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Chemistry

Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson

Chapter 21

Nuclear Chemistry

Educators


Problem 1

Write the following isotopes in hyphenated form (e.g." "carbon-14")
(a) 24
(b) 11
(b) 29
(c) $\frac{73}{13} \mathrm{Kr}$
(d) $\frac{73}{36} \mathrm{Kr}$
(d) $\frac{194}{77} \mathrm{Ir}$

Rikhil M.
Numerade Educator

Problem 2

Write the following isotopes in nuclide notation (e.g., $\stackrel{n 14}{6} \mathrm{C}^{\prime \prime} )$
(a) oxygen-14
(b) copper-70
(c) tantalum-175
(d) francium-217

Aadit S.
Numerade Educator

Problem 3

For the following isotopes that have missing information, fill in the missing information to complete the
notation
(a) $\frac{34}{14} \mathrm{X}$
(b) $\quad \stackrel{36}{\mathrm{X}} \mathrm{P}$
(c) $\quad \mathrm{x}^{57} \mathrm{Mn}$
(d) $\frac{121}{56} \mathrm{X}$

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Problem 4

For each of the isotopes in Exercise 21.1, determine the numbers of protons, neutrons, and electrons in a
neutral atom of the isotope.

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Problem 5

Write the nuclide notation, including charge if applicable, for atoms with the following characteristics:
(a) 25 protons, 20 neutrons, 24 electrons
(b) 45 protons, 24 neutrons, 43 electrons
(c) 53 protons, 89 neutrons, 54 electrons
(d) 97 protons, 146 neutrons, 97 electrons

Rikhil M.
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Problem 6

Calculate the density of the 24 Mg nucleus in $\mathrm{g} / \mathrm{mL}$ , assuming that the typical nuclear diameter of $1 \times$ $10^{-13} \mathrm{cm}$ and is spherical in shape.

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Problem 7

What are the two principal differences between nuclear reactions and ordinary chemical changes?

Rikhil M.
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Problem 8

The mass of the atom 11 $\mathrm{Na}$ is 22.9898 amu.
(a) Calculate its binding energy per atom in millions of electron volts.
(b) Calculate its binding energy per nucleon.

Aadit S.
Numerade Educator

Problem 9

Which of the following nuclei lie within the band of stability shown in Figure 21.2$?$
(a) chlorine-37
(b) calcium- 40
(c) 204 $\mathrm{Bi}$
(d) 56 $\mathrm{Fe}$
(e) $^{206} \mathrm{Pe}$
(f) $^{211} \mathrm{P} \mathrm{b}$
(g) 222 $\mathrm{Rn}$
(h) carbon-14

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Problem 10

Which of the following nuclei lie within the band of stability shown in Figure 21.2$?$
(a) argon-40
(b) oxygen-16
(c) $^{122} \mathrm{Ba}$
(d) $^{58} \mathrm{Ni}$
(e) $^{205} \mathrm{Tl}$
(f) $^{210} \mathrm{T} 1$
(g) 226 $\mathrm{Ra}$
(h) magnesium- 24

Aadit S.
Numerade Educator

Problem 11

Write a brief description or definition of each of the following:
(a) nucleon
(b) $\alpha$ particle
(c) $\beta$ particle
(d) positron
(e) positron
(f) $\mathrm{Y}$ ray
(f) nuclide
(g) mass number
(g) atomic number

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Problem 12

Which of the various particles (? particles, ? particles, and so on) that may be produced in a nuclear reaction are actually nuclei?

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Problem 13

Complete each of the following equations by adding the missing species:
(a) $\frac{27}{13} \mathrm{Al}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{0}^{1} \mathrm{n}$
(b) $239 \mathrm{Pu}+? \longrightarrow_{96}^{242} \mathrm{Cm}+_{0}^{1} \mathrm{n}$
(c) $14 \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{1}^{1} \mathrm{H}$
(d) $\frac{235}{92} \mathrm{U} \longrightarrow ?+\frac{135}{55} \mathrm{Cs}+4_{0}^{1} \mathrm{n}$

