Content check — Chemistry 2e, Chapter 21: Nuclear Chemistry

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Chapter 21: Nuclear Chemistry

39 problems · 1 figure

Example 21.1 §21.1 source ↗

Find the density of a neutron star with a mass of 1.97 solar masses and a diameter of 13 km, and compare it to the density of a hydrogen nucleus, which has a diameter of 1.75 fm (1 fm = 1

\times

10^–15 m).

Answer

The density of the neutron star is 3.4

\times

10¹⁸ kg/m³. The density of a hydrogen nucleus is 6.0

\times

10¹⁷ kg/m³. The neutron star is 5.7 times denser than the hydrogen nucleus.

Example 21.2 §21.1 source ↗

What is the binding energy for the nuclide

_{9}^{19} F

(atomic mass: 18.9984 amu) in MeV per nucleus?

Answer

148.4 MeV

Example 21.3 §21.1 source ↗

What is the binding energy per nucleon in

_{9}^{19} F

(atomic mass, 18.9984 amu)?

Answer

7.810 MeV/nucleon

Example 21.4 §21.2 source ↗

The nuclide

_{53}^{125} I

combines with an electron and produces a new nucleus and no other massive particles. What is the equation for this reaction?

Answer

_{53}^{125} I +

_{−1}^{0} e ⟶

_{52}^{125} Te

Example 21.5 §21.3 source ↗

Radon-222,

_{86}^{222} Rn,

has a half-life of 3.823 days. How long will it take a sample of radon-222 with a mass of 0.750 g to decay into other elements, leaving only 0.100 g of radon-222?

Answer

11.1 days

Example 21.6 §21.3 source ↗

More accurate dates of the reigns of ancient Egyptian pharaohs have been determined recently using plants that were preserved in their tombs. Samples of seeds and plant matter from King Tutankhamun’s tomb have a C-14 decay rate of 9.07 disintegrations/min/g of C. How long ago did King Tut’s reign come to an end?

Answer

about 3350 years ago, or approximately 1340 BC

Example 21.7 §21.3 source ↗

A sample of rock contains 6.14

\times

10^–4 g of Rb-87 and 3.51

\times

10^–5 g of Sr-87. Calculate the age of the rock. (The half-life of the β decay of Rb-87 is 4.7

\times

10¹⁰ y.)

Answer

3.7

\times

10⁹ y

Example 21.8 §21.6 source ↗

Tritium is a radioactive isotope of hydrogen (t_1/2 = 12.32 y) that has several uses, including self-powered lighting, in which electrons emitted in tritium radioactive decay cause phosphorus to glow. Its nucleus contains one proton and two neutrons, and the atomic mass of tritium is 3.016 amu. What is the activity of a sample containing 1.00mg of tritium (a) in Bq and (b) in Ci?

Answer

(a) 3.56

\times

10¹¹ Bq; (b) 0.962 Ci

21-1 §21.1 source ↗

Write the following isotopes in hyphenated form (e.g., “carbon-14”)

(a) $_{11}^{24} Na$

(b) $_{13}^{29} Al$

(d) $_{77}^{194} Ir$

Answer

(a) sodium-24; (b) aluminum-29; (c) krypton-73; (d) iridium-194

21-3 §21.1 source ↗

For the following isotopes that have missing information, fill in the missing information to complete the notation

(a) $_{14}^{34} X$

(b) $_{X}^{36} P$

(d) $_{56}^{121} X$

Answer

(a)

_{14}^{34} Si;

(b)

_{15}^{36} P;

(c)

_{25}^{57} Mn;

(d)

_{56}^{121} Ba

21-5 §21.1 source ↗

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

(d) 97 protons, 146 neutrons, 97 electrons

Answer

(a)

_{25}^{45} {Mn}^{+1};

(b)

_{45}^{69} {Rh}^{+2};

(c)

_{53}^{142} I^{−1};

(d)

_{97}^{243} Bk

21-7 §21.1 source ↗

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

Answer

Nuclear reactions usually change one type of nucleus into another; chemical changes rearrange atoms. Nuclear reactions involve much larger energies than chemical reactions and have measureable mass changes.

21-9 §21.1 source ↗

Which of the following nuclei lie within the band of stability shown in Figure 21.2?

