Chapter20

Chapter 20Nuclear Chemistry

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Contents and Concepts

1. Radioactivity

2. Nuclear Bombardment Reactions

3. Radiations and Matter: Detection and Biological Effects

4. Rate of Radioactive Decay

5. Applications of Radioactive Isotopes

Radioactivity and Nuclear Bombardment Reactions


Energy of Nuclear Reactions

6. Mass–Energy Calculations

7. Nuclear Fission and Nuclear Fusion


1. Radioactivity

a. Define radioactive decay and nuclear bombardment reaction.

b. Learn the nuclear symbols for positron, gamma photon, electron, neutron, and proton.

c. Write a nuclear equation.

d. Deduce a product or reactant in a nuclear equation.

e. Describe the shell model of the nucleus.

f. Explain the band of stability.

Learning Objectives


g. Predict the relative stabilities of nuclides.h. List the six types of radioactive decay.i. Predict the type of radioactive decay.j. Define radioactive decay series.

2. Nuclear Bombardment Reactionsa. Define transmutation.b. Use the notation for a bombardment

reaction.c. Locate the transuranium elements on the

periodic table.d. Determine the product nucleus in a nuclear

bombardment reaction.


3. Radiation and Matter: Detection and Biological Effects

a. State the purpose of a Geiger counter and a scintillation counter.

b. Define activity of a radioactive source and curie (Ci).

c. State the relationship between a rad and a rem.


4. Rate of Radioactive Decaya. Define radioactive decay constant.b. Calculate the decay constant from activity.c. Define half−life.d. Draw a typical half−life decay curve of a

radioactive element.e. Calculate the half−life from the decay

constant.f. Calculate the decay constant and activity

from the half−life.g. Determine the fraction of nuclei remaining

after a specified time.h. Apply the carbon−14 dating method.


5. Applications of Radioactive Isotopesa. State the ways in which radioactive

isotopes are used for chemical analysis.b. Describe how isotopes are used for medical

therapy and diagnosis.

6. Mass–Energy Calculationsa. Calculate the energy changes for a nuclear

reaction.b. Define nuclear binding energy and mass

defect.c. Compare and contrast nuclear fission and

nuclear fusion.


7. Nuclear Fission and Nuclear Fusion

a. Explain how a controlled chain reaction is applied in a nuclear fission reactor using a critical mass of fissionable material.

b. Write the reaction of the nuclear fusion of deuterium and tritium.


In chemical reactions, only the outer electrons of the atoms are disturbed.

In nuclear reactions, the nuclear changes that occur are independent of the chemical environment of the atom.


Radioactive decay is the process in which a nucleus spontaneously disintegrates, giving off radiation.

A nuclear bombardment reaction is a nuclear reaction in which a nucleus is bombarded, or struck, by another nucleus or by a nuclear particle.


The phenomenon of radioactivity was discovered by Henri Becquerel in 1896. Becquerel noted that photographic plates had bright spots when they were exposed to uranium minerals. This radiation was found to be composed of three types when exposed to an electric field.


We write nuclear equations using nuclide symbols. Nuclear equations are balanced when the total mass number and the atomic number on both reactant and product sides are equal.

Let’s look at the decay of uranium−238.

238 234 492 90 2U Th He


Symbols for other particles are given below:

γphoton Gamma

βor ePositron

βor eElectron

nNeutron

Por HProton

00

01

01

01-

01-

10

11

11


A beta particle is an electron. Beta emission occurs when a nucleus decays by emitting a beta particle, an electron.

A positron is similar to an electron, but has a positive charge. Positron emission occurs when a nucleus decays by emitting a positron.

A gamma photon is a particle of electromagnetic radiation that has higher energy and a smaller wavelength than an x−ray.

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Radon−222 is a radioactive noble gas that is sometimes present as an air pollutant in homes built over soil with high uranium content (uranium−238 decays to radium−226, which in turn decays to radon−222). A radon−222 nucleus decays to polonium−218 by emitting an alpha particle. Write the nuclear equation for this decay process.