Rikhil M.
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Problem 14

Complete each of the following equations:
(a) $\frac{7}{3} \mathrm{Li}+? \longrightarrow 2_{2}^{4} \mathrm{He}$
(b) $14 \mathrm{C} \longrightarrow^{14} \mathrm{N}+?$
(c) $27 \mathrm{Al}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{0}^{1} \mathrm{n}$
(d) $_{96}^{250} \mathrm{Cm} \longrightarrow 2+_{38}^{98} \mathrm{Sr}+4_{0}^{1} \mathrm{n}$

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Problem 15

Write a balanced equation for each of the following nuclear reactions:
(a) the production of 17 $\mathrm{O}$ from $^{14} \mathrm{N}$ by $\alpha$ particle bombardment
(b) the production of $^{14} \mathrm{C}$ from 14 $\mathrm{N}$ by neutron bombardment
(c) the production of $^{233}$ Th from $^{232}$ Th by neutron bombardment
(d) the production of 399 $\mathrm{U}$ from $^{238} \mathrm{U}$ by $_{1}^{2} \mathrm{H}$ bombardment

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Problem 16

Technetium- 99 is prepared from $^{98}$ Molybdenum- 98 combines with a neutron to give molybdenum- $99,$ an unstable isotope that emits a ? particle to yield an excited form of technetium-99, represented as 99 $\mathrm{Tc}^{*} .$ This excited nucleus relaxes to the ground state, represented as $99 \mathrm{Tc},$ by emitting a y ray. The ground state of $^{99} \mathrm{Tc}$ then emits a $\beta$ particle. Write the equations for each of these nuclear reactions.

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Problem 17

The mass of the atom $\quad \stackrel{19}{9} \mathrm{F}$ is 18.99840 amu.
(a) Calculate its binding energy per atom in millions of electron volts.
(b) Calculate its binding energy per nucleon.

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Problem 18

For the reaction $14 \mathrm{C} \longrightarrow \stackrel{14}{7} \mathrm{N}+?,$ if 100.0 $\mathrm{g}$ of carbon reacts, what volume of nitrogen gas $\left(\mathrm{N}_{2}\right)$ is produced at 273 $\mathrm{K}$ and 1 atm?

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Problem 19

What are the types of radiation emitted by the nuclei of radioactive elements?

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Problem 20

What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios?
(a) an $\alpha$ particle is emitted
(b) a $\beta$ particle is emitted
(c) $\mathrm{y}$ radiation is emitted
(d) a positron is emitted
(e) an electron is captured

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Problem 21

What is the change in the nucleus that results from the following decay scenarios?
(a) emission of a $\beta$ particle
(b) emission of a $\beta^{+}$ particle
(c) capture of an electron

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Problem 22

Many nuclides with atomic numbers greater than 83 decay by processes such as electron emission. Explain the observation that the emissions from these unstable nuclides also normally include ? particles.

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Problem 23

Why is electron capture accompanied by the emission of an X-ray?

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Problem 24

Explain, in terms of Figure 21.2, how unstable heavy nuclides (atomic number > 83) may decompose to form nuclides of greater stability (a) if they are below the band of stability and (b) if they are above the band of stability.

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Problem 25

Which of the following nuclei is most likely to decay by positron emission? Explain your choice.
(a) chromium- 53
(b) manganese- 51
(c) iron- 59

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Problem 26

The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer
(a) $\frac{34}{15} \mathrm{P}$
(b) $\frac{239}{92} \mathrm{U}$
(c) $\frac{38}{20} \mathrm{Ca}$
(d) 3 $\mathrm{H}$
(e) 245 $\mathrm{Pu}$

Aadit S.
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Problem 27

The following nuclei do not lie in the band of stability. How would they be expected to decay?
(a) 28 $\mathrm{P}$
(b) $\frac{235}{92} \mathrm{U}$
(c) 37 $\mathrm{Ca}$
(d) 9 $\mathrm{Li}$
(e) $\stackrel{245}{96} \mathrm{Cm}$

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Problem 28

Predict by what mode(s) of spontaneous radioactive decay each of the following unstable isotopes might proceed:
(a) $_{2}^{6} \mathrm{He}$
(b) 60 $\mathrm{Zn}$
(c) $\frac{235}{91} \mathrm{Pa}$
(d) 241
(e) $^{18} \mathrm{F}$

Aadit S.
Numerade Educator

Problem 29

Write a nuclear reaction for each step in the formation of $\frac{218}{84} \mathrm{Po}$ from $\frac{238}{98} \mathrm{U}$ which proceeds by a series of decay reactions involving the step-wise emission of $\alpha, \beta, \beta, \alpha, \alpha, \alpha$ particles, in that order.

