Chemistry HP Unit 11 Nuclear Chemistry Learning Targets ...11... · Learning Targets (Your exam at the ... Perform calculations involving half-life in order to solve for mass, time,

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Chemistry HP Unit 11 – Nuclear Chemistry

Learning Targets (Your exam at the end of Unit 11 will assess the following:)

11. Nuclear Chemistry

11-1. Write the nuclide symbol for a given isotope.

11-2. Describe alpha, beta, and gamma radiation and give the appropriate symbol for each.

11-3. Define a transmutation and state what types of radiation can lead to a transmutation.

11-4. Define penetrating power and rank alpha, beta, and gamma radiation according to their strength.

11-5. Complete nuclear reactions including those involving alpha, beta, or gamma radiations as well as neutrons and

protons.

11-6. Define half-life.

11-7. Perform calculations involving half-life in order to solve for mass, time, original mass, and half-life.

11-8. Describe the factors effecting nuclear stability including binding energy, band of stability, and magic numbers.

11-9. Calculate the binding energy for a given isotope. Name the isotope with the highest binding energy. Define

fission and fusion and classify a nuclear reaction as either a fission or fusion reaction.

11-10. Determine if a given isotope is found on the band of stability and use this to predict if it will be stable/non-

radioactive or unstable/radioactive.

11-11. Describe some of the main applications of nuclear chemistry including nuclear energy, nuclear medicine, and

radioactive dating.

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11-1. Write the nuclide symbol for a given isotope.

Nuclear Chemistry is the branch of chemistry that deals with the nucleus of an atom.

If we could magnify the simplest hydrogen atom to the size of the earth, then the nucleus would be about the size of a

basketball.

It would be at the very center of the earth and that lonely electron would be found somewhere out in earth's

atmosphere.

All of the space in between the electron and the basketball-size nucleus would be empty!

If the electromagnetic attraction between protons in the basketball at the center of earth and the electrons as far out as

the atmosphere keep an atom together…

What could possibly keep the mutually repulsive protons together in an area as relatively small as a basketball?

The Strong Nuclear Force

The Strong Nuclear Force is the force which holds the protons and neutrons together in the nucleus.

Over short distances, such as the diameter of a medium sized nucleus, the strong force overcomes the

electromagnetic repulsion of the protons and holds the nucleus intact.

Over larger distances, the Strong Force does not have a large enough range to overcome the electromagnetic

repulsion in larger nuclei.

Radioactivity, also known as radioactive decay, is the giving off of products as unstable nuclei become stable.

Large Atoms are Radioactive

Nuclei larger than atomic number 83 “decay” to more stable, smaller, nuclei.

Nuclide Symbols

A nuclide symbol gives the mass and the number of protons for a given isotope of an atom.

Recall that isotopes are atoms of the same element that have different numbers of neutrons.

ex. The nuclide symbol for radium-228 is 𝑅𝑎88228

ex. Write the nuclide symbol for chlorine-37

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Worksheet 11-1 (Learning Target 11-1)

(1) Give the Nuclide symbol for the following atoms.

(a) Carbon-14

(b) Uranium-235

(c) Hafnium-177

(d) Mercury-204

(e) Potassium-38

(f) Tin-124

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protons.

Nuclear Radiation

The nucleus of certain isotopes of some atoms is unstable. These are called radioactive isotopes. These isotopes can

emit radiation.

Types of Radiation

The three main types of radiation are alpha, beta, and gamma.

Type of Radiation Symbol Notes Example

Alpha 𝐻𝑒24 Alpha radiation produces an

alpha particle, which has the same structure as a helium nucleus.

𝑃𝑜 →84210 𝑃𝑏 + 𝐻𝑒2

482

206

Beta 𝑒−10 Beta radiation produces a beta

particle, which has the same structure as an electron. In the nucleus, a neutron changes into a proton and an electron.

𝐶 →614 𝑁 + 𝑒−1

07

14

Gamma 𝛾00 Gamma radiation does not

give off a particle, instead high energy radiation is given off in the form of electromagnetic waves. An “excited” element gives off gamma radiation and returns to the “ground” state.

𝐵𝑎 →56137 𝐵𝑎 + 𝛾0

056

137

Transmutation: A nuclear process in which one chemical element is converted into a different chemical element. Only alpha and beta radiation can result in a transmutation.

Penetrating Power: Describes the strength of each form of nuclear radiation.

