Chapter 21

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{25}^{55} \mathrm{Mn}\), (b) \({ }^{201} \mathrm{Hg}\), (c) potassium-39.

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{55}^{126} \mathrm{Cs}\), (b) \({ }^{119} \mathrm{Sn}\), (c) barium-141.

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 decay; (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) gold-191 undergoes electron capture; (b) gold-201 decays to a mercury isotope; (c) gold198 undergoes beta decay; (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) radium-226 by alpha decay?

What particle is produced during the following decay processes: (a) sodium-24 decays to magnesium-24; (b) mercury-188 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 \({ }^{202} \mathrm{~Pb}\) 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 \({ }_{9}^{23} \mathrm{Th}\) ends with formation of the stable nuclide \({ }_{82}^{208} \mathrm{~Pb}\). How many alpha-particle 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) phosphorus32, (d) chlorine-39.

Each of the following nuclei undergoes either beta or positron emission. Predict the type of emission for each: (a) \({ }_{32}^{66} \mathrm{Ge}\), (b) \({ }_{45}^{105} \mathrm{Rh}\), (c) iodine-137, (d) cerium-133.

Each of the following nuclei undergoes either beta or positron emission. Predict the type of emission for each: (a) \({ }_{32}^{66} \mathrm{Ge}\), (b) \({ }_{45}^{105} \mathrm{Rh}\), (c) iodine-137, (d) cerium-133.

In each of the following pairs, which nuclide would you expect to be the more abundant in nature: (a) \({ }_{48}^{115} \mathrm{Cd}\) or \({ }_{48}^{12} \mathrm{Cd}\), (b) \({ }_{13}^{30} \mathrm{Al}\) or \({ }_{13}^{27} \mathrm{Al}\), (c) palladium- 106 or palladium113, (d) xenon-128 or cesium-128? Justify your choices.

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

Tin has 10 stable isotopes, but antimony only has two. How can we explain this difference?

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: \({28}^{2} \mathrm{Ni},{ }_{29}^{58} \mathrm{Cu},{ }_{47}^{108} \mathrm{Ag}\), tungsten- 184, polonium206 ? Justify your choices.

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

Rutherford was able to carry out the first nuclear transmutation reactions by bombarding nitrogen-14 nuclei with alpha particles. In the famous experiment on scattering of alpha particles by gold foil (Section 2.2), however, a nuclear transmutation reaction did not occur. What is the difference between the two experiments? What would one need to do to carry out a successful nuclear transmutation reaction involving gold nuclei and alpha particles?

Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{98}^{25} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow 3_{0}^{1} \mathrm{n}+?\) (b) \({ }_{1}^{2} \mathrm{H}+{ }_{2}^{3} \mathrm{He} \longrightarrow{ }_{2}^{4} \mathrm{He}+?\)

Complete and balance the following nuclear equations by supplying the missing particle: (a) \(_{16}^{32} S+{ }_{0}^{1} n \longrightarrow 1_{1} p+?\) (b) \({ }_{4}^{7} \mathrm{Be}+{ }_{-1}^{0}\) (orbital electron) \(\longrightarrow\) ? (c) ? \(\underset{76}{\longrightarrow} \frac{187}{76}+{ }_{-1}^{0}\) (d) \({ }_{42}^{98} \mathrm{Mo}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{0}^{1} \mathrm{n}+?\) (e) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow 135 \mathrm{Xe}+2{ }_{0}^{1} \mathrm{n}+?\)

Write balanced equations for (a) \({ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n})^{241} \mathrm{Pu}\), (b) \({ }_{7}^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }_{8}^{17} \mathrm{O}\), (c) \({ }_{26}^{56} \mathrm{Fe}(\alpha, \beta)_{29}^{60} \mathrm{Cu}\).

Write balanced equations for each of the following nuclear reactions: (a) \({ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma)^{239} \mathrm{G}_{2} \mathrm{U}\), (b) \({ }_{7}^{14} \mathrm{~N}(\mathrm{p}, \alpha)^{11}{\underline{\phantom{xx}}}_{6} \mathrm{C}\), (c) \({ }^{18} \mathrm{O}(\mathrm{n}, \beta)^{1} \mathrm{~g} \mathrm{~F}\).

Each statement below 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 \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}\), A has a larger decay rate constant. (b) If \(X\) is "notradioactive," its half-life is essentially zero. (c) If A has a half-life of 10 years, and \(\mathrm{X}\) 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 \(\infty 00(\) Section \(14.5) ?\) Discuss.

The half-life of tritium (hydrogen-3) is \(12.3\) yr. If \(56.2 \mathrm{mg}\) of tritium is released from a nuclear power plant during the course of an accident, what mass of this nuclide will remain after \(12.3\) yr? After 100 yr?

It takes \(5.2\) minutesfor 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 \(5.26 \mathrm{yr}\). The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to \(75 \%\) of the original sample. (a) If an original sample was purchased in June 2006, when will it be necessary to replace the cobalt-60? (b) How can you store cobalt-60 so that it is safe to handle?