Rikhil M.
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Problem 30

Write a nuclear reaction for each step in the formation of 208 $\mathrm{Pb}$ from 2228 $\mathrm{Th}$ , which proceeds by a series of decay reactions involving the step-wise emission of $\alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha$ particles, in that order.

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Problem 31

Define the term half-life and illustrate it with an example.

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Problem 32

$\mathrm{A} 1.00 \times 10^{-6}-\mathrm{g}$ sample of nobelium, 254 $\mathrm{No}$ has a half-life of 55 seconds after it is formed. What is the percentage of $\frac{254}{102}$ No remaining at the following times?
(a) 5.0 min after it forms
(b) 1.0 $\mathrm{h}$ after it forms

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Problem 33

239 $\mathrm{Pu}$ is a nuclear waste byproduct with a half-life of $24,000 \mathrm{y}$ . What fraction of the 239 Pu present today will be present in 1000 y?

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Problem 34

The isotope 208 Tl undergoes $\beta$ decay with a half-life of 3.1 $\mathrm{min}$ .
(a) What isotope is produced by the decay?
(b) How long will it take for 99.0$\%$ of a sample of pure $^{208} \mathrm{T}$ to decay?
(c) What percentage of a sample of pure $^{208}$ Tl remains un-decayed after 1.0 $\mathrm{h} ?$

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Problem 35

If 1.000 g of 226 Ra produces 0.0001 $\mathrm{mL}$ of the gas 222 $\mathrm{Rn}$ at STP (standard temperature and pressure) in 24 h, what is the half-life of 226 Ra in years?

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Problem 36

The isotope $\frac{\gamma_{0}}{38} \mathrm{Sr}$ is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500 -g sample diminishes to 0.393 $\mathrm{g}$ in 10.0 y. Calculate the half-life.

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Problem 37

Technetium- 99 is often used for assessing heart, liver, and lung damage certain technetium compounds
are absorbed by damaged tissues. It has a half-life of 6.0 $\mathrm{h}$ . Calculate the rate constant for the decay of $\frac{99}{43} \mathrm{Tc}$

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Problem 38

What is the age of mummified primate skin that contains 8.25$\%$ of the original quantity of $^{14} \mathrm{C} ?$

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Problem 39

A sample of rock was found to contain 8.23 $\mathrm{mg}$ of rubidium- 87 and 0.47 $\mathrm{mg}$ of strontium- 87
(a) Calculate the age of the rock if the half-life of the decay of rubidium by $\beta$ emission is $4.7 \times 10^{10} \mathrm{y} .$
(b) If some $\frac{87}{38} \mathrm{Sr}$ was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in $(\mathrm{a})$ ? Explain your answer.

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Problem 40

A laboratory investigation shows that a sample of uranium ore contains 5.37 $\mathrm{mg}$ of 238 $\mathrm{U}$ and 2.52 $\mathrm{mg}$ of $_{82}^{206} \mathrm{Pb}$ Calculate the age of the ore. The half-life of 238 $\mathrm{U}$ is $4.5 \times 10^{9} \mathrm{yr.}$

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Problem 41

Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in $1941 .$ They proposed that the source of this $^{239} \mathrm{Pu}$ was the capture of neutrons by $^{238} \mathrm{U}$ nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed $4.7 \times 10^{9}$ years ago?

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Problem 42

A $\frac{7}{4}$ Be atom (mass $=7.0169$ amu) decays into a $\frac{7}{3}$ Li atom (mass $=7.0160$ amu) by electron capture. How much energy (in millions of electron volts, MeV) is produced by this reaction?

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Problem 43

$A_{5}^{8} B$ atom $(\operatorname{mas} s=8.0246 \text { amu) }$ decays into a $_{4}^{8} \mathrm{B}$ atom (mass $=8.0053$ amu) by loss of a $\beta^{4}$ particle (mass $=$ 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

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Problem 44

Isotopes such as $^{26} \mathrm{Al}$ (half-life: $7.2 \times 10^{5}$ years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclides. .
(a) 26 Al decays by $\beta^{+}$ emission or electron capture. Write the equations for these two nuclear transformations.
(b) The earth was formed about $4.7 \times 10^{9}(4.7 \text { billion) years ago. How old was the earth when } 99.999999 \% \text { of the }$ 26 Al originally present had decayed?

