Chemistry

Raymond Chang, Jason Overby

Chapter 19

Nuclear Chemistry - all with Video Answers

Educators

+ 3 more educators

Chapter Questions

Problem 1

How do nuclear reactions differ from ordinary chemical reactions?

David Collins

David Collins

Numerade Educator

Problem 2

What are the steps in balancing nuclear equations?

David Collins

Numerade Educator

Problem 3

What is the difference between $_{-1}^{0} e$ and ${ }_{-1}^{0} \beta ?$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 4

What is the difference between $_{-1}^{0} e$ and $_{-1}^{0} \beta ?$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 5

Which of the following nuclear decays produces a daughter nucleus with a higher atomic number:
(a) $\gamma,(\mathrm{b}){ }_{+1}^{0} \beta,(\mathrm{c})-{ }_{-1}^{0} \beta$
(d) $\alpha ?$

Tom Comey

Numerade Educator

Problem 6

The table here is a summary of different modes of nuclear decay. Fill in the changes in atomic number (Z), number of neutrons $(N),$ and mass number $(A)$ in each case. Use "+" sign for increase,"-" sign for decrease, and "0" for no change.

Shazia Naz

Numerade Educator

Problem 7

Complete the following nuclear equations and identify $\mathrm{X}$ in each case:
(a) ${ }_{12}^{26} \mathrm{Mg}+{ }_{1}^{1} \mathrm{p} \longrightarrow{ }_{2}^{4} \alpha+\mathrm{X}$
(b) ${ }_{27}^{59} \mathrm{Co}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{27}^{60} \mathrm{Co}+\mathrm{X}$
(c) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{36}^{94} \mathrm{Kr}+{ }_{56}^{139} \mathrm{Ba}+3 \mathrm{X}$
(d) ${ }_{24}^{53} \mathrm{Cr}+{ }_{2}^{4} \alpha \longrightarrow{ }_{0}^{1} \mathrm{n}+\mathrm{X}$
(e) ${ }_{8}^{20} \mathrm{O} \longrightarrow{ }_{9}^{20} \mathrm{~F}+\mathrm{X}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 8

Complete the following nuclear equations and identify $\mathrm{X}$ in each case:
(a) ${ }_{53}^{135} \mathrm{I} \longrightarrow{ }_{54}^{135} \mathrm{Xe}+\mathrm{X}$
(b) ${ }_{19}^{40} \mathrm{~K} \longrightarrow{ }_{-1}^{0} \beta+\mathrm{X}$
(c) ${ }_{27}^{59} \mathrm{Co}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{25}^{56} \mathrm{Mn}+\mathrm{X}$
(d) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{40}^{99} \mathrm{Zr}+{ }_{52}^{135} \mathrm{Te}+2 \mathrm{X}$.

Shazia Naz

Numerade Educator

Problem 9

State the general rules for predicting nuclear stability.

David Collins

Numerade Educator

Problem 10

What is the belt of stability?

David Collins

Numerade Educator

Problem 11

Why is it impossible for the isotope ${ }_{2}^{2}$ He to exist?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 12

Define nuclear binding energy, mass defect, and nucleon.

David Collins

Numerade Educator

Problem 13

How does Einstein's equation, $E=m c^{2},$ enable us to calculate nuclear binding energy?

David Collins

Numerade Educator

Problem 14

Why is it preferable to use nuclear binding energy per nucleon for a comparison of the stabilities of different nuclei?

David Collins

Numerade Educator

Problem 15

The radius of a uranium-235 nucleus is about $7.0 \times 10^{-3} \mathrm{pm} .$ Calculate the density of the nucleus in $\mathrm{g} / \mathrm{cm}^{3}$. (Assume the atomic mass is 235 amu.)

David Collins

Numerade Educator

Problem 16

For each pair of isotopes listed, predict which one is less stable:
(a) ${ }_{3}^{6} \mathrm{Li}$ or ${ }_{3}^{9} \mathrm{Li}$,
(b) ${ }_{11}^{23} \mathrm{Na}$ or ${ }_{11}^{25} \mathrm{Na}$
(c) ${ }_{20}^{48} \mathrm{Ca}$ or ${ }_{21}^{48} \mathrm{Sc}$.

David Collins

Numerade Educator

Problem 17

For each pair of elements listed, predict which one has more stable isotopes: (a) Co or $\mathrm{Ni}$, (b) $\mathrm{F}$ or Se, (c) Ag or Cd.

