Chapter 21

Which type or types of nuclear reactors have these characteristics? \(\begin{array}{l}{\text { (a) Can use natural uranium as a fuel }} \\ {\text { (b) Does not use a moderator }} \\ {\text { (c) Can be refueled without shutting down }}\end{array}\)

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?

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

A 65-kg person is accidentally exposed for 240 s to a 15-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 the beta particles is \(1.0,\) what is the effective dose in mrem and in sieverts? (d) Is the radiation dose equal to, greater than, or less than that for a typical 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?

Chlorine has two stable nuclides, \(^{35} \mathrm{Cl}\) and \(^{37} \mathrm{Cl} .\) In contrast, \(^{36} \mathrm{Cl}\) is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of \(^{36} \mathrm{Cl} ?\) (b) Based on the empirical rules about nuclear stability, explain why the nucleus of \(^{36} \mathrm{C}\) is less stable than either \(^{35}\mathrm{Cl}\) or \(^{37} \mathrm{Cl}\).

When two protons fuse in a star, the product is \(^{2} \mathrm{H}\) plus a positron. Write the nuclear equation for this process.

Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments: \begin{equation} (a) \stackrel{6}{3} \mathrm{Li}+\stackrel{56}{28} \mathrm{Ni} \longrightarrow ? \end{equation}\begin{equation}(b) \stackrel{40}{20} \mathrm{Ca}+\stackrel {248}{96} \mathrm{Cm} \longrightarrow \stackrel{147}{62} \mathrm{Sm} + ? \end{equation}\begin{equation}(c) \stackrel{88}{38} \mathrm{Sr}+\stackrel{84}{36} \mathrm{Kr} \longrightarrow \stackrel{116}{46} \mathrm{Pd} + ?\end{equation}\begin{equation} (d)\stackrel{40}{20} \mathrm{Ca}+\stackrel{238}{92} \mathrm{U} \longrightarrow \stackrel{70}{30} \mathrm{Zn}+4 \stackrel{1}{0}\mathrm{n}+2 ?\end{equation}

In 2010, a team of scientists from Russia and the United States reported creation of the first atom of element 117, which is named tennessine, and whose symbol is Ts. The synthesis involved the collision of a target of \(_{97}^{249} \mathrm{Bk}\) with accelerated ions of an isotope which we will denote Q. The product atom, which we will call Z, immediately releases neutrons and forms \(_{97}^{249} \mathrm{Bk} :\) $$_{97}^{249} \mathrm{Bk}+\mathrm{Q} \longrightarrow \mathrm{Z} \longrightarrow_{117 \mathrm{Ts}}^{294 \mathrm{Ts}}+3_{0}^{1} \mathrm{n}$$ (a) What are the identities of isotopes Q and Z? (b) Isotope Q is unusual in that it is very long-lived (its half-life is on the order of 1019 yr) in spite of having an unfavorable neutron-to-proton ratio (Figure 21.1). Can you propose a reason for its unusual stability? (c) Collision of ions of isotope Q with a target was also used to produce the first atoms of livermorium, Lv. The initial product of this collision was \(_{116}^{296} \mathrm{Zn}\). What was the target isotope with which Q collided in this experiment?

According to current regulations, the maximum permissible dose of strontium-90 in the body of an adult is 1\(\mu \mathrm{Ci}\left(1 \times 10^{-6} \mathrm{Ci}\right) .\) Using the relationship rate \(=k N,\) calculate the number of atoms of strontium-90 to which this dose corresponds. To what mass of strontium-90 does this correspond? The half-life for strontium-90 is 28.8 yr.

Methyl acetate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\right)\) is formed by the reaction of acetic acid with methyl alcohol. If the methyl alcohol is labeled with oxygen-18, the oxygen-18 ends up in the methyl acetate: \(\begin{array}{l}{\text { (a) Do the } \mathrm{C}-\mathrm{OH} \text { bond of the acid and the } \mathrm{O}-\mathrm{H} \text { bond }} \\ {\text { of the alcohol break in the reaction, or do the } \mathrm{O}-\mathrm{H} \text { bond }} \\ {\text { of the acid and the } \mathrm{C}-\mathrm{OH} \text { bond of the alcohol break? }}\end{array}\) \(\begin{array}{l}{\text { (b) Imagine a similar experiment using the radioisotope }^{3} \mathrm{H} \text { , }} \\ {\text { which is called tritium and is usually denoted T. Would the }} \\ {\text { reaction between } \mathrm{CH}_{3} \mathrm{COH} \text { and } \mathrm{TOCH}_{3} \text { provide the same }} \\ {\text { information about which bond is broken as does the above }} \\ {\text { experiment with } \mathrm{H}^{18} \mathrm{OCH}_{3} ?}\end{array}\)