Po α Rn 21884

42

22286

Po He Rn 21884

42

22286

From the periodic table, we can see that the atomic number of radon is 86 and the atomic number of polonium is 84. For the alpha particle symbol, both He and α are correct.

To check, total the mass numbers and atomic numbers on each side of the reaction.Mass numbers: 222 = 4 + 218 Atomic numbers: 86 = 2 + 84

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Iodine−131 is used in the diagnosis and treatment of thyroid cancer. This isotope decays by beta emission. What is the product nucleus?


X β I AZ

01-

13153

X e I AZ

01-

13153

Xe β I 13154

01-

13153 Xe e I 131

5401-

13153

From the periodic table, we find that the atomic number of iodine is 53. The beta particle symbol is correct as either e or β.

Now find the atomic and mass number of the product:

131 = 0 + A 53 = –1 + ZA = 131 Z = 54

Next, use the atomic number to find the symbol: Xe.


Nuclear StabilityIt is reasonable to wonder how a nucleus with positively charged protons is held together, given that positively charged particles repel each other.

The stability of the nucleus is due to the strong nuclear force. The nuclear force acts only at very short distances, about 10−13 m. At this distance it is stronger than the electric repulsion.


The shell model of the nucleus is a nuclear model in which protons and neutrons exist in levels, or shells, analogous to the shell structure that exists for electrons.


Just as certain very stable numbers of electrons (2, 10, 18, and so on) occur when a shell is filled, so there are magic numbers for nucleons.

A magic number is the number of nuclear particles in a completed shell of protons and neutrons.

For protons, the magic numbers are 2, 8, 20, 28, 50, and 82. For neutrons, the magic numbers also include 122.



A plot of number of protons versus number of neutrons for each stable nuclide yields a band of stability, the region in which stable nuclides lie.


For stable nuclides with Z ≤ 20, the ratio of neutrons to protons is between 1 and 1.1.

For stable nuclides with Z > 20, the ratio of neutrons to protons increases to about 1.5. This is believed to be due to the increasing repulsion between protons, which requires more neutrons to increase the strong nuclear force.

No stable nuclide exists for Z > 83, perhaps because the proton repulsion becomes too great.

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Predict which nucleus in each pair should be more stable and explain why.

a. astatine−210 and lead−207

b. molybdenum−91 and molybdenum−92

c. calcium−37 and calcium−42


a. Astatine−210 has 85 protons and 125 neutrons.

Lead−207 has 82 protons and 125 neutrons.

Lead−207 is more stable because it has a magic number of protons. Also, At has > 83 protons.

b. Molybdenum−91 has 42 protons and 49 neutrons.

Molybdenum−92 has 42 protons and 50 neutrons.

Molybdenum−92 is more stable because it has a magic number of neutrons.


c. Calcium−37 has 20 protons and 17 neutrons.

Calcium−42 has 20 protons and 22 neutrons.

Calcium−42 is more stable because it has an even number of neutrons. (Both have a magic number of protons.)


There are six common types of radioactive decay.

1. Alpha emissionEmission of an alpha particle from an unstable nucleus.

226 222 488 86 2Ra Rn He


2. Beta emissionEmission of a beta particle from an unstable nucleus. Beta emission is equivalent to a neutron converting to a proton.

14 14 06 7 1C N e


3. Positron emissionEmission of a positron particle from an unstable nucleus. Positron emission is equivalent to a proton converting to a neutron.

95 95 043 42 1Tc Mo e


4. Electron captureThe decay of an unstable nucleus by capture of an electron from an inner orbital of the atom. Electron capture is equivalent to a proton converting to a neutron.

40 0 4019 1 18K e Ar


5. Gamma emissionEmission from an excited nucleus of a gamma photon, corresponding to radiation with a wavelength of approximately 10−12 m. Technetium−99m is an example of a metastable nucleus; it is in an excited state and has a lifetime of ≥ 10−9 s.