David Collins

Numerade Educator

Problem 18

In each pair of isotopes shown, indicate which one you would expect to be radioactive: (a) ${ }_{10}^{20} \mathrm{Ne}$ and ${ }_{10}^{17} \mathrm{Ne},(\mathrm{b}){ }_{20}^{40} \mathrm{Ca}$ and ${ }_{20}^{45} \mathrm{Ca},$ (c) ${ }_{42}^{95} \mathrm{Mo}$ and ${ }_{43}^{92} \mathrm{Tc},$ (d) ${ }_{80}^{195} \mathrm{Hg}$
and ${ }_{80}^{196} \mathrm{Hg},$ (e) ${ }_{83}^{209} \mathrm{Bi}$ and ${ }_{96}^{242} \mathrm{Cm}$

Anand Jangid

Numerade Educator

Problem 19

Given that
$$\mathrm{H}(g)+\mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=-436.4 \mathrm{~kJ} / \mathrm{mol}$$
calculate the change in mass (in $\mathrm{kg}$ ) per mole of $\mathrm{H}_{2}$ formed.

David Collins

Numerade Educator

Problem 20

Estimates show that the total energy output of the sun is $5 \times 10^{26} \mathrm{~J} / \mathrm{s}$. What is the corresponding mass loss in $\mathrm{kg} / \mathrm{s}$ of the sun?

David Collins

Numerade Educator

Problem 21

Calculate the nuclear binding energy (in $\mathrm{J}$ ) and the binding energy per nucleon of the following isotopes: (a) ${ }_{3}^{7} \mathrm{Li}(7.01600 \mathrm{amu}),(\mathrm{b}){ }_{17}^{35} \mathrm{Cl}(34.95952 \mathrm{amu})$.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 22

Calculate the nuclear binding energy (in $J$ ) and the binding energy per nucleon of the following isotopes:
(a) ${ }_{2}^{4} \mathrm{He}(4.0026 \mathrm{amu})$
(b) ${ }_{74}^{184} \mathrm{~W}(183.9510 \mathrm{amu})$.

Shalini Tyagi

Numerade Educator

Problem 23

Discuss factors that lead to nuclear decay.

David Collins

Numerade Educator

Problem 24

Outline the principle for dating materials using radioactive isotopes.

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 25

Fill in the blanks in the following radioactive decay series:
(a)
(b)
(c)

David Collins

Numerade Educator

Problem 26

A radioactive substance undergoes decay as follows:
$$\begin{array}{cc}\hline \text { Time (days) } & \text { Mass (g) } \\\hline 0 & 500 \\1 & 389 \\2 & 303 \\3 & 236 \\4 & 184 \\5 & 143 \\6 & 112 \\\hline\end{array}$$
Calculate the first-order decay constant and the halflife of the reaction.

Shazia Naz

Numerade Educator

Problem 27

The radioactive decay of T1-206 to $\mathrm{Pb}-206$ has a half-life of 4.20 min. Starting with $5.00 \times 10^{22}$ atoms of T1-206, calculate the number of such atoms left after $42.0 \mathrm{~min} .$

Tom Comey

Numerade Educator

Problem 28

A freshly isolated sample of ${ }^{90} \mathrm{Y}$ was found to have an activity of $9.8 \times 10^{5}$ disintegrations per minute at 1: 00 P.M. on December 3,2003 . At 2: 15 P.M. on December $17,2003,$ its activity was redetermined and found to be $2.6 \times 10^{4}$ disintegrations per minute. Calculate the half-life of ${ }^{90} \mathrm{Y}$.

Shazia Naz

Numerade Educator

Problem 29

Why do radioactive decay series obey first-order kinetics?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 30

In the thorium decay series, thorium- 232 loses a total of $6 \alpha$ particles and $4 \beta$ particles in a 10 -stage process. What is the final isotope produced?