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Problem 45

Write a balanced equation for each of the following nuclear reactions:
(a) bismuth-212 decays into polonium- 212
(b) beryllium- 8 and a positron are produced by the decay of an unstable nucleus
(c) neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium- $-239$
(d) strontium- 90 decays into yttrium-90

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Problem 46

Write a balanced equation for each of the following nuclear reactions:
(a) mercury-180 decays into platinum-176
(b) zirconium $-90$ and an electron are produced by the decay of an unstable nucleus
(c) neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium- 239
(d) neon-19 decays into fluorine- 19

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Problem 47

Write the balanced nuclear equation for the production of the following transuranium elements:
(a) berkelium-244, made by the reaction of Am-241 and He-4
(b) fermium-254, made by the reaction of Pu-239 with a large number of neutrons
(c) lawrencium-257, made by the reaction of Cf-250 and B-11
(d) dubnium-260, made by the reaction of Cf-249 and N-15

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Problem 48

How does nuclear fission differ from nuclear fusion? Why are both of these processes exothermic?

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Problem 49

Both fusion and fission are nuclear reactions. Why is a very high temperature required for fusion, but not for fission?

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Problem 50

Cite the conditions necessary for a nuclear chain reaction to take place. Explain how it can be controlled to produce energy, but not produce an explosion

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Problem 51

Describe the components of a nuclear reactor.

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Problem 52

In usual practice, both a moderator and control rods are necessary to operate a nuclear chain reaction safely for the purpose of energy production. Cite the function of each and explain why both are necessary.

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Problem 53

Describe how the potential energy of uranium is converted into electrical energy in a nuclear power plant.

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Problem 54

The mass of a hydrogen atom $\left(_{1}^{1} \mathrm{H}\right)$ is 1.007825 amu; that of a tritium atom $\left(\begin{array}{c}{3} \\ {1}\end{array}\right)$ is 3.01605 amu; and that of an a particle is 4.00150 amu. How much energy in killojoules per mole of $\frac{4}{2}$ He produced is released by the following fusion reaction: $1 \mathrm{H}+_{1}^{3} \mathrm{H} \longrightarrow_{2}^{4} \mathrm{He}$

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Problem 55

How can a radioactive nuclide be used to show that the equilibrium:
$\mathrm{AgCl}(s) \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q)$
is a dynamic equilibrium?

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Problem 56

Technetium-99m has a half-life of 6.01 hours. If a patient injected with technetium-99m is safe to leave the hospital once 75% of the dose has decayed, when is the patient allowed to leave?

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Problem 57

Iodine that enters the body is stored in the thyroid gland from which it is released to control growth and
metabolism. The thyroid can be imaged if iodine-131 is injected into the body. In larger doses, I-133 is also used as a means of treating cancer of the thyroid. I-131 has a half-life of 8.70 days and decays by ?? emission.

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Problem 58

If a hospital were storing radioisotopes, what is the minimum containment needed to protect against:
(a) cobalt-60 (a strong y emiter used for iradiation)
(b) molybdenum- 99 (a beta emitter used to produce technetium- 99 for imaging)

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Problem 59

Based on what is known about Radon-2222's primary decay method, why is inhalation so dangerous?

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Problem 60

Given specimens uranium-232 $\left(t_{12}=68.9 \mathrm{y}\right)$ and uranium-233 $\left(t_{1 / 2}=159,200 \mathrm{y}\right)$ of equal mass, which one would have greater activity and why?

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Problem 61

A scientist is studying a 2.234 g sample of thorium-229 $\left(t_{1 / 2}=7340 \mathrm{y}\right)$ in a laboratory.
(a) What is its activity in Bq?
(b) What is its activity in Ci?

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Problem 62

Given specimens neon- 24$\left(t_{1 / 2}=3.38 \text { min) and bismuth-211 }\left(t_{1 / 2}=2.14 \text { min) of equal mass, which one would }\right.\right.$ have greater activity and why?

Aadit S.
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