Alpha Particles: weakest form of radiation, can be stopped by paper

Beta Particles: intermediate in strength, can be stopped by aluminum foil

Gamma Rays: strongest form of radiation, can be blocked by 1 cm of lead or 6 cm of concrete

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protons.

Nuclear Reactions

Nuclear reactions affect the nucleus of an atom. In a nuclear reaction, the mass and the number of protons must be

equal on both sides of the reaction.

ex. Complete the following nuclear reactions.

𝑅𝑛 →86222 𝑃𝑜84

218 + _____

𝑇𝑐 →4399 ______ + 𝑒−1

0

𝐼𝑛 →49111 𝐼𝑛49

111 + _____

𝐶𝑢 + 𝐻12 →29

63 𝑍𝑛3064 + _____

𝑈 + 𝑛01 →92

235 𝑇𝑒52137 + _____ +2 𝑛0

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ex. Complete the following nuclear reactions.

Write the nuclear reaction for the alpha decay of Thorium-232.

The product of the above alpha decay undergoes beta decay. Write its nuclear reaction.

The product of the above beta decay gives off gamma radiation. Write its nuclear reaction of this gamma radiation.

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Worksheet 11-2 (Learning Targets 11-5)

Complete the following nuclear reactions.

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11-6. Define half-life.

11-7. Perform calculations involving half-life in order to solve for mass, time, original mass, and half-life.

Half-life

Half-life: The amount of time required for the mass of a radioactive element to decay to half of the original amount.

Different radioactive isotopes decay at very different rates.

Isotope Half-Life

Carbon-14 5730 years

Uranium-238 4.46 x 109 years

Cobalt-60 10.47 minutes

Astatine-218 1.6 s

Phosphorus-32 14.28 days

Polonium-214 1.64 x 10-4 seconds

Potassium-40 1.3 x 109 years

Half-Life Equation

𝐴 = 𝐼(0.5)𝑡ℎ

A = amount remaining

I = initial amount

t = time

h = half-life

(1) Carbon-14 has a half-life of 5730 years.

(a) What mass of a 100. g sample would remain after 22920 years?

(b) How long would it take for a 256.0 g sample to decay to 8.000 g?

(c) How long would it take for a sample to decay to 12.5% of the original amount?

(d) If 3.00 g of a sample remain after 34380 years, what was the mass of the original sample?

(2) A 50 g sample of cesium-137 decays to 12.5 g in 180 years. What is the half-life of cesium-137?

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Half-Lives

(1) How much of a 100 g sample of gold-198 is left after 8.10 days if the half-life is 2.70 days?

(2) A 50.0 g sample of polonium-218 decays to 12.5 g in 9.0 minutes. What is the half-life of polonium-218?

(3) The half-life of plutonium-239 is 24110 years. If there are 2.0 g of a sample left after 48220 years, how many grams

were in the original sample?

(4) A radiation leak releases 200.0 g of uranium-238. If uranium-238 has a half-life of 4.460 x 109 years, how long will it

take for the mass of sample to decrease to one-eighth of the original amount?

(5) Hydrogen-3 has a half-life of 12.32 years. (a) How long will it take for a 512 mg sample to decay to 16.0 mg? (b) How

many grams of a 240.0 g sample would be left after 98.56 years?

(6) There are 4.00 g of iodine-131 left after 40.35 days. If the half-life of iodine-131 is 8.07 days, how many grams were

in the original sample?

(7) The half-life of radon-222 is 3.82 days. How long would it take for a sample to decrease to 3.125% of the original

mass?

(8) A sample of thorium-227 decays to one-eighth of its original mass in 56.16 days. What is the half-life of thorium-227?

Answers. (1) 12.5 g (2) 4.5 minutes (3) 8.0 g (4) 1.338 x 1010 years (5) (a) 61.6 years (b) 0.9375 g (6) 128 g (7) 19.1 days (8)

18.72 days

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radioactive dating.

Applications of Nuclear Chemistry

(1) Nuclear Energy

Nuclear Reactors can be used to harness the energy produced in nuclear reactions. In a reactor, the energy from the

reactions is used to heat large quantities of water to produce steam. The energy from this process is harnessed using a

generator and converted to electricity. The main component of nuclear fuel is Uranium. Uranium is mines as uranium

(IV) oxide and then enriched to 3% uranium-235

Advantages: Nuclear energy is efficient and does not contribute to greenhouse gases associated with climate change

Disadvantages: Uranium is a non-renewable resource and the waste products made in reactors are difficult to dispose

of. There is also a risk of possible nuclear accidents such as those that occurred in Three Mile Island in Pennsylvania in

1979, Chernobyl in the Ukraine in 1986, and Fukushima Daiichi in Japan in 2011.