Shazia Naz

Numerade Educator

Problem 31

Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for $1.00 \mathrm{~g}$ of the isotope to be reduced to $0.200 \mathrm{~g}$ by decay.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 32

Consider the decay series
$$\mathrm{A} \longrightarrow \mathrm{B} \longrightarrow \mathrm{C} \longrightarrow \mathrm{D}$$
where $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ are radioactive isotopes with halflives of $4.50 \mathrm{~s}, 15.0$ days, and $1.00 \mathrm{~s},$ respectively, and $\mathrm{D}$ is nonradioactive. Starting with 1.00 mole of A, and none of $\mathrm{B}, \mathrm{C},$ or $\mathrm{D},$ calculate the number of moles of $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ left after 30 days.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 33

Two radioactive isotopes $\mathrm{X}$ and $\mathrm{Y}$ have the same molar amount at $t=0 .$ A week later, there are four times as many $\mathrm{X}$ as there are $\mathrm{Y} .$ If the half-life of $\mathrm{X}$ is $2.0 \mathrm{~d}$, calculate the half-life of $\mathrm{Y}$ in days.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 34

Determine the symbol ${ }_{Z}^{A} \mathrm{X}$ for the parent nucleus whose $\alpha$ decay produces the same daughter as the ${ }_{-1}^{0} \beta$ decay of ${ }^{220} \mathrm{At} .$

Chareen Guzman

Numerade Educator

Problem 35

What is the difference between radioactive decay and nuclear transmutation?

David Collins

Numerade Educator

Problem 36

How is nuclear transmutation achieved in practice?

David Collins

Numerade Educator

Problem 37

Write balanced nuclear equations for the following reactions and identify X:
(a) $\mathrm{X}(\mathrm{p}, \alpha){ }_{6}^{12} \mathrm{C}$
(b) ${ }_{13}^{27} \mathrm{Al}(\mathrm{d}, \alpha) \mathrm{X}$
(c) $\frac{55}{25} \mathrm{Mn}(\mathrm{n}, \gamma) \mathrm{X}$.

David Collins

Numerade Educator

Problem 38

Write balanced nuclear equations for the following reactions and identify X:
(a) $\mathrm{X}(\mathrm{p}, \alpha){ }_{6}^{12} \mathrm{C}$
(b) ${ }_{13}^{27} \mathrm{Al}(\mathrm{d}, \alpha) \mathrm{X}$
(c) $\frac{55}{25} \mathrm{Mn}(\mathrm{n}, \gamma) \mathrm{X}$.

David Collins

Numerade Educator

Problem 39

Describe how you would prepare astatine- 211 , starting with bismuth-209.

David Collins

Numerade Educator

Problem 40

A long-cherished dream of alchemists was to produce gold from cheaper and more abundant elements. This dream was finally realized when ${ }_{80}^{198} \mathrm{Hg}$ was converted into gold by neutron bombardment. Write a balanced equation for this reaction.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 41

Define nuclear fission, nuclear chain reaction, and critical mass.

David Collins

Numerade Educator

Problem 42

Which isotopes can undergo nuclear fission?

David Collins

Numerade Educator

Problem 43

Explain how an atomic bomb works.

David Collins

Numerade Educator

Problem 44

Explain the functions of a moderator and a control rod in a nuclear reactor.

David Collins

Numerade Educator

Problem 45

Discuss the differences between a light water and a heavy water nuclear fission reactor. What are the advantages of a breeder reactor over a conventional nuclear fission reactor?

David Collins

Numerade Educator

Problem 46

No form of energy production is without risk. Make a list of the risks to society involved in fueling and operating a conventional coal-fired electric power plant, and compare them with the risks of fueling and operating a nuclear fission-powered electric plant.

David Collins

Numerade Educator

Problem 47

Define nuclear fusion, thermonuclear reaction, and plasma.

David Collins

Numerade Educator

Problem 48

Why do heavy elements such as uranium undergo fission while light elements such as hydrogen and lithium undergo fusion?

Shazia Naz

Numerade Educator

Problem 49

How does a hydrogen bomb work?

David Collins

Numerade Educator

Problem 50

What are the advantages of a fusion reactor over a fission reactor? What are the practical difficulties in operating a large-scale fusion reactor?

David Collins

Numerade Educator

Problem 51

Describe how you would use a radioactive iodine isotope to demonstrate that the following process is in dynamic equilibrium:
$$\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)$$

David Collins

Numerade Educator

Problem 52

Consider the following redox reaction:
$$\begin{array}{r}\mathrm{IO}_{4}^{-}(a q)+2 \mathrm{I}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\\mathrm{I}_{2}(s)+\mathrm{IO}_{3}^{-}(a q)+2 \mathrm{OH}^{-}(a q)\end{array}$$
When $\mathrm{KIO}_{4}$ is added to a solution containing iodide ions labeled with radioactive iodine- $128,$ all the radioactivity appears in $\mathrm{I}_{2}$ and none in the $\mathrm{IO}_{3}^{-}$ ion. What can you deduce about the mechanism for the redox process?