6. Spontaneous fissionThe spontaneous decay of an unstable nucleus in which a heavy nucleus of mass number greater than 89 splits into lighter nuclei and energy is released.

236 96 136 192 39 53 0U Y I 4 n


Nuclides to the left of the band of stability have a neutron−to−proton ratio, N/Z, that is too large. They decay by beta emission, which reduces the N/Z ratio by converting a neutron to a proton.

Nuclides to the right of the band of stability have an N/Z ratio that is too small. These nuclides decay by either positron emission or electron capture. Either process increases the N/Z ratio by converting a proton to a neutron.


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Thallium−201 is a radioactive isotope used in the diagnosis of circulatory impairment and heart disease. How do you expect it to decay?

Thallium−201 has 81 protons and 120 neutrons. N/Z < 1.5 (too small).

Thallium−201 will decay by either electron capture or positron emission—probably electron capture, given that it is a heavy element.


Radioactive Decay SeriesA sequence in which one radioactive nucleus decays to a second, which then decays to a third, and so forth, until a stable nucleus of lead is formed.

Three radioactive decay series are found naturally: uranium−238, uranium−235, and thorium−232.


The radioactive decay series for uranium−238 ends withlead−206

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You have two samples of water, each made up of different isotopes of hydrogen: one contains hydrogen−1 and the other contains hydrogen−3.

a. Would you expect these two water samples to be chemically similar?

b. Would you expect these two water samples to be physically the same?

c. Which one of these water samples would you expect to be radioactive?


a. Yes, isotopes have similar chemical properties.

b. No, the hydrogen−3 water has more mass than the hydrogen−1 water.

c. The hydrogen−3 (tritium) water should be radioactive.


Nuclear Bombardment ReactionsNuclear bombardment reactions are not spontaneous. They involve the collision of a nucleus with another particle.

Transmutation is the change of one element into another by bombarding the nucleus of the element with nuclear particles or nuclei.


When Rutherford allowed alpha particles to collide with nitrogen nuclei, he found that a proton was ejected and oxygen was formed.

14 4 17 17 2 8 1N He O H


James Chadwick proposed the existence of the neutron based on the result of bombarding beryllium−9 with alpha particles. The product included neutral radiation we now know as neutrons.

The first radioactive nucleus produced in the laboratory was phosphorus−30.

n C He Be 1

0

12

6

4

2

9

4

n P He Al 1

0

30

15

4

2

27

13

Phosphorus−30 decays by positron emission.

e Si P 01

3014

3015


In the abbreviated notation for nuclear bombardment reactions, the starting nucleus is written first. It is followed by, within parentheses, the bombarding particle, a comma, and then the ejected particle. Finally, the product nucleus is written.


For example, for the bombardment of nitrogen−14 with an alpha particle, which leads to the ejection of a proton, the reaction is written as follows:

The abbreviated notation is

H O He N 11

178

42

147

Op He,N17

811

42

147


The following symbols are used for nuclide particles when writing them using the abbreviated notation for a nuclear bombardment reaction.

Neutron, n

Proton, p

Deuteron (hydrogen−2), d

Alpha (helium−4), α

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Na d,Mg: notation dAbbreviate 2211

2412


Sodium−22 is made by the bombardment of magnesium−24 (the most abundant isotope of magnesium) with deuterons. An alpha particle is the other product. Write the abbreviated notation for the nuclear reaction.

He Na H Mg: Reaction 42

2211

21

2412

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A neutron is produced when lithium−7 is bombarded with a proton. What product nucleus is obtained in this reaction?

n Be H Li: Reaction 10

74

11

73

Be.is product The 74


When heavy nuclei are bombarded, the bombarding particles are scattered or deflected. To produce transmutation, the bombarding particles must be accelerated.

A particle accelerator is a device used to accelerate electrons, protons, alpha particles, and other ions to very high speeds.


A cyclotron is a type of particle accelerator consisting of two hollow, semicircular metal electrodes called dees (because the shape resembles the letter D), in which charged particles are accelerated by stages to higher and higher kinetic energies.



