Holt: Modern Chemistry

Mickey Sarquis, Jerry L. Sarquis

Chapter 21

Nuclear Chemistry - all with Video Answers

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Chapter Questions

Problem 1

a. How does mass defect relate to nuclear binding energy?
b. How does binding energy per nucleon vary with mass number?
c. How does binding energy per nucleon affect the stability of a nucleus?

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Problem 2

Describe three ways in which the number of protons and the number of neutrons in a nucleus affect the
stability of the nucleus.

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Problem 3

The mass of a $_{11}^{20} \mathrm{Ne}$ atom is 19.99244 u. Calculate the atom's mass defect.

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Problem 4

The mass of a 7 Li atom is 7.01600 u. Calculate the atom's mass defect.

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Problem 5

Calculate the nuclear binding energy of one lithium-6 atom. The measured atomic mass of lithium- 6 is
6.015 u.

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Problem 6

Calculate the binding energies of the following two nuclei, and indicate which nucleus releases more
energy when formed. You will need information from the periodic table and the text.
a. atomic mass 34.988011 u, 35
b. atomic mass $22.989767 \mathrm{u},_{11}^{23} \mathrm{Na}$

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Problem 7

a. What is the binding energy per nucleon for each nucleus in the previous problem?
b. Which nucleus is more stable?

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Problem 8

The mass of 7 Li is 7.01600 u. Calculate the binding energy per nucleon for 3 Li.

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Problem 9

Calculate the neutron-proton ratios for the following
nuclides:
a. $\quad \frac{12}{6} \mathrm{C}$
b. $_{1}^{3} \mathrm{H}$
c. c. $\quad 206$ 82 $\mathrm{Pb}$
d. $\quad 134$ 50 $\mathrm{Sn}$

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Problem 10

a. Locate the nuclides in problem 9 on the graph in Figure $1.2 .$ Which ones lie within the band of
stability?
b. For the stable nuclides, determine whether their neutron-proton ratio tends toward $1 : 1$ or $1.5 : 1 .$

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Problem 11

Balance the following nuclear equations. (Hint: See Sample Problem A.)
a. $\quad$ a $3 \mathrm{K} \longrightarrow_{20}^{43} \mathrm{Ca}+$\underline{?}
b. $\quad_{92}^{233} \mathrm{U} \longrightarrow_{90}^{229} \mathrm{Th}+\underline{?}
c. $\quad_{6}^{11} \mathrm{C}+\underline{?} \longrightarrow^{11}_{5} \mathrm{B}$
d. $\quad_{7}^{13} \mathrm{N} \longrightarrow+_{0}^{1} \beta+\underline{?}

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Problem 12

Write the nuclear equation for the release of an alpha particle by 210 84 $\mathrm{P}_{0}$

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Problem 13

Write the nuclear equation for the release of a beta particle by $\underset{82}{210} \mathrm{Pb}$

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Problem 14

Where on the periodic table are most of the natural radioactive nuclides located?

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Problem 15

What changes in atomic number and mass number occur in each of the following types of radioactive
decay?
a. alpha emission
b. beta emission
c. positron emission
d. electron capture

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Problem 16

Which types of radioactive decay cause the transmutation of a nuclide? (Hint: Review the definition of transmutation.)

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Problem 17

Explain how beta emission, positron emission, and electron capture affect the neutron-proton ratio.

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Problem 18

Write the nuclear reactions that show particle conversion for the following types of radioactive decay:
a. beta emission
b. positron emission
c. electron capture

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Problem 19

Compare electrons, beta particles, and positrons.

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Problem 20

a. What are gamma rays?
b. How do scientists think gamma rays are produced?

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Problem 21

How does the half-life of a nuclide relate to the stability of the nuclide?

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Problem 22

List the three parent nuclides of the natural decay series.

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Problem 23

How are artificial radioactive isotopes produced?

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Problem 24

Neutrons are more effective for bombarding atomic nuclei than protons or alpha particles are. Why?

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Problem 25

Why are all of the transuranium elements radioactive? (Hint: See Section 1.)

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Problem 26

The half-life of plutonium- 239 is 24110 years. Of an original mass of $100 .$ g, how much plutonium-239 remains after 96440 years? (Hint: See Sample Problem B.)

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Problem 27

The half-life of thorium-22 7 is 18.72 days. How many days are required for three-fourths of a given amount of thorium-227 to decay?

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Problem 28

Exactly $\frac{1}{16}$ of a given amount of protactinium- 234 remains after 26.76 hours. What is the half-life of protactinium-2 34$?$

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Problem 29

How many milligrams of a 15.0 mg sample of radium-22 6 remain after 6396 years? The half-life of radium-226 is 1599 years.

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Problem 30

Why can a radioactive material affect photographic film even though the film is completely wrapped in
black paper?

