlife. html[2] http:/ / en. wikipedia. org/ wiki/ Classical_physics

Next page

AQA A-Level Physics/Particles and Anti-particles/Constituents of the particle 71

AQA A-Level Physics/Particles andAnti-particles/Constituents of the particleYou may have learnt that matter is made up out of three types of particles; protons and neutrons in the nucleus andelectrons orbiting around outside. You might think that these particles are the basic building blocks for all matter.While it is true that the electrons cannot be broken down into any smaller particles, it is possible to smash up protonsand neutrons into smaller bits. For this reason we say that the electron is a fundamental particle and that protons andneutrons are not fundamental.The electron belongs to the family of fundamental particles called Leptons. These small particles typically have verysmall masses. The proton and the neutron belong to a family of heavier particles called Baryons.

What makes up the proton and the neutron?Protons and neutrons are made up of smaller, fundamental particles known as quarks. Just like all of the otherbaryons, protons and neutrons consist of three quarks. The three quarks add together to make the baryon, so in thecase of a neutron we require the charges on the quarks to cancel out. In the case of the proton the charges must addup to give e.To keep things simple in Particle Physics, we can call the proton charge +1 and give each quark a fractional chargeas shown in the table below.

Name Charge Baryon Number Strangeness Up (u) +2/3 1/3 0

Down (d) -1/3 1/3 0 Charm (c) +2/3 1/3 0 Strange (s) -1/3 1/3 -1

Top (t) +2/3 1/3 0 Bottom (b) -1/3 1/3 0

Explaining the properties of quarksThe first thing you'll be unfamiliar with is the term Baryon Number.This is a term that's basically either as "yes" or"no", and it's called boolean, so yes is +1 and no is 0. If there's an anti-particle, the number will be -1.

Anti-particles exist, and so do anti-quarks! They're represented with what's known as a bar, which is drawn abovethe shorthand name, so for instance, we have for a u-bar, an anti-up-quark! So, let's look at how a proton is madeof quarks! Look:

An example of calculating quarksA proton, is made up of 3 quarks, and so is a neutron, because it's a pretty big particle in comparison to others. So,we remember from before that a proton is a baryon, and it must therefore have a baryon number of +1 and a chargeof +1. So, let's start off.

= Charge of +2/3 and a baryon number of 1/3. So, we add that to:= Charge of -1/3 and a baryon number of 1/3, so we have... charge and a baryon

number of 2/3.= Charge of +2/3, so we add that to the +1/3 of U + D, and we get +1 (the charge of a proton) and a baryon

number of +1!

AQA A-Level Physics/Particles and Anti-particles/Forces 72

AQA A-Level Physics/Particles andAnti-particles/ForcesYou may have learnt that there are many different types of forces such as friction and tension. However only fourfundemental forces are at a basic level responsible for all interactions in the universe.

Strong Nuclear ForceThis type of force is only experianced by hadrons (baryons with 3 quarks). The exchange particles for this force arethe pions. This force is responsible for keeping the protons and neutrons in a atomic nucleus together.

Weak Nuclear ForceThis type of force is experianced by both baryons and leptons. The exchange particle for this type of force is the Wor the K boson. This force is responsible for decay interactions (such as beta decay) and interactions wherestrangeness is not conserved or where quarks change flavour (or type).

Electromagnatic ForceThis type of force is experianced by particles which are charged (such as electrons and protons). The exchangeparticle for this type of force is the virtual photon. This force is responsible for the repulsion of two electrons andattraction of a electron to a proton.

AQA A-Level Physics/Past paper questions

Atomic Structure1) Give the number of nucleons and the number of electrons in an atom of 22Na. (2 marks)Nucleons =Electrons =2) What is meant by the term isotope?3) Define the following (3 marks)When removed from an atom, forms a chargeHas the largest mass-charge ratioWhen removed from an atom, lowers overall mass

Article Sources and Contributors 73

Article Sources and ContributorsA-level Physics  Source: http://en.wikibooks.org/w/index.php?oldid=2091697  Contributors: AdRiley, Adrignola, Charlie123, Cometstyles, Dallas1278, Derbeth, Jguk, John Cross, Krackpipe,Mitchc, Nikki, QuiteUnusual, Recent Runes, Selden, Sjlegg, Tannersf, Wrolf, 15 anonymous edits

A-level Physics/Forces, Fields and Energy  Source: http://en.wikibooks.org/w/index.php?oldid=692404  Contributors: Conrad.Irwin, Jguk, Krackpipe, Tannersf

A-level Physics/Forces, Fields and Energy/Further dynamics  Source: http://en.wikibooks.org/w/index.php?oldid=1656503  Contributors: Conrad.Irwin, Jguk, Krackpipe, Markharper,QuiteUnusual, 6 anonymous edits

