Fundamentals of General, Organic, and Biological Chemistry

John McMurry, David S. Ballantine, Carl A. Hoeger

Chapter 11

Nuclear Chemistry - all with Video Answers

Educators

Chapter Questions

Problem 1

High levels of radioactive radon- $222\left(\begin{array}{c}222 \\ 86\end{array} \mathrm{Rn}\right)$ have been found in many homes built on radium-containing rock, leading to the possibility of health hazards. What product results from $\alpha$ emission by radon- $222 ?$

John Nicolle

John Nicolle

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Problem 2

What isotope of radium (Ra) is converted into radon-222 by $\alpha$ emission?

John Nicolle

Numerade Educator

Problem 3

Strontium- 89 is a short-lived $\beta$ emitter often used in the treatment of bone tumors. Write a nuclear equation for the decay of strontium- $89 .$

John Nicolle

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Problem 4

Write nuclear equations for the formation of each of the following nuclides by $\beta$ emission.
(a) ${ }_{2}^{3} \mathrm{He}$
(b) ${ }_{83}^{210} \mathrm{Bi}$
(c) ${ }_{10}^{20} \mathrm{Ne}$

John Nicolle

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Problem 5

Write nuclear equations for positron emission from the following radioisotopes:
(a) ${ }_{20}^{38} \mathrm{Ca}$
(b) ${ }_{54}^{118} \mathrm{Xe}$
(c) ${ }_{37}^{79} \mathrm{Rb}$

John Nicolle

Numerade Educator

Problem 6

Write nuclear equations for the formation of the following radioisotopes by electron capture:
(a) ${ }_{29}^{62} \mathrm{Cu}$
(b) ${ }_{49}^{110} \operatorname{In}$
(c) ${ }_{35}^{81} \mathrm{Br}$

John Nicolle

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Problem 7

The red arrow in the graph (see margin) indicates the changes that occur in the nucleus of an atom during a nuclear reaction. Identify the isotopes involved as product and reactant, and name the type of decay process.

John Nicolle

Numerade Educator

Problem 8

The half-life of carbon-14, an isotope used in archaeological dating, is 5730 years. What percentage of ${ }_{6}^{14} \mathrm{C}$ remains in a sample estimated to be 17,000 years old?

John Nicolle

Numerade Educator

Problem 9

A $1.00 \mathrm{~mL}$ sample of red blood cells containing chromium- 51 as a tracer was injected into a patient. After several hours, a $5.00 \mathrm{~mL}$ sample of blood was drawn and its activity compared to the activity of the injected tracer sample. If the collected sample activity was $0.10 \%$ of the original tracer, calculate the total blood volume of the patient (see the Chemistry in Action "Medical Uses of Radioactivity," p. 372 ).

John Nicolle

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Problem 10

The first four radioisotopes in Table 11.3 are included in Figure 11.2 . They all undergo $\beta$ decay.
(a) Locate the position of these radioisotopes in Figure 11.2 .
(b) Write the balanced decay reactions for these radioisotopes, and locate the position of the product nuclei in Figure 11.2 .

Jesse Leeder

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Problem 11

What is the half-life of the radionuclide that shows the decay curve indicated in the graph (see margin)?

John Nicolle

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Problem 12

A $\beta$ -emitting radiation source gives 250 units of radiation at a distance of $4.0 \mathrm{~m}$. At what distance does the radiation drop to one-tenth its original value?

Susan Hallstrom

Susan Hallstrom

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Problem 13

A solution of selenium- $75,$ a radioisotope used in the diagnosis of pancreatic disease, is found just prior to administration to have an activity of $1.62 \times 10^{6} \mathrm{~Bq} / \mathrm{mL}$. If 3.98 $\mathrm{mL}$ were delivered intravenously to the patient, what dose of Se- 75 (in $\mu \mathrm{Ci}$ ) did the patient receive?

John Nicolle

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Problem 14

A typical chest $X$ ray exposes a patient to an effective dose of $0.02 \mathrm{mSv}$. How many rem is this, and how many chest X rays would a patient have to receive before biological effects would be observed? (The limit from Table 11.6 is $>0.25$ Sv.)