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Problem 31

How does the penetrating ability of gamma rays compare with that of alpha particles and beta particles?

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Problem 32

How does nuclear radiation damage biological tissue?

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Problem 33

Explain how film badges, Geiger-Müller counters, and scintillation detectors are used to detect radiation and measure radiation exposure.

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Problem 34

How is the age of an object that contains a radioactive nuclide estimated?

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Problem 35

How is the fission of a uranium-235 nucleus induced?

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Problem 36

How does the fission of uranium-235 produce a chain reaction?

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Problem 37

Describe the purposes of the five major components of a nuclear power plant.

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Problem 38

Describe the reaction that produces the sun’s energy.

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Problem 39

What is one problem that must be overcome before controlled fusion reactions that produce energy are
a reality?

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Problem 40

Balance the following nuclear reactions:
a. $\quad_{93}^{239} \mathrm{Np} \longrightarrow-1^{0} \beta+\underline{?}
b. $\quad_{4}^{9} \mathrm{Be}+_{2}^{4} \mathrm{He} \longrightarrow \underline{?}$
c. $\quad \frac{32}{15} \mathrm{P}+\underline{?} \longrightarrow_{15}^{33} \mathrm{P}$
d. $\quad_{92}^{236} \mathrm{U} \longrightarrow_{36}^{94} \mathrm{Kr}+\underline{?}+3_{0}^{1} n$

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Problem 41

After 4797 years, how much of the original 0.250 g of radium-22 6 remains? The half-life of radium- 226 is 1599 years.

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Problem 42

The parent nuclide of the thorium decay series is 232 90 $\mathrm{Th}$ The first four decays are as follows: alpha emission, beta emission, beta emission, and alpha emission. Write the nuclear equations for this series of emissions.

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Problem 43

The half-life of radium- 224 is 3.66 days. What was the original mass of radium-2224 if 0.0500 g remains after 7.32 days?

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Problem 44

Calculate the neutron-proton ratios for the following
nuclides, and determine where they lie in relation to
the band of stability.
a. $\quad 235$ 92 $\mathrm{U}$
b. $\quad$ 16 $ 8$ \mathrm{O}$
c. $\quad 56$ 26 $\mathrm{Fe}$
d. $\quad 156$ 60 $\mathrm{Nd}$

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Problem 45

Calculate the binding energy per nucleon of 238 92 $\mathrm{U}$ in joules. The atomic mass of a 238
92 $\mathrm{U}$ nucleus is 238.050784 $\mathrm{u}$

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Problem 46

The energy released by the formation of a nucleus of 56 $\mathrm{Fe}$ is $7.89 \times 10^{-11} \mathrm{J} .$ Use Einstein's equation, $E=m c^{2},$ to determine how much mass (in kilograms) is lost in this process.

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Problem 47

Calculate the binding energy for one mole of deuterium atoms. The measured mass of deuterium is 2.0140 $\mathrm{u}$ .

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Problem 48

Why do we compare binding energy per nuclear particle of different nuclides instead of the total binding energy per nucleus of different nuclides?

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Problem 49

Why is the constant rate of decay of radioactive nuclei so important in radioactive dating?

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Problem 50

Which of the following nuclides of carbon is more likely to be stable? State reasons for your answer.
a. $_{6}^{11} \mathrm{C}$
b. $_{6}^{12} \mathrm{C}$

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Problem 51

Which of the following nuclides of iron is more likely to be stable? State reasons for your answer.
a. $_{26}^{56} \mathrm{C}$
b. $_{26}^{59} \mathrm{C}$

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Problem 52

Use the data shown below to determine the following:
a. the isotopes that would be best for dating ancient rocks
b. the isotopes that could be used as tracers
State reasons for your answers.
$$
\begin{array}{ll}{\text { Element }} & {\text { Half-Life }} \\ {\text { potassium- } 40} & {1.28 \times 10^{9} \mathrm{y}} \\ {\text { potassium-42 }} & {12.36 \mathrm{h}} \\ {\text { uranium-238 }} & {4.468 \times 10^{9} \mathrm{y}} \\ {\text { uranium-239 }} & {23.47 \mathrm{min}}\end{array}
$$

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Problem 53

Investigate the history of the Manhattan Project.

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Problem 54

Research the 1986 nuclear reactor accident at Chernobyl, Ukraine. What factors combined to cause the accident?

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Problem 55

Find out about the various fusion-energy research projects that are being conducted in the United States
and other parts of the world. What obstacles in finding an economical method of producing energy must still be overcome?

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Problem 56

Using the library, research the medical uses of radioactive isotopes such as cobalt-60 and technetium-99. Evaluate the benefits and risks of using radioisotopes in the diagnosis and treatment of medical conditions. Report your findings to the class.

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