A-level Physics/Forces, Fields and Energy/Work and energy  Source: http://en.wikibooks.org/w/index.php?oldid=1482507  Contributors: Adrignola, Hoogli, Mike.lifeguard, 10 anonymousedits

A-level Physics/Forces, Fields and Energy/Motion in a circle  Source: http://en.wikibooks.org/w/index.php?oldid=2052886  Contributors: Avicennasis, Jguk, Krackpipe, Studiesrule, Wisden,Wutsje, 4 anonymous edits

A-level Physics/Forces, Fields and Energy/Oscillations  Source: http://en.wikibooks.org/w/index.php?oldid=2052887  Contributors: Avicennasis, Jguk, Krackpipe, 12 anonymous edits

A-level Physics/Forces, Fields and Energy/Gravitational fields  Source: http://en.wikibooks.org/w/index.php?oldid=1716220  Contributors: Jguk, Jomegat, Krackpipe, Mike.lifeguard, Pienis,QuiteUnusual, Swift, 9 anonymous edits

A-level Physics/Forces, Fields and Energy/Electric fields  Source: http://en.wikibooks.org/w/index.php?oldid=2084180  Contributors: Dudboi, Jguk, Krackpipe, QuiteUnusual, 17 anonymousedits

A-level Physics/Forces, Fields and Energy/Capacitors  Source: http://en.wikibooks.org/w/index.php?oldid=1685786  Contributors: Adrignola, Ameagle2, Hagindaz, Jguk, QuiteUnusual,Tannersf, 11 anonymous edits

A-level Physics/Forces, Fields and Energy/Electromagnetism  Source: http://en.wikibooks.org/w/index.php?oldid=2082955  Contributors: Inkerman, QuiteUnusual, Whiteknight, 5 anonymousedits

A-level Physics/Forces, Fields and Energy/Electromagnetic induction  Source: http://en.wikibooks.org/w/index.php?oldid=1897660  Contributors: Fishpi, Jguk, Krackpipe, QuiteUnusual, 14anonymous edits

A-level Physics/Forces, Fields and Energy/Thermal physics  Source: http://en.wikibooks.org/w/index.php?oldid=2052890  Contributors: Avicennasis, Jguk, Jomegat, Krackpipe,WakiMakiRolls, 28 anonymous edits

A-level Physics/Forces, Fields and Energy/The nuclear atom  Source: http://en.wikibooks.org/w/index.php?oldid=2052889  Contributors: Adrignola, Avicennasis, Jguk, Krackpipe, Webaware,11 anonymous edits

A-level Physics/Forces, Fields and Energy/Radioactivity  Source: http://en.wikibooks.org/w/index.php?oldid=2052888  Contributors: Avicennasis, Introspectre, Jguk, Krackpipe, Xenon 2k6,17 anonymous edits

A-level Physics/Cosmology  Source: http://en.wikibooks.org/w/index.php?oldid=1504629  Contributors: Jguk, Krackpipe, 2 anonymous edits

A-level Physics/Cosmology/Models of the known universe  Source: http://en.wikibooks.org/w/index.php?oldid=2083125  Contributors: Avicennasis, Common Good, Comrade42, Jguk,Krackpipe, QuiteUnusual, Xania, 39 anonymous edits

A-level Physics/Cosmology/Stars and Galaxies  Source: http://en.wikibooks.org/w/index.php?oldid=2052884  Contributors: Avicennasis, Dauto, Jguk, Krackpipe, Webaware, 7 anonymousedits

A-level Physics/Cosmology/Structure of the universe  Source: http://en.wikibooks.org/w/index.php?oldid=1661582  Contributors: Adrignola, Jguk, 4 anonymous edits

A-level Physics/Cosmology/Information from stellar observation  Source: http://en.wikibooks.org/w/index.php?oldid=1656082  Contributors: Adrignola, QuiteUnusual, 2 anonymous edits

A-level Physics/Cosmology/How the universe may evolve  Source: http://en.wikibooks.org/w/index.php?oldid=2052882  Contributors: Adrignola, Arsenalfan, Avicennasis, Ferranti, 3anonymous edits

A-level Physics/Cosmology/Relativity  Source: http://en.wikibooks.org/w/index.php?oldid=1656091  Contributors: Ati3414, D3r2000, Krackpipe, QuiteUnusual, Tannersf, 7 anonymous edits

A-level Physics/Health Physics  Source: http://en.wikibooks.org/w/index.php?oldid=1093194  Contributors: Mike.lifeguard, Nicholas.thorley, 2 anonymous edits

A-level Physics/Health Physics/Body Mechanics  Source: http://en.wikibooks.org/w/index.php?oldid=1529779  Contributors: Adrignola, 1 anonymous edits

A-level Physics/Health Physics/Medical Imaging  Source: http://en.wikibooks.org/w/index.php?oldid=1526289  Contributors: Adrignola, QuiteUnusual, 1 anonymous edits

