Chapter 21

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{22}^{55} \mathrm{Mn},(\mathbf{b}){ }^{201} \mathrm{Hg},(\mathbf{c})\) potassium- \(39 .\)

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{52}^{124} \mathrm{Te},(\mathbf{b}){ }^{37} \mathrm{Cl},(\mathrm{c})\) thorium- \(232 .\)

Give the symbol for (a) a neutron, (b) an alpha particle, (c) gamma radiation.

Give the symbol for (a) a proton, (b) a beta particle, (c) a positron.

Write balanced nuclear equations for the following processes: (a) rubidium-90 undergoes beta emission; (b) selenium-72 undergoes electron capture; (c) krypton-76 undergoes positron emission; (d) radium-226 emits alpha radiation.

Write balanced nuclear equations for the following transformations: (a) bismuth- 213 undergoes alpha decay; (b) nitrogen-13 undergoes electron capture; (c) technicium-98 undergoes electron capture; (d) gold-188 decays by positron emission.

Decay of which nucleus will lead to the following products: (a) bismuth-211 by beta decay; (b) chromium-50 by positron emission; (c) tantalum-179 by electron capture; (d) radium226 by alpha decay?

What particle is produced during the following decay processes: (a) sodium- 24 decays to magnesium- \(24 ;\) (b) mercury188 decays to gold-188; (c) iodine-122 decays to xenon-122; (d) plutonium-242 decays to uranium-238?

The naturally occurring radioactive decay series that begins with \({ }_{92}^{235} \mathrm{U}\) stops with formation of the stable \({ }_{82}^{207} \mathrm{~Pb}\) nucleus. The decays proceed through a series of alpha-particle and beta-particle emissions. How many of each type of emission are involved in this series?

A radioactive decay series that begins with \({ }_{90}^{232}\) Th ends with formation of the stable nuclide \({ }_{82}^{208} \mathrm{~Pb}\). How many alphaparticle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?

Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{5}^{8} \mathrm{~B},\) (b) \({ }_{29}^{68} \mathrm{Cu},\) (c) phosphorus-32, (d) chlorine- 39 .

Each of the following nuclei undergoes either beta decay or positron emission. Predict the type of emission for each: (a) tritium, \({ }_{1}^{3} \mathrm{H},(\mathbf{b}){ }_{38}^{89} \mathrm{Sr}\), (c) iodine-120, (d) silver-102.

One of the nuclides in each of the following pairs is radioactive. Predict which is radioactive and which is stable: (a) \({ }_{19}^{39} \mathrm{~K}\) and \({ }_{19}^{40} \mathrm{~K}\), (b) \({ }^{209} \mathrm{Bi}\) and \({ }^{208} \mathrm{Bi}\), (c) nickel-58 and nickel-65. Explain.

One nuclide in each of these pairs is radioactive. Predict which is radioactive and which is stable: (a) \({ }_{20}^{40} \mathrm{Ca}\) and \({ }_{20}^{45} \mathrm{Ca},(\mathbf{b}){ }^{12} \mathrm{C}\) and \({ }^{14} \mathrm{C},(\mathrm{c})\) lead- 206 and thorium- \(230 .\) Explain your choice in each case.

Which of the following nuclides have magic numbers of both protons and neutrons: (a) helium- \(4,(\mathbf{b})\) oxygen \(-18,(\mathbf{c})\) calcium\(40,(\mathbf{d}) \operatorname{zinc}-66,(\mathbf{e})\) lead \(-208 ?\)

Using the concept of magic numbers, explain why alpha emission is relatively common, but proton emission is nonexistent.

Which of the following nuclides would you expect to be radioactive: \({ }_{28}^{62} \mathrm{Ni},{ }_{29}^{58} \mathrm{Cu},{ }_{47}^{108} \mathrm{Ag},\) tungsten- \(184,\) polonium- \(206 ?\) Justify your choices.

Why are nuclear transmutations involving neutrons generally easier to accomplish than those involving protons or alpha particles?

In 1930 the American physicist Ernest Lawrence designed the first cyclotron in Berkeley, California. In 1937 Lawrence bombarded a molybdenum target with deuterium ions, producing for the first time an element not found in nature. What was this element? Starting with molybdenum-96 as your reactant, write a nuclear equation to represent this process.

Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{98}^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow 3{ }_{0}^{1} \mathrm{n}+?\) (b) \({ }_{1}^{2} \mathrm{H}+{ }_{2}^{3} \mathrm{He} \longrightarrow{ }_{2}^{4} \mathrm{He}+\) ? (c) \({ }_{1}^{1} \mathrm{H}+{ }_{5}^{11} \mathrm{~B} \longrightarrow 3\) ? (d) \({ }_{53}^{122} \mathrm{I} \longrightarrow{ }_{54}^{122} \mathrm{Xe}+?\) (e) \(\frac{59}{26} \mathrm{Fe} \longrightarrow{ }_{-1}^{0} \mathrm{e}+?\)

Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{7}^{14} \mathrm{~N}+{ }_{2}^{4} \mathrm{He} \longrightarrow ?+{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{19}^{40} \mathrm{~K}+{ }_{-1}^{0} \mathrm{e}\) (orbital electron) \(\longrightarrow\) (c) ? \(+{ }_{2}^{4} \mathrm{He} \longrightarrow{ }_{14}^{30} \mathrm{Si}+{ }_{1}^{1} \mathrm{H}\) (d) \({ }_{26}^{58} \mathrm{Fe}+2{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{27}^{60} \mathrm{Co}+?\) (e) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{54}^{135} \mathrm{Xe}+2{ }_{0}^{1} \mathrm{n}+?\)

Write balanced equations for (a) \({ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n}){ }_{94}^{241} \mathrm{Pu},\) (b) \({ }_{7}^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }^{17} \mathrm{O}\) (c) \({ }_{26}^{56} \mathrm{Fe}(\alpha, \beta)_{29}^{60} \mathrm{Cu}\).

Write balanced equations for each of the following nuclear reactions: (a) \({ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U}\) (b) \({ }_{7}^{14} \mathrm{~N}(\mathrm{p}, \alpha)^{11}{\underline{\phantom{xx}}}_{6} \mathrm{C}\) (c) \({ }_{8}^{18} \mathrm{O}(\mathrm{n}, \beta){ }^{19}{\underline{\phantom{xx}}}_{9} \mathrm{~F}\).

Each statement that follows refers to a comparison between two radioisotopes, \(\mathrm{A}\) and \(\mathrm{X}\). Indicate whether each of the following statements is true or false, and why. (a) If the half-life for \(A\) is shorter than the half-life for \(X, A\) has a larger decay rate constant. (b) If \(X\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 years, and \(X\) has a half-life of 10,000 years, A would be a more suitable radioisotope to measure processes occurring on the 40 -year time scale.

It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5\() ?\) Discuss.

It takes 5.2 min for a 1.000 -g sample of \({ }^{210} \mathrm{Fr}\) to decay to \(0.250 \mathrm{~g}\). What is the half-life of \({ }^{210} \mathrm{Fr}\) ?

Cobalt- 60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt- 60 in a radiotherapy unit must be replaced when its radioactivity falls to \(75 \%\) of the original sample. If an original sample was purchased in June 2010 , when will it be necessary to replace the cobalt- \(60 ?\)

Cobalt- 60 , which undergoes beta decay, has a half-life of 5.26 yr. (a) How many beta particles are emitted in \(600 \mathrm{~s}\) by a \(3.75-\mathrm{mg}\) sample of \({ }^{60} \mathrm{Co} ?\) (b) What is the activity of the sample in \(\mathrm{Bq}\) ?

The cloth shroud from around a mummy is found to have a \({ }^{14} \mathrm{C}\) activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for \({ }^{14} \mathrm{C}\) decay, \(5715 \mathrm{yr},\) calculate the age of the shroud.

A wooden artifact from a Chinese temple has a \({ }^{14} \mathrm{C}\) activity of 38.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. From the halflife for \({ }^{14} \mathrm{C}\) decay, \(5715 \mathrm{yr}\), determine the age of the artifact.

Potassium-40 decays to argon-40 with a half-life of \(1.27 \times 10^{9}\) yr. What is the age of a rock in which the mass ratio of \({ }^{40} \mathrm{Ar}\) to \({ }^{40} \mathrm{~K}\) is \(4.2 ?\)

The half-life for the process \({ }^{238} \mathrm{U} \longrightarrow{ }^{206} \mathrm{~Pb}\) is \(4.5 \times 10^{9} \mathrm{yr}\). A mineral sample contains \(75.0 \mathrm{mg}\) of \({ }^{238} \mathrm{U}\) and \(18.0 \mathrm{mg}\) of \({ }^{206} \mathrm{~Pb}\). What is the age of the mineral?

The thermite reaction, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(s)+\) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s), \Delta H^{\circ}=-851.5 \mathrm{~kJ} / \mathrm{mol},\) is one of the most exother-mic reactions known. Because the heat released is sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How much heat is released per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) produced? How does this amount of thermal energy compare with the energy released when 2 mol of protons and 2 mol of neutrons combine to form 1 mol of alpha particles?