John Nicolle

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Problem 15

What isotope results from $\alpha$ decay of the americium- 241 in smoke detectors?

John Nicolle

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Problem 16

The element berkelium, first prepared at the University of California at Berkeley in 1949 , is made by $\alpha$ bombardment of ${ }^{241}$ 95 $\mathrm{Am}$. Two neutrons are also produced during the reaction. What isotope of berkelium results from this transmutation? Write a balanced nuclear equation.

John Nicolle

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Problem 17

Write a balanced nuclear equation for the reaction of argon- 40 with a proton:
$$
{ }_{18}^{40} \mathrm{Ar}+{ }_{1}^{1} \mathrm{H} \longrightarrow ?+{ }_{0}^{1} \mathrm{n}
$$

John Nicolle

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Problem 18

What other isotope besides tellurium- 137 is produced by nuclear fission of uranium- 235 ?
$$
{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{52}^{137} \mathrm{Te}+2{ }_{0}^{1} \mathrm{n}+?
$$

John Nicolle

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Problem 19

Uranium- 238 is not used as a nuclear power source because it does not undergo nuclear fission. However, it can absorb a neutron and then undergo a series of $\beta$ decays to produce plutonium- $239,$ which is fissionable and can also be used as a nuclear fuel. Complete the following nuclear reaction:
$$
{ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} n \longrightarrow ? ? \stackrel{\beta}{\longrightarrow} ? ? \stackrel{\beta}{\longrightarrow}{ }_{94}^{239} \mathrm{Pu}
$$

John Nicolle

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Problem 20

One of the possible reactions for nuclear fusion involves the collision of 2 deuterium nuclei. Complete the reaction by identifying the missing particle:

John Nicolle

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Problem 21

Magnesium- 28 decays by $\beta$ emission to give aluminum-28. If yellow spheres represent ${ }_{12}^{28} \mathrm{Mg}$ atoms and blue spheres represent ${ }_{13}^{28} \mathrm{Al}$ atoms, how many half-lives have passed in the following sample?

Rakesh Singhi

Numerade Educator

Problem 22

Write a balanced nuclear equation to represent the decay reaction described in Problem 11.21 .

Daphne G. Moore

Daphne G. Moore

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Problem 23

Refer to Figure 11.4 and then make a drawing similar to those in Problem 11.21 representing the decay of a sample of ${ }_{12}^{28} \mathrm{Mg}$ after approximately four half-lives have passed.

Babita Kumari

Numerade Educator

Problem 24

Write the symbol of the isotope represented by the following drawing. Blue spheres represent neutrons and red spheres represent protons. Based on Figure $11.2,$ would you expect this to be a stable or an unstable isotope?

UO

Umut Ozuguzel

Texas Tech University

Problem 25

Shown in the following graph is a portion of the decay series for plutonium- $241\left({ }_{94}^{241} \mathrm{Pu}\right)$. The series has two kinds of arrows: shorter arrows pointing right and longer arrows pointing left. Which arrow corresponds to an $\alpha$ emission, and which to a $\beta$ emission? Explain.

David Roberts

Numerade Educator

Problem 26

Identify and write the symbol for each of the five nuclides in the decay series shown in Problem $11.25 .$

Jorge Villanueva

Jorge Villanueva

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Problem 27

Identify the isotopes involved, and tell the type of decay process occurring in the following nuclear reaction:

Ronald Prasad

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Problem 28

What is the half-life of the radionuclide that shows the following decay curve?

John Nicolle

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Problem 29

What is wrong with the following decay curve? Explain.

Chengyu Li

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Problem 30

What does it mean to say that a substance is radioactive?

John Nicolle

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Problem 31

Describe how $\alpha$ radiation, $\beta$ radiation, $\gamma$ radiation, positron emission, and electron capture differ.

John Nicolle

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Problem 32

List three of the five ways in which a nuclear reaction differs from a chemical reaction.

John Nicolle

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Problem 33

What happens when ionizing radiation strikes an atom in a chemical compound?

John Nicolle

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Problem 34

How does ionizing radiation lead to cell damage?

John Nicolle

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Problem 35

What are the main sources of background radiation?