Each of the following transmutations produces a radionuclide used in positron emission tomography (PET). (a) Inequations (i) and (ii), identify the species signified as "X." (b) In equation (iii), one of the species is indicated as "d." What do you think it represents? \begin{equation}\begin{array}{l}{(\mathrm{i})^{14} \mathrm{N}(\mathrm{p}, \alpha) \mathrm{X}} \\ {(\mathrm{ii})^{18} \mathrm{O}(\mathrm{p}, \mathrm{X})^{18} \mathrm{F}} \\ {\text { (iii) }^{14} \mathrm{N}(\mathrm{d}, \mathrm{n})^{15} \mathrm{O}}\end{array}\end{equation}

The nuclear masses of \(^{7}\mathrm{Be},^{9} \mathrm{Be},\) and \(^{10} \mathrm{Be}\) are \(7.0147,9.0100\) and 10.0113 amu, respectively. Which of these nuclei has the largest binding energy per nucleon?

A \(26.00-\mathrm{g}\) sample of water containing tritium, \(_{1}^{3} \mathrm{H},\) emits \(1.50 \times 10^{3}\) beta particles per second. Tritium is a weak beta emitter with a half-life of 12.3 yr. What fraction of all the hydrogen in the water sample is tritium?

The average energy released in the fission of a single uranium-235 nucleus is about \(3 \times 10^{-11} \mathrm{J} .\) If the conversion of this energy to electricity in a nuclear power plant is 40\(\%\) efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 1000 megawatts? Recall that a watt is 1 \(\mathrm{J} / \mathrm{s}\) .

Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{J}\) of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Naturally found uranium consists of 99.274\(\%^{238} \mathrm{U}\) \(0.720 \%^{233} \mathrm{U},\) and 0.006\(\%^{233} \mathrm{U}\) As we have seen, \(^{235} \mathrm{U}\) is the isotope that can undergo a nuclear chain reaction. Most of the \(^{255}\) U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF \(_{6}(g) .\) (a) What is the mass of UF \(_{6}\) in a 30.0 -L vessel of UF \(_{6}\) at a pressure of 695 torr at 350 \(\mathrm{K} ?\) (b) What is the mass of \(^{235} \mathrm{U}\) in the sample described in part (a)? (c) Now suppose that the \(\mathrm{UF}_{6}\) is diffused through a porous barrier and that the change in the ratio of of \(^{238} \mathrm{U}\) and \(^{235} \mathrm{U}\) in the diffused gas can be described by Equation 10.23. What is the mass of \(^{235} \mathrm{U}\) in a sample of the diffused gas analogous to that in part (a)? (d) After one more cycle of gaseous diffusion, what is the percentage of \(^{235} \mathrm{UF}_{6}\) in the sample?

A sample of an alpha emitter having an activity of 0.18 Ci is stored in a 25.0 -mL sealed container at \(22^{\circ} \mathrm{C}\) for 245 days. (a) How many alpha particles are formed during this time? (b) Assuming that each alpha particle is converted to a helium atom, what is the partial pressure of helium gas in the container after this 245 -day period?

A 25.0 -mL sample of 0.050\(M\) barium nitrate solution was mixed with 25.0 mL of 0.050\(M\) sodium sulfate solution labeled with radioactive sulfur-35. The activity of the initial sodium sulfate solution was \(1.22 \times 10^{6} \mathrm{Bq} / \mathrm{mL}\) . After the resultant precipitate was removed by filtration, the remaining filtrate was found to have an activity of 250 \(\mathrm{Bq} / \mathrm{mL}\) . (a) Write a balanced chemical equation for the reaction that occurred. (b) Calculate the \(K_{s p}\) for the precipitate under the conditions of the experiment.