(a) chlorine-37

(b) calcium-40

(d) ⁵⁶Fe

(e) ²⁰⁶Pb

(f) ²¹¹Pb

(g) ²²²Rn

(h) carbon-14

A graph is shown where the x-axis is labeled “Number of neutrons, open parenthesis, n, close parenthesis” and has values of 0 to 180 in increments of 10. The y-axis is labeled “Number of protons, open parenthesis, Z, close parenthesis” and has values of 0 to 120 in increments of 10. A green shaded band of varying width, labeled “Radioactive,” extends from point 0 on both axes to 178 on the y-axis and 118 on the x-axis in a linear manner. The width of this band varies from 8 to 18 units in width according to the x-axis measurements. A blue line in a roughly zig-zag pattern runs through the middle of the shaded band and stops at 128 on the y-axis and 82 on the x-axis. This line is labeled “Nonradioactive.” An unlabeled, black, solid line extends from point 0, 0 to 120, 120 in a linear manner. — Figure 21.2 in the book ↗

Answer

(a), (b), (c), (d), and (e)

21-11 §21.2 source ↗

Write a brief description or definition of each of the following:

(a) nucleon

(b) α particle

(d) positron

(e) γ ray

(f) nuclide

(g) mass number

(h) atomic number

Answer

(a) A nucleon is any particle contained in the nucleus of the atom, so it can refer to protons and neutrons. (b) An α particle is one product of natural radioactivity and is the nucleus of a helium atom. (c) A β particle is a product of natural radioactivity and is a high-speed electron. (d) A positron is a particle with the same mass as an electron but with a positive charge. (e) Gamma rays compose electromagnetic radiation of high energy and short wavelength. (f) Nuclide is a term used when referring to a single type of nucleus. (g) The mass number is the sum of the number of protons and the number of neutrons in an element. (h) The atomic number is the number of protons in the nucleus of an element.

21-13 §21.2 source ↗

Complete each of the following equations by adding the missing species:

(a) $_{13}^{27} Al +$ $_{2}^{4} He ⟶$ $? +$ $_{0}^{1} n$

(b) $_{94}^{239} Pu +$ $? ⟶$ $_{96}^{242} Cm +$ $_{0}^{1} n$

(d) $_{92}^{235} U ⟶$ $? +$ $_{55}^{135} Cs +$ $4_{0}^{1} n$

Answer

(a)

_{13}^{27} Al +

_{2}^{4} He ⟶

_{15}^{30} P +

_{0}^{1} n;

(b)

_{94}^{239} Pu +

_{2}^{4} He ⟶

_{96}^{242} Cm +

_{0}^{1} n;

(c)

_{7}^{14} N +

_{2}^{4} He ⟶

_{8}^{17} O +

_{1}^{1} H;

(d)

_{92}^{235} U ⟶

_{37}^{96} Rb +

_{55}^{135} Cs +

4_{0}^{1} n

21-15 §21.2 source ↗

Write a balanced equation for each of the following nuclear reactions:

(a) the production of ¹⁷O from ¹⁴N by α particle bombardment

(b) the production of ¹⁴C from ¹⁴N by neutron bombardment

(d) the production of ²³⁹U from ²³⁸U by $_{1}^{2} H$ bombardment

Answer

(a)

_{7}^{14} N +

_{2}^{4} He ⟶

_{8}^{17} O +

_{1}^{1} H;

(b)

_{7}^{14} C +

_{0}^{1} n ⟶

_{6}^{14} C +

_{1}^{1} H;

(c)

_{90}^{232} Th +

_{0}^{1} n ⟶

_{90}^{233} Th;

(d)

_{92}^{238} U +

_{1}^{2} H ⟶

_{92}^{239} U +

_{1}^{1} H

21-17 §21.2 source ↗

The mass of the atom $_{9}^{19} F$ is 18.99840 amu.

(a) Calculate its binding energy per atom in millions of electron volts.

(b) Calculate its binding energy per nucleon.

Answer

(a) 148.8 MeV per atom; (b) 7.808 MeV/nucleon

21-19 §21.3 source ↗

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

Answer

α (helium nuclei), β (electrons), β⁺ (positrons), and η (neutrons) may be emitted from a radioactive element, all of which are particles; γ rays also may be emitted.

21-21 §21.3 source ↗

What is the change in the nucleus that results from the following decay scenarios?