John Nicolle

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Problem 36

How can a nucleus emit an electron during $\beta$ decay when there are no electrons present in the nucleus to begin with?

John Nicolle

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Problem 37

What is the difference between an $\alpha$ particle and a helium atom?

John Nicolle

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Problem 38

What does it mean to say that a nuclear equation is balanced?

John Nicolle

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Problem 39

What are transuranium elements, and how are they made? Are they stable or unstable?

John Nicolle

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Problem 40

What happens to the mass number and atomic number of an atom that emits an $\alpha$ particle? A $\beta$ particle?

John Nicolle

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Problem 41

What happens to the mass number and atomic number of an atom that emits a $\gamma$ ray? A positron?

John Nicolle

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Problem 42

How does nuclear fission differ from normal radioactive decay?

John Nicolle

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Problem 43

What characteristic of uranium- 235 fission causes a chain reaction?

John Nicolle

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Problem 44

What products result from radioactive decay of the following $\beta$ emitters?
(a) ${ }_{16}^{35} \mathrm{~S}$
(b) ${ }_{10}^{24} \mathrm{Ne}$
(c) ${ }_{38}^{90} \mathrm{Sr}$

Ronald Prasad

Numerade Educator

Problem 45

What radioactive nuclides will produce the following products following $\alpha$ decay?
(a) ${ }_{76}^{186} \mathrm{Os}$
(b) ${ }_{85}^{204} \mathrm{At}$
(c) ${ }_{94}^{241} \mathrm{Pu}$

John Nicolle

Numerade Educator

Problem 46

Identify the starting radioisotopes needed to balance each of these nuclear reactions:
(a) $?+{ }_{2}^{4} \mathrm{He} \longrightarrow{ }_{49}^{113} \mathrm{In}$
(b) $?+{ }_{2}^{4} \mathrm{He} \longrightarrow{ }_{7}^{13} \mathrm{~N}+{ }_{0}^{1} \mathrm{n}$

John Nicolle

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Problem 47

Identify the radioisotope product needed to balance each of these nuclear reactions:
(a) ${ }_{11}^{26} \mathrm{Na} \longrightarrow ?+{ }_{-1}^{0} \mathrm{e}$
(b) ${ }_{83}^{212} \mathrm{Bi} \longrightarrow ?+{ }_{2}^{4} \mathrm{He}$

John Nicolle

Numerade Educator

Problem 48

Balance the fulluwing equations for the nuclear fission of ${ }_{92}^{235} \mathrm{U}$ :
(a) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{72} \mathrm{Zn}+?{ }_{0}^{1} \mathrm{n}$
(b) ${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{35}^{87} \mathrm{Br}+?+3{ }_{0}^{1} \mathrm{n}$

John Nicolle

Numerade Educator

Problem 49

Complete the following nuclear equations and identify each as $\alpha$ decay, $\beta$ decay, positron emission, or electron capture:
(a) ${ }_{50}^{126} \mathrm{Sn} \longrightarrow ?+{ }_{51}^{126} \mathrm{Sb}$
(b) ${ }_{88}^{210} \mathrm{Ra} \longrightarrow ?+{ }_{86}^{206} \mathrm{Rn}$
(c) ${ }_{36}^{76} \mathrm{Kr}+? \longrightarrow{ }_{35}^{76} \mathrm{Br}$

Rakesh Singhi

Numerade Educator

Problem 50

For centuries, alchemists dreamed of turning base metals into gold. The dream finally became reality when it was shown that mercury-198 can be converted into gold-198 when bombarded by neutrons. What small particle is produced in addition to gold-198? Write a balanced nuclear equation for the reaction.

John Nicolle

Numerade Educator

Problem 51

Cobalt-60 (half-life $=5.3$ years ) is used to irradiate food, to treat cancer, and to disinfect surgical equipment. It is produced by irradiation of cobalt- 59 in a nuclear reactor. It decays to nickel-60. Write nuclear equations for the formation and decay reactions of cobalt- 60 .

John Nicolle

Numerade Educator

Problem 52

Bismuth- 212 attaches readily to monoclonal antibodies and is used in the treatment of various cancers. This bismuth- 212 is formed after the parent isotope undergoes a decay series consisting of four $\alpha$ decays and one $\beta$ decay (the decays could be in any order). What is the parent isotope for this decay series?