David Collins

Numerade Educator

Problem 53

Explain how you might use a radioactive tracer to show that ions are not completely motionless in crystals.

David Collins

Numerade Educator

Problem 54

Each molecule of hemoglobin, the oxygen carrier in blood, contains four Fe atoms. Explain how you would use the radioactive ${ }_{26}^{59} \mathrm{Fe}\left(t_{\frac{1}{2}}=46\right.$ days $)$ to show that the iron in a certain food is converted into hemoglobin.

Shazia Naz

Numerade Educator

Problem 55

In the chapter, we saw that the unit curie corresponds to exactly $3.70 \times 10^{10}$ nuclear disintegration per second for $1 \mathrm{~g}$ of radium. Derive this unit given that the half-life of ${ }_{88}^{226} \mathrm{Ra}$ is $1.6 \times 10^{3} \mathrm{yr}$.

Shalini Tyagi

Numerade Educator

Problem 56

Manganese- 50 (red spheres) decays via ${ }_{+1}^{0} \beta$ particle emission with a half-life of $0.282 \mathrm{~s}$. (a) Write a balanced nuclear equation for the process. (b) From the diagram shown here, determine how many halflives have elapsed. (The green spheres represent the decay product.)

Cheryl Glor

Numerade Educator

Problem 57

How does a Geiger counter work?

David Collins

Numerade Educator

Problem 58

Nuclei with an even number of protons and an even number of neutrons are more stable than those with an odd number of protons and/or an odd number of neutrons. What is the significance of the even numbers of protons and neutrons in this case?

David Collins

Numerade Educator

Problem 59

Tritium, ${ }^{3} \mathrm{H},$ is radioactive and decays by electron emission. Its half-life is $12.5 \mathrm{yr}$. In ordinary water the ratio of ${ }^{1} \mathrm{H}$ to ${ }^{3} \mathrm{H}$ atoms is $1.0 \times 10^{17}$ to 1 .
(a) Write a balanced nuclear equation for tritium decay.
(b) How many disintegrations will be observed per minute in a 1.00 -kg sample of water?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 60

(a) What is the activity, in millicuries, of a $0.500-\mathrm{g}$ sample of ${ }_{93}^{237} \mathrm{~Np} ?$ (This isotope decays by $\alpha$ -particle emission and has a half-life of $2.20 \times 10^{6}$ yr.
(b) Write a balanced nuclear equation for the decay of ${ }_{93}^{237} \mathrm{~Np}$.

Shalini Tyagi

Numerade Educator

Problem 61

The following equations are for nuclear reactions that are known to occur in the explosion of an atomic bomb. Identify X.
(a) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{140} \mathrm{Ba}+3{ }_{0}^{1} \mathrm{n}+\mathrm{X}$
(b) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{55}^{144} \mathrm{Cs}+{ }_{37}^{90} \mathrm{Rb}+2 \mathrm{X}$
(c) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{35}^{87} \mathrm{Br}+3{ }_{0}^{1} \mathrm{n}+\mathrm{X}$
(d) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{72} \mathrm{Zn}+4 \mathrm{X}$.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 62

Calculate the nuclear binding energies, in J/nucleon, for the following species: (a) ${ }^{10} \mathrm{~B}(10.0129 \mathrm{amu})$,
(b) ${ }^{11} \mathrm{~B}(11.00931 \mathrm{amu})$
(c) ${ }^{14} \mathrm{~N}(14.00307 \mathrm{amu})$
(d) ${ }^{56} \mathrm{Fe}(55.9349 \mathrm{amu})$.

David Collins

Numerade Educator

Problem 63

Write complete nuclear equations for the following processes: (a) tritium, ${ }^{3} \mathrm{H},$ undergoes $\beta$ decay;
(b) ${ }^{242}$ Pu undergoes $\alpha$ -particle emission;
(c) ${ }^{131} \mathrm{I}$ undergoes $\beta$ decay; (d) ${ }^{251} \mathrm{Cf}$ emits an $\alpha$ particle.

David Collins

Numerade Educator

Problem 64

The nucleus of nitrogen-18 lies above the stability belt. Write an equation for a nuclear reaction by which nitrogen- 18 can achieve stability.

David Collins

Numerade Educator

Problem 65

Why is strontium-90 a particularly dangerous isotope for humans?