(2) Nuclear Medicine

Nuclear chemistry is used for several diagnostic or medical imaging techniques including Bone Scans and Positron

Emission Tomography (PET) Scans.

Bone Scans

For a bone scan, a patient is administered technetium-99. The body will take up technetium-99 with other minerals

required in metabolism. Areas of higher than normal uptake will generally be indicative of fractures, infections, or

tumors. Technetium-99 emits gamma rays which can be detected by cameras to create a detailed picture of the body.

The decay of technetium-99 is shown below.

𝑇𝑐 → 𝑇𝑐 +4399

4399 𝛾0

0

PET Scans

In a PET scan, a patient is given a radioactive form of a chemical required in metabolism. Fluorine-18 is one of the most

common radioisotopes used in PET scans. The decay of fluorine-18 produces a positron. A positron is the antimatter

counterpart of an electron/beta particle and has the symbol 𝑒+10

.

The positron decay of fluorine-18 is shown below.

𝐹 → 𝑒 ++10

918 𝑂8

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When the positron that is produced encounters an electron, the matter-antimatter pair annihilate one another and

produce gamma rays. The position of the gamma rays is determined by a computer in order to create a three

dimensional picture of the patient’s organs. PET scans are used in diagnosing cancer, detecting heart disease, and

analyzing brain disorders.

Radiation Therapy

Radioactive isotopes can also be used in medical treatments. In radiation therapy, a patient is given a specific dose of

radioactive medicine. Radiation therapy is frequently used to treat cancer because fast growing cancer cells are more

susceptible to damage by high-energy radiation than are healthy cells.

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radioactive dating.

(3) Radioactive Dating

Carbon Dating

All organisms take in carbon (plants by photosynthesis and animals by ingestion). The percentage of carbon-14 in the atmosphere is

constant and a living organism will have the same percentage. When an organism dies it no longer takes in new carbon-14. Carbon-

14 has a half-life of 5730 years, so as time passes the carbon-14 in the tissue decays. Carbon-14 decays be emission of a beta

particle. 𝐶 → 𝑁 +714

614 𝑒−1

0

The percentage of carbon-14 remaining in an organism can be used to determine its age. Carbon dating is best for dating organic

materials younger than 50000 years.

ex. What would be the age of a sample with 25% of the carbon-14 remaining?

ex. What percentage carbon-14 would remain in a 2000-year-old sample?

Potassium/Argon (K/Ar) Dating

Potassium is found in rocks produced during volcanic eruptions. Potassium-40 has a half-life of 1.3 x 109 years. As time passes, the

potassium undergoes beta capture to become argon gas. 𝐾 + 𝑒−10 → 𝐴𝑟18

141940

The argon becomes trapped in air bubbles in the rock. The ratio of K:Ar in an object can be used to determine the its age. K/Ar dating

is best for inorganic materials older than 100 000 years.

ex. How old is a rock with a K:Ar ratio of 0.40?

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Carbon Dating. Use the graph to answer the questions below.

(1) The half-life of carbon-14 is 5730 years.

(a) What mass of a 1.0 g sample will remain after 5730 years?

(b) What percentage of a 1.0 g sample will remain after 11 460 years?

(2) Use the graph to estimate the approximate age of each sample.

(a) A bone that has 50% of the original carbon-14 remaining

(b) A shark’s tooth that has 20% of the original carbon-14 remaining

(c) A fragment of paper with 70% of the original carbon-14 remaining

(3) Use the graph to determine the approximate percentage of the carbon-14 that would remain in each sample.

(a) A piece of wood that is 12500 years old

(b) A shell that is 30000 years old

(c) A piece of silk that is 5000 years old.

(4) How long would it take for a 50.0 g sample to have 12.5 g of carbon-14 remaining?

(5) What mass of carbon-14 would remain in a 2.00 g sample after 22920 years?

Answers: (1) (a) 0.50 g (b) 25% (2) (As long as you’re close, it’s fine!) (a) 5730 years (b) 13305 years (c) 2945 years (3) (As long as you’re close, it’s

fine!) (a) 22% (b) 2.7% (c) 55% (4) 11 460 years (5) 1.25 g

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11-9. Calculate the binding energy for a given isotope. Name the isotope with the highest binding energy. Define fission

and fusion and classify a nuclear reaction as either a fission or fusion reaction.