John Nicolle

Numerade Educator

Problem 53

Meitnerium-266 $\left({ }_{109}^{266} \mathrm{Mt}\right)$ was prepared in 1982 by bombardment of bismuth-209 atoms with iron- 58 . What other product must also have been formed? Write a balanced nuclear equation for the transformation.

John Nicolle

Numerade Educator

Problem 54

What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?

John Nicolle

Numerade Educator

Problem 55

How many half lives must pass for the mass of a radioactive sample to decrease to $35 \%$ of the original mass? To $10 \%$ ?

John Nicolle

Numerade Educator

Problem 56

Selenium-75, a $\beta$ emitter with a half-life of 120 days, is used medically for pancreas scans.
(a) Approximately how long would it take for a $0.050 \mathrm{~g}$ sample of selenium- 75 to decrease to $0.010 \mathrm{~g}$ ?
(b) Approximately how much selenium- 75 would remain from a $0.050 \mathrm{~g}$ sample that has been stored for one year? (Hint: How many half-lives are in one year?)

John Nicolle

Numerade Educator

Problem 57

Approximately how long would it take a sample of selenium- 75 to lose $75 \%$ of its radioactivity? To lose $99 \%$ ? (See Problem 11.56.)

John Nicolle

Numerade Educator

Problem 58

The half-life of mercury-197 is 64.1 hours. If a patient undergoing a kidney scan is given 5.0 ng of mercury-197, how much will remain after 7 days? After 30 days?

John Nicolle

Numerade Educator

Problem 59

Gold-198, a $\beta$ emitter used to treat leukemia, has a half-life of 2.695 days. The standard dosage is about $37 \mathrm{MBq} / \mathrm{kg}$ body weight.
(a) What is the product of the $\beta$ emission of gold-198?
(b) How long does it take a $11.1 \times 10^{8} \mathrm{~Bq}$ sample of gold198 to decay so that only $1.39 \times 10^{8}$ Bq remains?
(c) How many becquerels are required in a single dosage administered to a $70.0 \mathrm{~kg}$ adult?

John Nicolle

Numerade Educator

Problem 60

Describe how a Geiger counter works.

John Nicolle

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Problem 61

Describe how a film badge works.

John Nicolle

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Problem 62

Describe how a scintillation counter works.

John Nicolle

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Problem 63

Why are rems the preferred units for measuring the health effects of radiation?

John Nicolle

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Problem 64

Approximately what amount (in Sv) of short-term exposure to radiation produces noticeable effects in humans?

John Nicolle

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Problem 65

Match each unit in the left column with the property being measured in the right column:
1. curie
(a) Ionizing intensity of radiation
2. rem
(b) Amount of tissue damage
3. rad
(c) Number of disintegrations per second
4. roentgen
(d) Amount of radiation per gram of tissue

John Nicolle

Numerade Educator

Problem 66

Technetium- $99 m$ is used for radioisotope-guided surgical biopsies of certain bone cancers. A patient must receive an injection of $10.4 \times 10^{8} \mathrm{~Bq}$ of technetium- $99 \mathrm{~m}$ 6-12 hours before surgery. If the activity of the solution is $5.55 \times 10^{8} \mathrm{~Bq} / \mathrm{mL},$ what volume should be injected?

Ren Jie Tuieng

Numerade Educator

Problem 67

Sodium- 24 is used to study the circulatory system and to treat chronic leukemia. It is administered in the form of saline $(\mathrm{NaCl})$ solution, with a therapeutic dosage of $6.66 \mathrm{MBq} / \mathrm{kg}$ body weight.
(a) What dosage (in MBq) would be administered to a $68 \mathrm{~kg}$ adult patient?
(b) How many milliliters of a $2.40 \times 10^{8} \mathrm{~Bq} / \mathrm{mL}$ solution are needed to treat a $68 \mathrm{~kg}$ adult?