Transuranium elements are elements with atomic numbers greater than that of uranium (Z = 92), the naturally occurring element of greatest atomic number.

In 1940, the first transuranium element was produced at the University of California, Berkeley, when element 93 (later named neptunium) was documented. It was created by bombarding uranium−238 with neutrons, producing uranium−239, which then decayed by beta emission to give neptunium−239.


Radiations and MatterRadiation from nuclear processes affects matter in part by dissipating energy in it.

The dissipation can ionize atoms and molecules and, in some cases, excite electrons in matter. When these electrons undergo transitions to their ground states, light is emitted.

Because nuclear radiations can form ions and break chemical bonds, they adversely affect biological organisms.


Radiation CountersThere are two types of devices:

ionization counters and scintillation counters.


The Geiger counter is an ionization counter used to count particles emitted by radioactive nuclei. It consists of a metal tube filled with gas, such as argon.


A scintillation counter detects nuclear radiation based on flashes of light generated in a material by the radiation. A phosphor is a substance that emits flashes of light when struck by radiation. In the scintillation counter, the flashes of light are detected by a photomultiplier tube.


The activity of a radioactive source is the number of nuclear disintegrations per unit time occurring in a radioactive material.

The curie (Ci) is a unit of activity equal to 3.700 × 1010 disintegrations per second.


Biological Effects and Radiation DosageThe rad (from radiation affected dose) is the dosage of radiation that deposits 1 × 10−2 J of energy per kilogram of tissue.


The rem is a unit of radiation dosage that is used to relate various kinds of radiation in terms of biological destruction. It equals the rad times a factor for the type of radiation, called the relative biological effectiveness (RBE).

rem = rad × RBE

Beta and gamma radiation have an RBE of about 1, neutron radiation has an RBE of about 5, and alpha radiation has an RBE of about 10.


The effect of radiation on a person depends on the dosage and the length of time of the exposure. A series of small doses have less overall effect than a large dose given all at once.

A single dose of 500 rems is fatal to most people. Detectable effects are seen at dosages as low as 30 rems. Background radiation averages about 0.1 rem per year but varies dramatically by location.


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If you are internally exposed to 10 rads of α, β, and γ radiation, which form of radiation will cause the greatest damage?

The α radiation has the highest RBE, so it will cause the greatest damage.


Rate of Radioactive DecayThe rate of radioactive decay is the number of nuclei disintegrating per unit time. It is proportional to the number of nuclei in the sample.

Rate = kNt

Nt = the number of radioactive nuclei at time, t.

k = the radioactive decay constant or rate constant for radioactive decay; it is characteristic of the nuclide.

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The thorium−234 isotope decays by emitting a beta particle. A 50.0−μg sample of thorium−234 has an activity of 1.16 Ci. What is the decay constant for thorium−234?


First, we find the number of nuclei of thorium−234.

mol 1

nuclei 10 6.022

g 232.04

mol 1 g 10 50.0

236-

tN

nuclei 10 1.298 17 Nt

Next, we convert the activity from curies to disintegrations per second.

10 disintegrations3.700 10

sRate 1.16 Ci 1 Ci

s

tionsdisintegra10 4.292 Rate 10


tNk

rate

/s10 3.31 -7 k

Finally, we use the rate equation, understanding that 1 disintegration = 1 nuclei.

nuclei 10 1.298s

tionsdisintegra 10 4.292

17

10

k


Half−life is the time it takes for one−half of the nuclei in a sample to decay.

Half−life is related to the decay constant by the following equation:

kt

0.693 1

2


After one half−life, half of the sample (0.5) remains.

After two half−lives, one−fourth of the sample (0.25) remains.

After three half−lives, one−eighth of the sample remains.

This relationship is summarized in the following equation and in the graph on the next slide.

lives-half of number where

,2

1 remaining Fraction

n

n


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Thallium−201 is used in the diagnosis of heart disease. This isotope decays by electron capture; the decay constant is 2.63 × 10−6/s. What is the half−life of thallium−201 in days?


kt

0.693

21

h 24

day 1

min 60

h 1

s 60

min 1 s 10 2.63 5 t

21

s10 2.63

0.693 6-1

2

t

days 3.05 2

1 t

?