A-level Physics/Nuclear and Particle Physics  Source: http://en.wikibooks.org/w/index.php?oldid=514293  Contributors: Jguk, 2 anonymous edits

A-level Physics/Nuclear and Particle Physics/The Nucleus  Source: http://en.wikibooks.org/w/index.php?oldid=2052893  Contributors: Alex Lee, Ambition, AntsOnToast, Avicennasis,Conrad.Irwin, Exfenestracide, Jguk, QuiteUnusual, 11 anonymous edits

A-level Physics/The SI System of Units  Source: http://en.wikibooks.org/w/index.php?oldid=2083102  Contributors: Avicennasis, Gakjab, Geocachernemesis, Gluk, Hcldesmond, Herbythyme,Jguk, Kivie, Krackpipe, Mattb112885, QuiteUnusual, Robert Horning, Wrolf, 15 anonymous edits

A-level Physics/Equation Sheet  Source: http://en.wikibooks.org/w/index.php?oldid=2083505  Contributors: Adrignola, Anton.mazurenko, Cspurrier, Jcc77, Jguk, John Cross, Jomegat,Krackpipe, QuiteUnusual, Technochef, 14 anonymous edits

A-level Physics/Glossary of Terms  Source: http://en.wikibooks.org/w/index.php?oldid=2089488  Contributors: Adrignola, Anonymous Dissident, Atheg, Avicennasis, Az1568, Dared111, Jguk,Joachim, Karen ho, Kivie, Krackpipe, Panic2k4, QuiteUnusual, Rubixwolf, 56 anonymous edits

AQA A-Level Physics  Source: http://en.wikibooks.org/w/index.php?oldid=1857385  Contributors: Adrignola, Dallas1278, Hoogli, James.Spudeman, Whiteknight

AQA A-Level Physics/Atomic structure  Source: http://en.wikibooks.org/w/index.php?oldid=2009306  Contributors: James.Spudeman, Neoptolemus, QuiteUnusual, TonyC, 10 anonymousedits

AQA A-Level Physics/Particles and Anti-particles  Source: http://en.wikibooks.org/w/index.php?oldid=1791129  Contributors: James.Spudeman, MalachiK, QuiteUnusual, 1 anonymous edits

AQA A-Level Physics/Particles and Anti-particles/Constituents of the particle  Source: http://en.wikibooks.org/w/index.php?oldid=2052919  Contributors: Avicennasis, James.Spudeman,MalachiK, 3 anonymous edits

AQA A-Level Physics/Particles and Anti-particles/Forces  Source: http://en.wikibooks.org/w/index.php?oldid=2096285  Contributors: Recent Runes, 2 anonymous edits

AQA A-Level Physics/Past paper questions  Source: http://en.wikibooks.org/w/index.php?oldid=1791737  Contributors: Adrignola, James.Spudeman