(a) emission of a β particle

(b) emission of a β⁺ particle

Answer

(a) conversion of a neutron to a proton:

_{0}^{1} n ⟶

_{1}^{1} p +

_{+1}^{0} e;

(b) conversion of a proton to a neutron; the positron has the same mass as an electron and the same magnitude of positive charge as the electron has negative charge; when the n:p ratio of a nucleus is too low, a proton is converted into a neutron with the emission of a positron:

_{1}^{1} p ⟶

_{0}^{1} n +

_{+1}^{0} e;

(c) In a proton-rich nucleus, an inner atomic electron can be absorbed. In simplest form, this changes a proton into a neutron:

_{1}^{1} p +

_{-1}^{0} e ⟶

_{0}^{1} p

21-23 §21.3 source ↗

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

Answer

The electron pulled into the nucleus was most likely found in the 1s orbital. As an electron falls from a higher energy level to replace it, the difference in the energy of the replacement electron in its two energy levels is given off as an X-ray.

21-25 §21.3 source ↗

Which of the following nuclei is most likely to decay by positron emission? Explain your choice.

(a) chromium-53

(b) manganese-51

Answer

Manganese-51 is most likely to decay by positron emission. The n:p ratio for Cr-53 is

\frac{29}{24}

= 1.21; for Mn-51, it is

\frac{26}{25}

= 1.04; for Fe-59, it is

\frac{33}{26}

= 1.27. Positron decay occurs when the n:p ratio is low. Mn-51 has the lowest n:p ratio and therefore is most likely to decay by positron emission. Besides,

_{24}^{53} Cr

is a stable isotope, and

_{26}^{59} Fe

decays by beta emission.

21-27 §21.3 source ↗

The following nuclei do not lie in the band of stability. How would they be expected to decay?

(a) $_{15}^{28} P$

(b) $_{92}^{235} U$

(d) $_{3}^{9} L i$

(e) $_{96}^{245} Cm$

Answer

(a) positron emission; (b) α decay; (c) positron emission; (d) β decay; (e) α decay

21-29 §21.3 source ↗

Write a nuclear reaction for each step in the formation of

_{84}^{218} Po

from

_{92}^{238} U,

which proceeds by a series of decay reactions involving the step-wise emission of α, β, β, α, α, α, α particles, in that order.

Answer

_{92}^{238} U ⟶

_{90}^{234} Th +

_{2}^{4} He;

_{90}^{234} Th ⟶

_{91}^{234} Pa +

_{-1}^{0} e;

_{91}^{234} Pa ⟶

_{92}^{234} U +

_{-1}^{0} e;

_{92}^{234} U ⟶

_{90}^{230} Th +

_{2}^{4} He

_{90}^{230} Th ⟶

_{88}^{226} Ra +

_{2}^{4} He

_{88}^{226} Ra ⟶

_{86}^{222} Rn +

_{2}^{4} He;

_{86}^{222} Rn ⟶

_{84}^{218} Po +

_{2}^{4} He

21-31 §21.3 source ↗

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

Answer

Half-life is the time required for half the atoms in a sample to decay. Example (answers may vary): For C-14, the half-life is 5770 years. A 10-g sample of C-14 would contain 5 g of C-14 after 5770 years; a 0.20-g sample of C-14 would contain 0.10 g after 5770 years.

21-33 §21.3 source ↗

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

Answer

{(\frac{1}{2})}^{0.04} =

0.973

or 97.3%

21-35 §21.3 source ↗

If 1.000 g of

_{88}^{226} Ra

produces 0.0001 mL of the gas

_{86}^{222} Rn

at STP (standard temperature and pressure) in 24 h, what is the half-life of ²²⁶Ra in years?

Answer

\times

10³ y

21-37 §21.3 source ↗

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

_{43}^{99} Tc .

Answer

0.12 h^–1

21-39 §21.3 source ↗

A sample of rock was found to contain 8.23 mg of rubidium-87 and 0.47 mg of strontium-87.

(a) Calculate the age of the rock if the half-life of the decay of rubidium by β emission is 4.7 $\times$ 10¹⁰ y.

(b) If some $_{38}^{87} Sr$ was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in (a)? Explain your answer.

Answer

(a) 3.8 billion years; (b) The rock would be younger than the age calculated in part (a). If Sr was originally in the rock, the amount produced by radioactive decay would equal the present amount minus the initial amount. As this amount would be smaller than the amount used to calculate the age of the rock and the age is proportional to the amount of Sr, the rock would be younger.

21-41 §21.3 source ↗

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 ²³⁹Pu was the capture of neutrons by ²³⁸U nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7

\times

10⁹ years ago?