John Nicolle

Numerade Educator

Problem 68

A selenium- 75 source is producing $3 \mathrm{~Sv}$ at a distance of $2.0 \mathrm{~m} ?$
(a) What is its intensity at $16 \mathrm{~m}$ ?
(b) What is its intensity at $25 \mathrm{~m}$ ?

John Nicolle

Numerade Educator

Problem 69

If a radiation source has an intensity of $6.50 \mathrm{~Sv}$ at $1.0 \mathrm{~m},$ what distance is needed to decrease the intensity of exposure to below $0.25 \mathrm{~Sv}$, the level at which no effects are detectable?

John Nicolle

Numerade Educator

Problem 70

Film badge dosimeters typically include filters to target specific types of radiation. A film badge is constructed that includes a region containing a tin foil filter, a region containing a plastic film filter, and a region with no filter. Which region monitors exposure to $\alpha$ -radiation? Which monitors exposure to $\beta$ -radiation? Which monitors $\gamma$ -radiation? Explain.

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 71

Some dried beans with a ${ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}$ ratio one-eighth of the current value are found in an old cave. How old are the beans?

John Nicolle

Numerade Educator

Problem 72

Harmful chemical spills can often be cleaned up by treatment with another chemical. For example, a spill of $\mathrm{H}_{2} \mathrm{SO}_{4}$ might be neutralized by addition of $\mathrm{NaHCO}_{3}$. Why is it that the harmful radioactive wastes from nuclear power plants cannot be cleaned up as easily?

Rakesh Singhi

Numerade Educator

Problem 73

Why is a scintillation counter or Geiger counter more useful for determining the existence and source of a new radiation leak than a film badge?

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 74

A Geiger counter records an activity of 28 counts per minute (cpm) when located at a distance of $10 \mathrm{~m} .$ What will be the activity (in $\mathrm{cpm}$ ) at a distance of $5 \mathrm{~m}$ ?

Bin Chen

Numerade Educator

Problem 75

Most of the stable isotopes for elements lighter than Ca-40 have equal numbers of protons and neutrons in the nucleus. What would be the most probable decay mode for an isotope that had more protons than neutrons? More neutrons than protons?

John Nicolle

Numerade Educator

Problem 76

Technetium-99m, used for brain scans and to monitor heart function, is formed by decay of molybdenum-99.
(a) By what type of decay does ${ }^{99}$ Mo produce ${ }^{99 m} \mathrm{Tc}$ ?
(b) Molybdenum-99 is formed by neutron bombardment of a natural isotope. If one neutron is absorbed and there are no other by-products of this process, from what isotope is ${ }^{99}$ Mo formed?

John Nicolle

Numerade Educator

Problem 77

The half-life of technetium-99m (Problem 11.76) is 6.01 hours. If a sample with an initial activity of $5.55 \times 10^{5} \mathrm{~Bq}$ is injected into a patient, what is the activity in 24 hours, assuming that none of the sample is excreted?

John Nicolle

Numerade Educator

Problem 78

Plutonium- 238 is an $\alpha$ emitter used to power batteries for heart pacemakers.
(a) Write the balanced nuclear equation for this emission.
(b) Why is a pacemaker battery enclosed in a metal case before being inserted into the chest cavity?

Rakesh Singhi

Numerade Educator

Problem 79

Sodium-24, a beta-emitter used in diagnosing circulation problems, has a half-life of 15 hours.
(a) Write the balanced nuclear equation for this emission.
(b) What fraction of sodium-24 remains after 50 hours?

John Nicolle

Numerade Educator

Problem 80

High levels of radioactive fallout after the 1986 accident at the Chernobyl nuclear power plant in what is now Ukraine resulted in numerous miscarriages in humans and many instances of farm animals born with severe defects. Why are embryos and fetuses particularly susceptible to the effects of radiation?

Nicholas Mogoi

Numerade Educator

Problem 81

Iodine-131 is a radioactive isotope used to treat thyroid conditions.
(a) What is the mode of radioactive decay for I-131? Write a balanced nuclear reaction to illustrate.
(b) The half-life of I-131 is eight days. What fraction of I-131 remains after four weeks? After eight weeks?

John Nicolle

Numerade Educator

Problem 82

What are the main advantages of nuclear fission relative to nuclear fusion as an energy source? What are the drawbacks?