Nuclear Stability

The stability of the nucleus of an atom is a combination of several factors including binding energy, band of stability, and

magic numbers. Nuclei that are stable are non-radioactive and nuclear that are unstable are radioactive.

(1) Binding Energy

When the nucleus of an atom is formed, some of the mass of the protons and neutrons is converted into binding energy

which holds the nucleus together.

The higher the binding energy, the more stable the nucleus.

Albert Einstein (1879-1955): Mass can be converted into energy according to the following equation:

𝐸 = 𝑚𝑐2 E = energy (Joules) m = mass (kg) c = speed of light (3.00 x 108 m/s)

ex. The mass lost when a helium-4 nucleus is formed in 5.05 x 10-29 kg. Determine the binding energy.

Binding energy is given in units called Mega electron Volts (MeV). 1 MeV = 1.602 x 10-13 J.

Binding energy is then calculated as energy per nucleon (protons and neutrons are both called nucleons, ie. Helium-4

has two protons and two neutrons, and therefore has four nucleons).

ex. Convert the binding energy of helium-4 in MeV/nucleon.

The binding energy for different isotopes is shown below.

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The isotope with the highest binding energy and therefore the most stable nucleus is iron-56.

Atoms with smaller atomic numbers undergo fusion (combination of nuclei) to increase atomic number and increase

binding energy and atoms with larger atomic numbers undergo fission (splitting of nuclei) to decrease atomic number

and increase binding energy.

Fusion takes place in stars to produce helium and energy.

𝐻 + 𝐻 → 𝐻𝑒 + 𝑛01

24

13

12

Fission takes place in nuclear reactors to release energy.

ex. 𝑈 + + 𝑛01 → 𝐵𝑎 + 𝐾𝑟 + 3 𝑛0

13692

56141

92235

Fusion actually releases more energy than fission, but requires a high temperature to initiate the process and is

therefore impractical to use to supply energy commercially.

(2) Band of Stability

The stability of the nucleus also depends on the ratio of neutrons to protons.

Since protons are positively charged, they will repel one another in the nucleus.

Neutrons act to decrease (or “buffer”) the repulsive forces and stabilize the nucleus.

If the number of neutrons vs. the number of protons for stable isotopes is graphed, it can be seen that stable

nuclei fit into the “band of stability.” Each point on the graph represents a stable/non-radioactive isotope.

Nuclei outside this band are generally unstable and are radioactive.

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Note: the ratio of neutrons to protons increases with an increasing number of protons because additional

neutrons are required to reduce proton-proton repulsion (initially, nuclei are stable with a n/p ratio close to one,

but as the number of protons increases, the n/p ratio for stable nuclei becomes closer to 1.5).

There are no stable nuclei with more than 83 protons (ie. the elements Polonium and above are all radioactive)

because the proton-proton repulsion is too great to be overcome.

(3) Magic Numbers: 2, 8, 20, 28, 50, 82, 126

Some nuclei are unusually stable because the number of protons, neutrons, an/or mass is equal to a “magic

number.”

It is suggested that protons/neutrons are found in “shells” or energy levels in the nucleus (similar to the electron

shells)

As with electrons, it is thought that full shells result in stability. A stable nucleus results in a non-radioactive

isotope.

Examples of isotopes that are particularly stable as a result of “magic numbers”:

𝐻𝑒 𝑂816

24 𝐶20

40

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Worksheet 11-5 (Learning Target 11-9 Binding Energy)

Directions. Solve the following problems.

Mass of a proton: 1.007825 u Mass of a neutron: 1.008665 u 1 u = 931 MeV

1. The mass of the tritium isotope, 𝐻13 , is 3.0160490 u.

a. What is the mass defect of this isotope? (To determine the mass defect, add together the masses of all the protons

and neutrons and subtract that from the given mass of the tritium isotope above).

b. What is the binding energy of this isotope?

2. The mass of a 𝐶612 nucleus is 12.00000 u.

a. What is the mass defect of this nucleus?

b. What is the binding energy of this nucleus?

3. An oxygen isotope, 𝑂816 , has a mass of 15.99491 u.

a. What is the mass defect of this isotope?

b. What is the binding energy of this isotope?