David Collins

Numerade Educator

Problem 66

How are scientists able to tell the age of a fossil?

David Collins

Numerade Educator

Problem 67

After the Chernobyl accident, people living close to the nuclear reactor site were urged to take large amounts of potassium iodide as a safety precaution. What is the chemical basis for this action?

David Collins

Numerade Educator

Problem 68

Astatine, the last member of Group $7 \mathrm{~A},$ can be prepared by bombarding bismuth- 209 with $\alpha$ particles. (a) Write an equation for the reaction. (b) Represent the equation in the abbreviated form, as discussed in Section 19.4 .

Shazia Naz

Numerade Educator

Problem 69

To detect bombs that may be smuggled onto airplanes, the Federal Aviation Administration (FAA) will soon require all major airports in the United States to install thermal neutron analyzers. The thermal neutron analyzer will bombard baggage with low-energy neutrons, converting some of the nitrogen- 14 nuclei to nitrogen- $15,$ with simultaneous emission of $\gamma$ rays. Because nitrogen content is usually high in explosives, detection of a high dosage of $\gamma$ rays will suggest that a bomb may be present. (a) Write an equation for the nuclear process. (b) Compare this technique with the conventional X-ray detection method.

David Collins

Numerade Educator

Problem 70

Explain why achievement of nuclear fusion in the laboratory requires a temperature of about $100 \mathrm{mil}-$ lion degrees Celsius, which is much higher than that in the interior of the sun $(15$ million degrees Celsius).

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 71

Tritium contains one proton and two neutrons. There is no proton-proton repulsion present in the nucleus. Why, then, is tritium radioactive?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 72

The carbon-14 decay rate of a sample obtained from a young tree is 0.260 disintegration per second per gram of the sample. Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.186 disintegration per second per gram of the sample. What is the age of the object?

David Collins

Numerade Educator

Problem 73

The usefulness of radiocarbon dating is limited to objects no older than $50,000 \mathrm{yr}$. What percent of the carbon-14, originally present in the sample, remains after this period of time?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 74

The radioactive potassium- 40 isotope decays to argon- 40 with a half-life of $1.2 \times 10^{9}$ yr. (a) Write a balanced equation for the reaction. (b) A sample of moon rock is found to contain 18 percent potassium-40 and 82 percent argon by mass. Calculate the age of the rock in years.

Shazia Naz

Numerade Educator

Problem 75

Both barium (Ba) and radium (Ra) are members of Group $2 \mathrm{~A}$ and are expected to exhibit similar chemical properties. However, $\mathrm{Ra}$ is not found in barium ores. Instead, it is found in uranium ores. Explain.

David Collins

Numerade Educator

Problem 76

Nuclear waste disposal is one of the major concerns of the nuclear industry. In choosing a safe and stable environment to store nuclear wastes, consideration must be given to the heat released during nuclear decay. As an example, consider the $\beta$ decay of ${ }^{90} \mathrm{Sr}$ $(89.907738 \mathrm{amu})$
$${ }_{38}^{90} \mathrm{Sr} \longrightarrow{ }_{39}^{90} \mathrm{Y}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=28.1 \mathrm{yr}$$
The ${ }^{90} \mathrm{Y}$ (89.907152 amu) further decays as follows:
$${ }_{39}^{90} \mathrm{Y} \longrightarrow{ }_{40}^{90} \mathrm{Zr}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=64 \mathrm{~h}$$
Zirconium-90 (89.904703 amu) is a stable isotope.
(a) Use the mass defect to calculate the energy released (in joules) in each of the above two decays. (The mass of the electron is $5.4857 \times 10^{-4}$ amu. $)$
(b) Starting with one mole of ${ }^{90} \mathrm{Sr}$, calculate the number of moles of ${ }^{90} \mathrm{Sr}$ that will decay in a year.
(c) Calculate the amount of heat released (in kilojoules) corresponding to the number of moles of ${ }^{90} \mathrm{Sr}$ decayed to ${ }^{90} \mathrm{Zr}$ in $(\mathrm{b})$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 77

Calculate the energy released (in joules) from the following fusion reaction:
$${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}$$
The atomic masses are ${ }_{1}^{2} \mathrm{H}=2.0140 \mathrm{amu},{ }_{1}^{3} \mathrm{H}=3.01603$
$\mathrm{amu},{ }_{2}^{4} \mathrm{He}=4.00260 \mathrm{amu},{ }_{0}^{1} \mathrm{n}=1.008665 \mathrm{amu}$.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 78

As a result of being exposed to the radiation released during the Chernobyl nuclear accident, the dose of iodine-131 in a person's body is $7.4 \mathrm{mCi}$ $\left(1 \mathrm{mCi}=1 \times 10^{-3} \mathrm{Ci}\right) .$ Use the relationship rate $=\lambda N$ to calculate the number of atoms of iodine- 131 to which this radioactivity corresponds. (The halflife of ${ }^{131} \mathrm{I}$ is 8.1 d. $)$.