Iodine−131 is used in the diagnosis and treatment of thyroid disorders. The half−life for the beta decay of iodine−131 is 8.07 days. a. What is the decay constant (in units

per second)?

b. What is the activity (in curies) of a 1.0−μg sample of iodine?


a.

21

0.693

tk

min 1s 60

h 1min 60

day 1

h 24 days 8.07

0.693

k

/s10 9.94 -7k


kN tRate

nuclei 10 4.745 15tN

b. mol 1

nuclei 10 6.022

g 126.90

mol 1 g 10 1.0

236-

tN

s

nuclei 10 4.72 Rate 9

nuclei 10 4.745 s

10 9.94Rate 15

-7


The rate constant is related to the fraction of nuclei remaining by the following equation:

ktN

N- ln

0

t

15 4.745 10 nucleitN

. time at remaining nuclei of fraction the is

. time at nuclei of number the is

nuclei. of number original the is

0

0

tN

N

tN

N

t

t

?


A 0.500−g sample of iodine−131 is obtained by a hospital. How much will remain after a period of one week? The half−life of this isotope is 8.07 days.


First, we find the value of k.

21

0.693

tk

day 7

week1 days 8.07

0.693

k

week

0.601 k


Next, we find the fraction of nuclei remaining.

0

ln tNkt

N

0

0.601ln 1 week

weektN

N

0

ln 0.601tN

N

remain. nuclei of 54.8%

0.548 0

N

Nt


Radioactive DatingBecause the rate of radioactive decay is constant, this rate can serve as a sort of clock for dating objects.

Carbon−14 is part of all living material. While a plant or animal is living, the fraction of carbon−14 in it remains constant due to exchange with the atmosphere. Once dead, the fraction of carbon−14 and, therefore, the rate of decay decrease. In this way, the fraction of carbon−14 present in the remains becomes a clock measuring the time since the plant’s or animal’s death.


The half−life of carbon−14 is 5730 years. Living organisms have a carbon−14 decay rate of 15.3 disintegrations per minute per gram of total carbon.

The ratio of disintegrations at time t to time 0 is equal to the ratio of nuclei at time t to time 0.

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A sample of wheat recovered from a cave was analyzed and gave 12.8 disintegrations of carbon−14 per minute per gram of carbon. What is the age of the grain?

Carbon from living material decays at a rate of 15.3 disintegrations per minute per gram of carbon. The half−life of carbon−14 is 5730 years.


Ratet = 12.8 disintegrations/min/g

Rate0 = 15.3 disintegrations/min/g

t1/2 = 5730 y

0

ln

tNN

tk

gtions/min/disintegra 15.3

gtions/min/disintegra 12.8

y10 1.48 3t

y57300.693

0.8366 ln

0

12

ln

0.693

tNN

t

0.8366 rate

rate

00

tt

N

N

?


Why do you think that carbon−14 dating is limited to materials that are less than 50,000 years old?

After 50,000 years, about ten half−lives would have passed, meaning there would be almost no carbon−14 present to detect and measure. (Only about 0.1% carbon−14 would remain.)


Applications of Radioisotopes: Chemical Analysis

A radioactive tracer is a very small amount of radioactive isotope that is added to a chemical, biological, or physical system so as to study the system.

Another example of the use of radioactive tracers is in isotope dilution, a technique to determine the quantity of a substance in a mixture or in the total volume of solution by adding a known amount of isotope to it.


Neutron activation analysis is an analysis of elements in a sample based on the conversion of stable isotopes to radioactive isotopes by bombarding a sample with neutrons.


Applications of Radioisotopes: Medical Therapy and DiagnosisRadioisotopes are used for diagnosis of many medical conditions. For example, they are used to develop images of internal body organs so those organs’ functioning can be examined. More than 100 different radioactive isotopes have been used in medicine.