How much energy must be supplied to break a single \({ }^{21}\) Ne nucleus into separated protons and neutrons if the nucleus has a mass of 20.98846 amu? What is the nuclear binding energy for \(1 \mathrm{~mol}\) of \({ }^{21} \mathrm{Ne} ?\)

The atomic masses of nitrogen- 14 , titanium- 48 , and xenon129 are 13.999234 amu, 47.935878 amu, and 128.904779 amu, respectively. For each isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon.

The energy from solar radiation falling on Earth is \(1.07 \times 10^{16} \mathrm{~kJ} / \mathrm{min} .\) (a) How much loss of mass from the Sun occurs in one day from just the energy falling on Earth? (b) If the energy released in the reaction $$ { }^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ \(\left({ }^{235} \mathrm{U}\right.\) nuclear mass, \(234.9935 \mathrm{amu} ;{ }^{141} \mathrm{Ba}\) nuclear mass, 140.8833 amu; \({ }^{92} \mathrm{Kr}\) nuclear mass, 91.9021 amu \()\) is taken as typical of that occurring in a nuclear reactor, what mass of uranium- 235 is required to equal \(0.10 \%\) of the solar energy that falls on Earth in 1.0 day?

Based on the following atomic mass values \(-1 \mathrm{H}\), 1.00782 amu; \({ }^{2} \mathrm{H}, 2.01410 \mathrm{amu} ;{ }^{3} \mathrm{H}, 3.01605 \mathrm{amu} ;{ }^{3} \mathrm{He}\) 3.01603 amu; \({ }^{4}\) He, 4.00260 amu- and the mass of the neutron given in the text, calculate the energy released per mole in each of the following nuclear reactions, all of which are possibilities for a controlled fusion process: (a) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}\) (b) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{1}^{2} \mathrm{H}+{ }_{2}^{3} \mathrm{He} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{1}^{1} \mathrm{H}\)

Which of the following nuclei is likely to have the largest mass defect per nucleon: (a) \({ }^{59} \mathrm{Co},(\mathbf{b}){ }^{11} \mathrm{~B},(\mathrm{c})^{118} \mathrm{Sn}\) (d) \({ }^{243} \mathrm{Cm} ?\) Explain your answer.

Iodine- 131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. (a) Why is NaI a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about \(12 \%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to \(0.01 \%\) of the original amount?

Why is it important that radioisotopes used as diagnostic tools in nuclear medicine produce gamma radiation when they decay? Why are alpha emitters not used as diagnostic tools?

What is the most common fissionable isotope in a commercial nuclear power reactor?

What is meant by enriched uranium? How is enriched uranium different from natural uranium?

What is the function of the control rods in a nuclear reactor? What substances are used to construct control rods? Why are these substances chosen?

(a) What is the function of the moderator in a nuclear reactor? (b) What substance acts as the moderator in a pressurized water generator? (c) What other substances are used as a moderator in nuclear reactor designs?

Complete and balance the nuclear equations for the following fission or fusion reactions: (a) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+\) (b) \({ }_{92}^{239} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{98} \mathrm{Nb}+{ }_{-0}^{1} \mathrm{n}\)

A portion of the Sun's energy comes from the reaction $$ 4_{1}^{1} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+2_{1}^{0} \mathrm{e} $$ which requires a temperature of \(10^{6}\) to \(10^{7} \mathrm{~K}\). (a) Use the mass of the helium- 4 nucleus given in Table 21.7 to determine how much energy is released when the reaction is run with \(1 \mathrm{~mol}\) of hydrogen atoms. (b) Why is such a high temperature required?

Which type or types of nuclear reactors have these characteristics? (a) Does not use a secondary coolant (b) Creates more fissionable material than it consumes (c) Uses a gas, such as He or \(\mathrm{CO}_{2}\), as the primary coolant

Which type or types of nuclear reactors have these characteristics? (a) Can use natural uranium as a fuel (b) Does not use a moderator (s) Can be refueled without shutting down

Hydroxyl radicals can pluck hydrogen atoms from molecules ("hydrogen abstraction"), and hydroxide ions can pluck protons from molecules ("deprotonation"). Write the reaction equations and Lewis dot structures for the hydrogen abstraction and deprotonation reactions for the generic carboxylic acid \(\mathrm{R}-\mathrm{COOH}\) with hydroxyl radical and hydroxide ion, respectively. Why is hydroxyl radical more toxic to living systems than hydroxide ion?

Which are classified as ionizing radiation: X-rays, alpha particles, microwaves from a cell phone, and gamma rays?