Image Sources, Licenses and Contributors 74

Image Sources, Licenses and ContributorsImage:Simple harmonic motion.png  Source: http://en.wikibooks.org/w/index.php?title=File:Simple_harmonic_motion.png  License: GNU Free Documentation License  Contributors:Abdullah Köroğlu, Maksim, Peppergrower, ShizhaoImage:Gravitymacroscopic.png  Source: http://en.wikibooks.org/w/index.php?title=File:Gravitymacroscopic.png  License: Creative Commons Attribution-Sharealike 2.5  Contributors:Enochlau, StanneredImage:Gravityroom.png  Source: http://en.wikibooks.org/w/index.php?title=File:Gravityroom.png  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Enochlau, Stanneredimage:InverseSquareLaw.png  Source: http://en.wikibooks.org/w/index.php?title=File:InverseSquareLaw.png  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Borb,Tano4595, 1 anonymous editsFile:VFPt minus thumb.svg  Source: http://en.wikibooks.org/w/index.php?title=File:VFPt_minus_thumb.svg  License: GNU Free Documentation License  Contributors: User:Geek3File:VFPt plus thumb.svg  Source: http://en.wikibooks.org/w/index.php?title=File:VFPt_plus_thumb.svg  License: GNU Free Documentation License  Contributors: User:Geek3File:VFPt capacitor.svg  Source: http://en.wikibooks.org/w/index.php?title=File:VFPt_capacitor.svg  License: GNU Free Documentation License  Contributors: User:Geek3Image:VFPt charges plus minus thumb.svg  Source: http://en.wikibooks.org/w/index.php?title=File:VFPt_charges_plus_minus_thumb.svg  License: GNU Free Documentation License Contributors: User:Geek3File:VFPt image charge plane horizontal.svg  Source: http://en.wikibooks.org/w/index.php?title=File:VFPt_image_charge_plane_horizontal.svg  License: GNU Free Documentation License Contributors: User:Geek3File:Capacitors in parallel.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Capacitors_in_parallel.svg  License: unknown  Contributors: User:OmegatronFile:Capacitors in series.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Capacitors_in_series.svg  License: unknown  Contributors: User:OmegatronImage:Temperature-time graph for water.png  Source: http://en.wikibooks.org/w/index.php?title=File:Temperature-time_graph_for_water.png  License: GNU Free Documentation License Contributors: KrackpipeImage:Plum_pudding_atom.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Plum_pudding_atom.svg  License: Public Domain  Contributors: User:FastfissionImage:Atom.png  Source: http://en.wikibooks.org/w/index.php?title=File:Atom.png  License: GNU Free Documentation License  Contributors: HereToHelp, King of Hearts, Mxn, Saperaud,Svdmolen, 2 anonymous editsImage:Alfa beta gamma radiation.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Alfa_beta_gamma_radiation.svg  License: Creative Commons Attribution 2.5  Contributors:User:StanneredImage:Parallax Example.png  Source: http://en.wikibooks.org/w/index.php?title=File:Parallax_Example.png  License: GNU Free Documentation License  Contributors: Booyabazooka,Hydrargyrum, Joanjoc, ShizhaoImage:Retrograde-motion-of-mars.png  Source: http://en.wikibooks.org/w/index.php?title=File:Retrograde-motion-of-mars.png  License: GNU Free Documentation License  Contributors:KrackpipeImage:Kepler-first-law.png  Source: http://en.wikibooks.org/w/index.php?title=File:Kepler-first-law.png  License: GNU Free Documentation License  Contributors: User:StwImage:Kepler-second-law.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Kepler-second-law.svg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: User:Harp,User:StwImage:Semimajoraxis.png  Source: http://en.wikibooks.org/w/index.php?title=File:Semimajoraxis.png  License: Public Domain  Contributors: JMCC1, Peppe83, Ruslik0Image:Phasesofvenus.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Phasesofvenus.jpg  License: Public Domain  Contributors: Bricktop, ComputerHotline, Conscious, Gentgeen,Theresa knottImage: NGC_4414_(NASA-med).jpg  Source: http://en.wikibooks.org/w/index.php?title=File:NGC_4414_(NASA-med).jpg  License: unknown  Contributors: NASA Headquarters - GreatestImages of NASA (NASA-HQ-GRIN)Image:Omega Nebula.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Omega_Nebula.jpg  License: unknown  Contributors: NASA, ESA and J. Hester (ASU)Image:NGC6543.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:NGC6543.jpg  License: unknown  Contributors: Dbenbenn, Denniss, Eleferen, KGyST, Kookaburra, Kurgus, LarsLindberg Christensen, Martin H., Misibacsi, Mo-Slimy, Niduzzi, RuM, Ruslik0, Saperaud, Shizhao, 1 anonymous editsimage:Crab Nebula.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Crab_Nebula.jpg  License: unknown  Contributors: NASAImage:Black Hole Milkyway.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Black_Hole_Milkyway.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors:CorvinZahn, Er Komandante, EvaK, Hotshot977, KaragouniS, Qblik, Tano4595, Warrakkk, 25 anonymous editsImage:Stellarparallax2.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Stellarparallax2.svg  License: Public Domain  Contributors: Original uploader was Booyabazooka aten.wikipediaImage:Milky Way galaxy.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Milky_Way_galaxy.jpg  License: unknown  Contributors: Duesentrieb, Duffman, Edward, Lars LindbergChristensen, MywoodImage:100%.png  Source: http://en.wikibooks.org/w/index.php?title=File:100%.png  License: Creative Commons Attribution-Sharealike 3.0  Contributors: TouzaxAImage:25%.png  Source: http://en.wikibooks.org/w/index.php?title=File:25%.png  License: Creative Commons Attribution-Sharealike 3.0  Contributors: TouzaxAImage:00%.png  Source: http://en.wikibooks.org/w/index.php?title=File:00%.png  License: GNU Free Documentation License  Contributors: Kilom691, ManuelGR, Sarang, SiebrandImage:Plum pudding atom.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Plum_pudding_atom.svg  License: Public Domain  Contributors: User:FastfissionImage:Rutherford gold foil experiment results.svg  Source: http://en.wikibooks.org/w/index.php?title=File:Rutherford_gold_foil_experiment_results.svg  License: Public Domain Contributors: User:FastfissionImage:Albert Einstein Head.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Albert_Einstein_Head.jpg  License: unknown  Contributors: User:DantaddImage:Dirac 3.jpg  Source: http://en.wikibooks.org/w/index.php?title=File:Dirac_3.jpg  License: anonymous-EU  Contributors: Cambridge University, Cavendish Laboratory

License 75

LicenseCreative Commons Attribution-Share Alike 3.0 Unportedhttp:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/