4. The mass of an iron-56 nucleus is 55.92066 u.

a. What is the mass defect of this nucleus?

b. What is the binding energy of the nucleus?

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Worksheet 11-6

Nuclear Chemistry Practice

(1) Complete the following nuclear reactions.

(2) Write an equation for the nuclear reaction being described.

(a) Radon-198 produces and alpha particle.

(b) Gold-211 undergoes beta decay.

(c) An excited atom of beryllium-7 emits a gamma ray.

(d) Neon-21 combines with a neutron to emit an alpha particle and another isotope.

(3) Iodine-126 has a half-life of 12.9 days. If a sample starts with a mass of 40.0 g, how much will remain after 64.5 days?

(4) Thallium-208 has a half-life of 3.05 minutes. How long would it take for 120 g to decay to 7.50 g?

(5) A sample of actinium-226 has an initial mass of 160 mg. After 87 hours, the sample has decayed to 20 mg. What is

the half-life of actinium-226?

(6) Thorium-232 has a half-life of 1.40 x 1010 years. After 4.20 x 1010 years, a sample has a mass of 25.0 g. What was the

original mass of the sample?

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Worksheet 11-6 (con’t)

(7) Mercury-175 has a half-life of 10.8 ms.

(a) Write the nuclide symbol for Mercury-175.

(b) Mercury-175 decays by giving off an alpha particle. Write a balanced equation for this reaction.

(c) What mass of a 10.0 g sample of Mercury-175 will remain after 43.2 ms?

(d) How long would it take for a 1.80 g sample of Mercury-175 to decay to 0.450 g?

(8) Selenium-83 has a half-life of 25 minutes.

(a) Write the nuclide symbol for Selenium-83.

(b) Selenium-83 undergoes beta decay. Write a balanced equation for this reaction.

(c) What mass of a 16 g sample of Selenium-83 will remain after 125 minutes?

(d) How long would it take for a 6.0 g sample of Selenium-83 to decay to 0.75 g?

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Worksheet 11-7

Review: Nuclear Chemistry

(1) Give the nuclide symbol for the following atoms.

(a) Cadmium-110 (b) Barium-137

(2) For each of the following statements, state which type(s) or radiation they describe.

(a) has the highest penetrating power (b) has the same structure as an electron (c) has the same structure as a helium nucleus (d) can be stopped by a piece of paper

(e) can be stopped by aluminum foil (f) can result in a transmutation (g) is energy released from an excited atom (h) is a type of particle

(3) Complete the following nuclear reactions.

(4) Iodine-131 has half-life of 8.0 days.

(a) How long would it take for a 6400 g sample to decay to 100.0 g?

(b) How much of a 512 g sample would remain after 72 days?

(5) Sodium-24 has a half-life of 15.02 hours.

(a) How long would it take for a 400 g sample to decay to 12.5 g?

(b) How much of an 80 g sample would remain after 45.06 hours?

(c) How long would it take for a sample to decay to 25.00% of the original amount?

(6) A 30.00 g sample of radium-226 decays to 7.500 g in 3200 years. What is the half-life of radium-226?

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Worksheet 11-7 (con’t)

(7) Rhodium-108 has a half-life of 17 seconds. After 85 seconds, there are 3.0 g or a sample remaining. What was the

mass of the original sample?

(8) The amount of mass lost when a lithium-7 nucleus is formed is 7.00 x 10-29 kg. Determine the binding energy of a

lithium nucleus.

(9) Fill in the blanks.

When an atom is formed, some of the mass is converted into _______________ that holds the nucleus together. The

_______________ the binding energy, the more stable the atom is. The most stable atom is _______________. Atoms

with a smaller mass will undergo _______________ which is the combination of nuclei and atoms with a larger mass will

undergo _______________ which is the splitting of nuclei. For example. _______________ takes place in stars and

_______________ takes place in nuclear reactors. Stability of an atom can also depend on the _______________ of

neutrons to protons. Stable or non-radioactive isotopes fit into the ______________________. Isotopes which do not fit

into this region are unstable and will be _______________. There are no stable nuclei with more than _______________

protons. Neutrons can stabilize a nucleus by _______________ proton-proton repulsion. Nuclei with protons, neutrons,

or mass equal to a ______________________ are unusually stable.

Documents

Chemistry HP Unit 11 Nuclear Chemistry Learning Targets ...11... · Learning Targets (Your exam at the ... Perform calculations involving half-life in order to solve for mass, time,