John Nicolle

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Problem 83

Although turning lead into gold in a nuclear reactor is technologically feasible (Problem 11.50 ), it is not economical. It is far easier to convert gold into lead. The process involves a series of neutron bombardments, and can be summarized as
$$
{ }_{79}^{197} \mathrm{Au}+?{ }_{0}^{1} n \longrightarrow{ }_{82}^{204} \mathrm{~Pb}+?{ }_{-1}^{0} e
$$
How many neutrons and $\beta$ particles are involved?

Rakesh Singhi

Numerade Educator

Problem 84

Balance the following transmutation reactions:
(a) ${ }_{99}^{253} \mathrm{Es}+? \longrightarrow \frac{256}{101} \mathrm{Md}+{ }_{0}^{1} \mathrm{n}$
(b) ${ }_{98}^{250} \mathrm{Cf}+{ }_{5}^{11} \mathrm{~B} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}$

John Nicolle

Numerade Educator

Problem 85

Boron is used in control rods for nuclear reactors because it can absorb neutrons to keep a chain reaction from becoming supercritical, and decays by emitting $\alpha$ particles (i.e., a He-4 nucleus). Balance the equation by supplying the missing product:
$$
{ }_{5}^{10} \mathrm{~B}+{ }_{0}^{1} \mathrm{n} \longrightarrow ?+{ }_{2}^{4} \mathrm{He}
$$

John Nicolle

Numerade Educator

Problem 86

Thorium-232 decays by a 10-step series, ultimately yielding lead-208. How many $\alpha$ particles and how many $\beta$ particles are emitted?

Ronald Prasad

Numerade Educator

Problem 87

Californium-246 is formed by bombardment of uranium-238 atoms. If four neutrons are formed as by-products, what particle is used for the bombardment?

John Nicolle

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Problem 88

The most recently discovered element 117 (Ununseptium, Uus) was synthesized by nuclear transmutation reactions in which berkelium- 249 was bombarded with calcium- 48 . Two isotopes of Uus were identified:
$$
\begin{array}{l}
{ }_{20}^{48} \mathrm{Ca}+{ }_{97}^{249} \mathrm{Bk} \longrightarrow{ }_{117}^{294} \mathrm{Uus}+?{ }_{0}^{1} n \\
{ }_{20}^{88} \mathrm{Ca}+{ }_{97}^{249} \mathrm{Bk} \longrightarrow{ }_{117}^{293} \mathrm{Uus}+?{ }_{0}^{1} n
\end{array}
$$
How many neutrons are produced in each reaction?

John Nicolle

Numerade Educator

Problem 89

One way to demonstrate the dose factor of ionizing radiation (penetrating distance $\times$ ionizing energy) is to think of radiation as cookies. Imagine that you have four cookiesan $\alpha$ cookie, a $\beta$ cookie, a $\gamma$ cookie, and a neutron cookie. Which one would you eat, which would you hold in your hand, which would you put in your pocket, and which would you throw away? Explain your reasoning.

John Nicolle

Numerade Educator

Problem 90

One approach for treating cancerous tumors is Boron Neutron Capture Therapy (BNCT). Perform an internet search on BNCT and answer the following:
(a) How is boron introduced to the tumors?
(b) How are neutrons generated and directed to the tumor site?
(c) What nuclear reactions occur? What are the products of the nuclear reaction, and why is this a particularly effective treatment for tumors?

Sharfa Farzandh

Sharfa Farzandh

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Problem 91

The nuclear disasters at the Chernobyl nuclear power plant disaster in 1986 and in Fukushima in 2011 resulted in significant releases of radioactive nuclear materials into the environment. Perform a web search to find information about one or both of these disasters and answer the following questions:
(a) What was the primary nuclear fuel? What other radioactive materials besides the fuel were released during the accident?
(b) What is the estimated amount of radioactive material released into the environment, and in what form was it released?
(c) How much additional radiation exposure would be expected for a person living near the power plant? How much additional radiation exposure would be expected for someone living at a considerable distance from the plant? How do these levels compare to the average background radiation dose for the average person? Express your answer as a percentage.

Carson Merrill

Numerade Educator