How much time is required for a \(6.25-\mathrm{mg}\) sample of \({ }^{51} \mathrm{Cr}\) to decay to \(0.75 \mathrm{mg}\) if it has a half-life of \(27.8\) days?

A wooden artifact from a Chinese temple has \(\mathrm{a}^{14} \mathrm{C}\) 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 half-life 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 \(4.5 \times 10^{9}\) 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, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(s)+\) \(\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})\), is one of the most exothermic reactions known. The heat released is sufficient to melt the iron product; consequently, the thermite reaction is used to weld metal under the ocean. \(\Delta H^{\circ}\) for the thermite reaction is \(-851.5 \mathrm{~kJ} / \mathrm{mole}\). What is the mass change per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) that accompanies this reaction?

An analytical laboratory balance typically measures mass to the nearest \(0.1 \mathrm{mg}\). What energy change would accompany the loss of \(0.1 \mathrm{mg}\) in mass?

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 \({ }^{21} \mathrm{Ne}\) ?

Calculate the binding energy per nucleon for the following nuclei: (a) \({ }_{7}^{14} \mathrm{~N}\) (nuclear mass, \(13.999234\) amu); (b) \({ }^{48} \mathrm{Ti}\) (nuclear mass, \(47.935878\) amu); (c) xenon-129 (atomic mass, \(128.904779\) amu).

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 $$ { }^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }^{141}{\underline{\phantom{xx}}}_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ \({ }^{235} \mathrm{U}\) nuclear mass, \(234.9935 \mathrm{amu} ;{ }^{141}\) Ba nuclear mass, \(140.8833 \mathrm{amu} ;{ }^{92} \mathrm{Kr}\) nuclear mass, \(91.9021 \mathrm{am} \mathrm{u}\) ) 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?

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

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a halflife 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 Nal 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?

Chlorine- 36 is a convenient radiotracer. It is a weak beta emitter, with \(t_{1 / 2}=3 \times 10^{5}\) yr. Describe how you would use this radiotracer to carry out each of the following experiments. (a) Determine whether trichloroacetic acid, \(\mathrm{CCl}_{3} \mathrm{COOH}\), undergoes any ionization of its chlorines as chloride ion in aqueous solution. (b) Demonstrate that the equilibrium between dissolved \(\mathrm{BaCl}_{2}\) and solid \(\mathrm{BaCl}_{2}\) in a saturated solution is a dynamic process. (c) Determine the effects of soil \(\mathrm{pH}\) on the uptake of chloride ion from the soil by soybeans.

Explain the following terms that apply to fission reactions: (a) chain reaction, (b) critical mass.

Explain the function of the following components of a nuclear reactor: (a) control rods, (b) moderator.

Complete and balance the nuclear equations for the following fission or fusion reactions: (a) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \cdots{ }_{2}^{3} \mathrm{He}+\underline{-}\) (b) \({ }_{92}^{233} \mathrm{U}+{ }_{0} \mathrm{n} \cdots \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{98} \mathrm{Nb}+-\mathrm{d} \mathrm{n}\)

Complete and balance the nuclear equations for the following fission reactions: (a) \({ }_{92}^{235} \mathrm{U}+{ }_{0} \mathrm{n} \cdots \rightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{72} \mathrm{Zn}+\ldots_{0}^{1} \mathrm{n}\) (b) \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{58}^{144} \mathrm{Ce}+\underline{+2}_{0}^{1} \mathrm{n}\)

A portion of the Sun's energy comes from the reaction $$ 4 \mathrm{l} \mathrm{H} \cdots{ }_{2}^{4} \mathrm{He}+2 \mathrm{le} $$ This reaction requires a temperature of about \(10^{6}\) to \(10^{7} \mathrm{~K}\). (a) Why is such a high temperature required? (b) Is the Sun solid?

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 R-COOH with hydroxyl radical and hydroxide ion, respectively. Why is hydroxyl radical more toxic to living systems than hydroxide ion?

A laboratory rat is exposed to an alpha-radiation source whose activity is \(14.3 \mathrm{mCi}\). (a) What is the activity of the radiation in disintegrations per second? In becquerels? (b) The rat has a mass of \(385 \mathrm{~g}\) and is exposed to the radiation for \(14.0 \mathrm{~s}\), absorbing \(35 \%\) of the emitted alpha particles, each having an energy of \(9.12 \times 10^{-13} \mathrm{~J} .\) Calculate the absorbed dose in millirads and grays. (c) If the RBE of the radiation is \(9.5\), calculate the effective absorbed dose in mrem and Sv.

A \(65-\mathrm{kg}\) person is accidentally exposed for \(240 \mathrm{~s}\) to a \(15-\mathrm{mCi}\) source of beta radiation coming from a sample of \({ }^{90}\) Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of \(8.75 \times 10^{-14} \mathrm{~J}\), and \(7.5 \%\) of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. (c) If the RBE of thebeta particles is \(1.0\), what is the effective dose in mrem and in sieverts? (d) How does the magnitude of this dose of radiation compare with that of a mammogram ( 300 mrem)?

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?