David Collins

Numerade Educator

Problem 79

Referring to the Chemistry in Action essay "Boron Neutron Capture Therapy" (Section 19.8 ), why is it highly unlikely that irradiated food would become radioactive?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 80

From the definition of curie, calculate Avogadro's number, given that the molar mass of ${ }^{226} \mathrm{Ra}$ is $226.03 \mathrm{~g} / \mathrm{mol}$ and that it decays with a half-life of $1.6 \times 10^{3} \mathrm{yr}$

Shazia Naz

Numerade Educator

Problem 81

As of $2011,$ elements 113 through 118 have all been synthesized. Element 113 (Uut) was formed by the alpha decay of element 115 (Uup); element 114 (Uuq) was created by bombarding ${ }^{244} \mathrm{Pu}$ with ${ }^{48} \mathrm{Ca}$; element 115 (Uup) was created by bombarding ${ }^{243} \mathrm{Am}$ with ${ }^{48} \mathrm{Ca}$; element 116 (Uuh) was created by bombarding ${ }^{248} \mathrm{Cm}$ with ${ }^{48} \mathrm{Ca}$; element 117 (Uus) was created by bombarding ${ }^{249} \mathrm{Bk}$ with ${ }^{48} \mathrm{Ca} ;$ element 118 (Uuo) was created by bombarding ${ }^{249} \mathrm{Cf}$ with ${ }^{48} \mathrm{Ca}$. Write an equation for each synthesis. Predict the chemical properties of these elements. (Before transuranium elements are given proper names, they are temporarily assigned three-letter symbols all starting with U.)

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 82

Sources of energy on Earth include fossil fuels, geothermal, gravitational, hydroelectric, nuclear fission, nuclear fusion, solar, wind. Which of these have a "nuclear origin," either directly or indirectly?

Shazia Naz

Numerade Educator

Problem 83

A person received an anonymous gift of a decorative box, which he placed on his desk. A few months later he became ill and died shortly afterward. After investigation, the cause of his death was linked to the box. The box was airtight and had no toxic chemicals on it. What might have killed the man?

Victoria Moyer

Numerade Educator

Problem 84

Identify two of the most abundant radioactive elements that exist on Earth. Explain why they are still present. (You may need to consult a handbook of chemistry.)

Shazia Naz

Numerade Educator

Problem 85

(a) Calculate the energy released when an U-238 isotope decays to Th-234. The atomic masses are $\begin{array}{llll}\text { given by } & \text { U-238: } & 238.0508 & \text { amu; } & \text { Th-234: }\end{array}$ 234.0436 amu; He-4: 4.0026 amu. (b) The energy released in (a) is transformed into the kinetic energy of the recoiling Th- 234 nucleus and the $\alpha$ particle. Which of the two will move away faster? Explain.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 86

Cobalt- 60 is an isotope used in diagnostic medicine and cancer treatment. It decays with $\gamma$ ray emission. Calculate the wavelength of the radiation in nanometers if the energy of the $\gamma$ ray is $2.4 \times 10^{-13} \mathrm{~J} /$ photon.

David Collins

Numerade Educator

Problem 87

Americium-241 is used in smoke detectors because it has a long half-life $(458 \mathrm{yr})$ and its emitted $\alpha$ particles are energetic enough to ionize air molecules. Given the schematic diagram of a smoke detector, explain how it works.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 88

The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 yr ago. To confirm its age, which of the isotopes would you choose in a radioactive dating study? The half-lives of the isotopes are ${ }^{13} \mathrm{C}: 5730 \mathrm{yr} ;{ }^{15} \mathrm{O}: 124 \mathrm{~s} ;{ }^{3} \mathrm{H}: 12.5 \mathrm{yr} .$ Assume that the activities of the isotopes were known at the time the bottle was sealed.