Radioimmunoassay is a technique for analyzing blood and other body fluids for the presence of very small quantities of biologically active substances.


Energy of Nuclear ReactionsNuclear reactions involve changes of energy on a much larger scale than occur in chemical reactions. This energy is used in nuclear power reactors and to provide the energy for nuclear weapons.


Mass–Energy CalculationsWhen nuclei decay, they form products of lower energy. The change of energy is related to changes of mass, according to the equation derived by Einstein, E = mc2.


E = (m)c2

We can compute the change in energy for a nuclear reaction by calculating the change in mass. The change in mass must be given in kilograms to satisfy Einstein’s equation.

The masses of some elements and other particles are given in Table 20.3.


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Consider the following nuclear reaction, in which a lithium−7 nucleus is bombarded with a hydrogen nucleus to produce two alpha particles:

He2 H Li 42

11

73

amu 4.00150 He,

amu 1.00728 H,

amu 7.01436 Li,

42

11

73

What is the energy change of this reaction per gram of lithium?

Nuclear masses:


First we find the change in mass for one mole of lithium−7.

Mass of products:

2(4.00150 × 10−3 kg) = 8.00300 × 10−3 kg

Mass of reactants:

7.01436 × 10−3 kg + 1.00728 × 10−3 kg

= 8.02164 × 10−3 kg

m = –1.864 × 10−5 kg


E = (–1.864 × 10−5 kg)(2.998 × 108 m/s)2

E = –1.675 × 1012 J

LiJ/g 10 2.388 Lig

Δ 73

1173

–E

Lig 7.01436

J 10 1.675

Lig

Δ73

12

73

–E


Nuclear Binding EnergyThe equivalence of mass and energy explains the mass defect—that is, the difference between the total mass of the nucleons that make up an atom and the mass of the atom. The difference in mass is the energy holding the nucleus together.

The binding energy of a nucleus is the energy needed to break a nucleus into its individual protons and neutrons.


Both the binding energy and the mass defect are indications of the stability of the nucleus.


The maximum binding energy per nucleon occurs for nuclides with mass numbers near 50


Nuclear fission is a nuclear reaction in which a heavy nucleus splits into lighter nuclei and releases energy.

This process sometimes occurs spontaneously, as with californium−252.

n4 Mo Ba Cf 10

10642

14256

25298


In other cases, a nucleus undergoes fission after being bombarded by neutrons.

When bombarded by a neutron, uranium−238 gives three possible sets of products.

n4 Sr Xe 10

9038

14254

n3 Kr Xe 10

9436

13956

n2 Rb Xe 10

9037

14455

U n 23592

10



Nuclear fusion is a nuclear reaction in which light nuclei combine to give a more stable, heavier nucleus plus possibly several neutrons. This process releases energy.

n He H H 10

42

31

21



Nuclear Fission; Nuclear ReactorsWhen the uranium−235 nucleus splits, it releases two or three neutrons. These neutrons are absorbed by other uranium−235 nuclei, which then release even more neutrons.

A nuclear chain reaction is a self−sustaining series of nuclear fissions caused by the absorption of neutrons released from previous nuclear fissions.


Representation of a chain reaction of nuclear fissions.


To sustain a chain reaction in a sample of fissionable material, a minimum amount of the particular fissionable material is needed—the critical mass.

If the mass is much larger (a supercritical mass), the number of nuclei that split will multiply rapidly. An atomic bomb is detonated by creating a supercritical mass of fissionable material.


A nuclear fission reactor is a device that permits a controlled chain reaction of nuclear fission.

Fuel rods contain the fissionable material. They alternate with control rods that absorb neutrons.



Nuclear FusionEnergy is released when light nuclei combine into a heavier nucleus in a fusion reaction. These reactions have been observed in the laboratory using particle accelerators.

For the nuclei to react, the bombarding nuclei must have enough kinetic energy to overcome the repulsion between positive nuclei.

The energy required is not practically available at this time.

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