Answer

c = 0; This shows that no Pu-239 could remain since the formation of the earth. Consequently, the plutonium now present could not have been formed with the uranium.

21-43 §21.3 source ↗

_{5}^{8} B

atom (mass = 8.0246 amu) decays into a

_{4}^{8} Be

atom (mass = 8.0053 amu) by loss of a β⁺ particle (mass = 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

Answer

17.5 MeV

21-45 §21.3 source ↗

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

Answer

(a)

_{83}^{212} Bi ⟶

_{84}^{212} Po +

_{-1}^{0} e;

(b)

_{5}^{8} B ⟶

_{4}^{8} B e +

_{-1}^{0} e;

(c)

_{92}^{238} U +

_{0}^{1} n ⟶

_{93}^{239} Np +

_{-1}^{0} N p,

_{93}^{239} Np ⟶

_{94}^{239} Pu +

_{-1}^{0} e;

(d)

_{38}^{90} Sr ⟶

_{39}^{90} Y +

_{-1}^{0} e

21-47 §21.4 source ↗

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

(d) dubnium-260, made by the reaction of Cf-249 and N-15

Answer

(a)

_{95}^{241} Am +

_{2}^{4} He ⟶

_{97}^{244} Bk +

_{0}^{1} n;

(b)

_{94}^{239} Pu +

15_{0}^{1} n ⟶

_{100}^{254} Fm +

6_{−1}^{0} e;

(c)

_{98}^{250} Cf +

_{5}^{11} B ⟶

_{103}^{257} Lr +

4_{0}^{1} n;

(d)

_{98}^{249} Cf +

_{7}^{15} N ⟶

_{105}^{260} Db +

4_{0}^{1} n

21-49 §21.4 source ↗

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

Answer

Two nuclei must collide for fusion to occur. High temperatures are required to give the nuclei enough kinetic energy to overcome the very strong repulsion resulting from their positive charges.

21-51 §21.4 source ↗

Describe the components of a nuclear reactor.

Answer

A nuclear reactor consists of the following:

1. A nuclear fuel. A fissionable isotope must be present in large enough quantities to sustain a controlled chain reaction. The radioactive isotope is contained in tubes called fuel rods.

2. A moderator. A moderator slows neutrons produced by nuclear reactions so that they can be absorbed by the fuel and cause additional nuclear reactions.

3. A coolant. The coolant carries heat from the fission reaction to an external boiler and turbine where it is transformed into electricity.

4. A control system. The control system consists of control rods placed between fuel rods to absorb neutrons and is used to adjust the number of neutrons and keep the rate of the chain reaction at a safe level.

5. A shield and containment system. The function of this component is to protect workers from radiation produced by the nuclear reactions and to withstand the high pressures resulting from high-temperature reactions.

21-53 §21.4 source ↗

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

Answer

The fission of uranium generates heat, which is carried to an external steam generator (boiler). The resulting steam turns a turbine that powers an electrical generator.

21-55 §21.5 source ↗

How can a radioactive nuclide be used to show that the equilibrium:

AgCl (s) ⇌

{Ag}^{+} (a q) +

{Cl}^{−} (a q)

is a dynamic equilibrium?

Answer

Introduction of either radioactive Ag⁺ or radioactive Cl^– into the solution containing the stated reaction, with subsequent time given for equilibration, will produce a radioactive precipitate that was originally devoid of radiation.

21-57 §21.5 source ↗

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 β⁻ emission.

(a) Write an equation for the decay.

(b) How long will it take for 95.0% of a dose of I-131 to decay?

Answer

(a)

_{53}^{133} I ⟶

_{54}^{133} Xe +

_{−1}^{0} e;

(b) 37.6 days

21-59 §21.6 source ↗

Based on what is known about Radon-222’s primary decay method, why is inhalation so dangerous?

Answer

Alpha particles can be stopped by very thin shielding but have much stronger ionizing potential than beta particles, X-rays, and γ-rays. When inhaled, there is no protective skin covering the cells of the lungs, making it possible to damage the DNA in those cells and cause cancer.

21-61 §21.6 source ↗

A scientist is studying a 2.234 g sample of thorium-229 (t_1/2 = 7340 y) in a laboratory.

(a) What is its activity in Bq?

(b) What is its activity in Ci?

Answer

(a) 7.64

\times

10⁹ Bq; (b) 2.06

\times

10⁻² Ci

End of the book.

Problems and answers are adapted from Chemistry 2e by Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.