Shazia Naz

Numerade Educator

Problem 89

Name two advantages of a nuclear-powered submarine over a conventional submarine.

David Collins

Numerade Educator

Problem 90

In $1997,$ a scientist at a nuclear research center in Russia placed a thin shell of copper on a sphere of highly enriched uranium- $235 .$ Suddenly, there was a huge burst of radiation, which turned the air blue. Three days later, the scientist died of radiation damage. Explain what caused the accident. (Hint: Copper is an effective metal for reflecting neutrons.)

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 91

A radioactive isotope of copper decays as follows:
$${ }^{64} \mathrm{Cu} \longrightarrow{ }^{64} \mathrm{Zn}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}^{1}=12.8 \mathrm{~h}$$
Starting with $84.0 \mathrm{~g}$ of ${ }^{64} \mathrm{Cu},$ calculate the quantity of ${ }^{64}$ Zn produced after $18.4 \mathrm{~h}$.

Cheryl Glor

Numerade Educator

Problem 92

A 0.0100 -g sample of a radioactive isotope with a half-life of $1.3 \times 10^{9} \mathrm{yr}$ decays at the rate of $2.9 \times$ $10^{4} \mathrm{dpm} .$ Calculate the molar mass of the isotope.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 93

In each of the diagrams (a)- $(\mathrm{c})$, identify the isotopes involved and the type of decay process. Use the ${ }_{Z}^{A} \mathrm{X}$ symbol for each isotope.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 94

The diagram here shows part of the thorium decay series. Write a nuclear equation for each step of decay. Use the ${ }_{Z}^{A} \mathrm{X}$ symbol for each isotope.

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 95

The half-life of ${ }^{27} \mathrm{Mg}$ is $9.50 \mathrm{~min}$. (a) Initially there were $4.20 \times 10^{12}{ }^{27} \mathrm{Mg}$ nuclei present. How many ${ }^{27} \mathrm{Mg}$ nuclei are left $30.0 \mathrm{~min}$ later? (b) Calculate the ${ }^{27} \mathrm{Mg}$ activities $($ in $\mathrm{Ci})$ at $t=0$ and $t=30.0 \mathrm{~min}$. (c) What is the probability that any one ${ }^{27} \mathrm{Mg}$ nucleus decays during a 1 -s interval? What assumption is made in this calculation?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 96

The radioactive isotope ${ }^{238} \mathrm{Pu},$ used in pacemakers, decays by emitting an alpha particle with a half-life of 86 yr. (a) Write an equation for the decay process.
(b) The energy of the emitted alpha particle is $9.0 \times 10^{-13} \mathrm{~J},$ which is the energy per decay. Assuming that all the alpha particle energy is used to run the pacemaker, calculate the power output at $t=0$ and $t=10 \mathrm{yr} .$ Initially $1.0 \mathrm{mg}$ of ${ }^{238} \mathrm{Pu}$ was present in the pacemaker. (Hint: After $10 \mathrm{yr}$, the activity of the isotope decreases by 8.0 percent. Power is measured in watts or $\mathrm{J} / \mathrm{s}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 97

(a) Assuming nuclei are spherical in shape, show that its radius $(r)$ is proportional to the cube root of mass number $(A) .(\mathrm{b})$ In general, the radius of a nucleus is given by $r=r_{0} A^{\frac{1}{3}},$ where $r_{0},$ the proportionality constant, is given by $1.2 \times 10^{-15} \mathrm{~m}$. Calculate the volume of the ${ }^{238} \mathrm{U}$ nucleus.

David Collins

Numerade Educator

Problem 98

The quantity of a radioactive material is often measured by its activity (measured in curies or millicuries) rather than by its mass. In a brain scan procedure, a $70-\mathrm{kg}$ patient is injected with $20.0 \mathrm{mCi}$ of ${ }^{99 \mathrm{~m}} \mathrm{Tc},$ which decays by emitting $\gamma$ -ray photons with a half-life of $6.0 \mathrm{~h}$. Given that the $\mathrm{RBE}$ of these photons is 0.98 and only two-thirds of the photons are absorbed by the body, calculate the rem dose received by the patient. Assume all of the ${ }^{99 \mathrm{~m}} \mathrm{Tc}$ nuclei decay while in the body. The energy of a gamma photon is $2.29 \times 10^{-14} \mathrm{~J}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 99

Describe, with appropriate equations, nuclear processes that lead to the formation of the noble gases He, Ne, Ar, Kr, Xe, and Rn. (Hint: Helium is formed from radioactive decay, neon is formed from the positron emission of ${ }^{22} \mathrm{Na}$, the formation of $\mathrm{Ar}, \mathrm{Xe},$ and Rn are discussed in the chapter, and $\mathrm{Kr}$ is produced from the fission of ${ }^{235} \mathrm{U} .$ )

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 100

Modern designs of atomic bombs contain, in addition to uranium or plutonium, small amounts of tritium and deuterium to boost the power of explosion. What is the role of tritium and deuterium in these bombs?

David Collins

Numerade Educator

Problem 101

What is the source of heat for volcanic activities on Earth?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 102

Alpha particles produced from radioactive decays eventually pick up electrons from the surroundings to form helium atoms. Calculate the volume (mL) of He collected at STP when $1.00 \mathrm{~g}$ of pure ${ }^{226} \mathrm{Ra}$ is stored in a closed container for 100 yr. (Hint: Focusing only on half-lives that are short compared to 100 years and ignoring minor decay schemes in Table $19.3,$ first show that there are $5 \alpha$ particles generated per ${ }^{226}$ Ra decay to $\left.{ }^{206} \mathrm{~Pb} .\right)$

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 103

In 2006 , an ex-KGB agent was murdered in London. Subsequent investigation showed that the cause of death was poisoning with the radioactive isotope ${ }^{210} \mathrm{Po},$ which was added to his drinks/food.
(a) ${ }^{210} \mathrm{Po}$ is prepared by bombarding ${ }^{209} \mathrm{Bi}$ with neutrons. Write an equation for the reaction. (b) Who discovered the element polonium? (Hint: See an Internet source such as Webelements.com.) (c) The half-life of ${ }^{210} \mathrm{Po}$ is $138 \mathrm{~d}$. It decays with the emission of an $\alpha$ particle. Write an equation for the decay process.
(d) Calculate the energy of an emitted $\alpha$ particle. Assume both the parent and daughter nuclei to have zero kinetic energy. The atomic masses are ${ }^{210} \mathrm{Po}(209.98285 \mathrm{amu})$ ${ }^{206} \mathrm{~Pb}(205.97444 \mathrm{amu}),{ }_{2}^{4} \alpha(4.00150 \mathrm{amu}) .(\mathrm{e})$ Inges-
tion of $1 \mu \mathrm{g}$ of ${ }^{210} \mathrm{Po}$ could prove fatal. What is the
total energy released by this quantity of ${ }^{210} \mathrm{Po} ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 104

An electron and a positron are accelerated to nearly the speed of light before colliding in a particle accelerator. The ensuing collision produces an exotic particle having a mass many times that of a proton. Does the result violate the law of conservation of mass?

Shazia Naz

Numerade Educator

Problem 105

The volume of an atom's nucleus is $1.33 \times 10^{-42} \mathrm{~m}^{3}$. The nucleus contains 110 neutrons. Identify the atom and write the symbol of the atom as ${ }_{Z}^{A} \mathrm{X} .$ (Hint: See Problem 19.97.)

David Collins

Numerade Educator

Problem 106

In the chapter, we learned to calculate the nuclear binding energy, which pertains to the stability of a particular nucleus. It is also possible to estimate the binding energy of a single nucleon (neutron or proton) to the remainder of the nucleus. (a) From the following nuclear equation and nuclear masses, calculate the binding energy of a single neutron:
$${ }_{7}^{14} \mathrm{~N} \longrightarrow{ }_{7}^{13} \mathrm{~N}+{ }_{0}^{1} \mathrm{n}$$
(Useful information: ${ }_{7}^{14} \mathrm{~N}: 14.003074 \mathrm{amu} ;{ }_{7}^{13} \mathrm{~N}:$
13.005738 amu; ${ }_{0}^{1} \mathrm{n}: 1.00866$ amu. $)$ (b) By a similar procedure, we can calculate the binding energy of a single proton according to the equation
$${ }_{7}^{14} \mathrm{~N} \longrightarrow{ }_{6}^{13} \mathrm{C}+{ }_{1}^{1} \mathrm{p}$$
(Useful information: ${ }_{6}^{13} \mathrm{C}: 13.003355 \mathrm{amu} ;{ }_{1}^{1} \mathrm{p}:$
1.00794 amu.) Comment on your results.

Susan Hallstrom

Susan Hallstrom

Numerade Educator