Chapter 21

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 \(\mathrm{RBE}\) of the beta 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 ( \(300 \mathrm{mrem}\) )?

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 \({ }^{36} \mathrm{Cl}\) 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 (Equation 21.26 ). Why do you think the more obvious product of the reaction, \({ }^{2} \mathrm{He},\) is unstable?

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

Suppose you had a detection device that could count every decay event from a radioactive sample of plutonium- \(239\left(t_{1 / 2}\right.\) is 24,000 yr). How many counts per second would you obtain from a sample containing \(0.385 \mathrm{~g}\) of plutonium- \(239 ?\)

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: Do the \(\mathrm{C}-\mathrm{OH}\) bond of the acid and the \(\mathrm{O}-\mathrm{H}\) bond of the alcohol break in the reaction, or do the \(\mathrm{O}-\mathrm{H}\) bond of the acid and the \(\mathrm{C}-\mathrm{OH}\) bond of the alcohol break? Explain.

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 Sun radiates energy into space at the rate of \(3.9 \times 10^{26} \mathrm{~J} / \mathrm{s}\). (a) Calculate the rate of mass loss from the Sun in \(\mathrm{kg} / \mathrm{s}\). (b) How does this mass loss arise? (c) It is estimated that the Sun contains \(9 \times 10^{56}\) free protons. How many protons per second are consumed in nuclear reactions in the Sun?

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 \(2 \mathrm{pCi}\) 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 \(75 \mathrm{~kg}\), calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Calculate the mass of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) that must be burned in air to evolve the same quantity of energy as produced by the fusion of \(1.0 \mathrm{~g}\) of hydrogen in the following fusion reaction: $$ 4_{1}^{1} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{1}^{0} \mathrm{e} $$ Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise \(21.50,\) Appendix \(\mathrm{C}\), and the inside covers of the text. The standard enthalpy of formation of octane is \(-250.1 \mathrm{~kJ} / \mathrm{mol}\)

A sample of an alpha emitter having an activity of \(0.18 \mathrm{i}\) is stored in a \(25.0-\mathrm{mL}\) 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?

Charcoal samples from Stonehenge in England were burned in \(\mathrm{O}_{2},\) and the resultant \(\mathrm{CO}_{2}\) gas bubbled into a solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) (limewater), resulting in the precipitation of \(\mathrm{CaCO}_{3} .\) The \(\mathrm{CaCO}_{3}\) was removed by filtration and dried. A \(788-\mathrm{mg}\) sample of the \(\mathrm{CaCO}_{3}\) had a radioactivity of \(1.5 \times 10^{-2} \mathrm{~Bq}\) due to carbon-14. By comparison, living organisms undergo 15.3 disintegrations per minute per gram of carbon. Using the half-life of carbon- \(14,5715 \mathrm{yr},\) calculate the age of the charcoal sample.

A \(25.0-\mathrm{mL}\) sample of \(0.050 \mathrm{M}\) barium nitrate solution was mixed with \(25.0 \mathrm{~mL}\) of \(0.050 \mathrm{M}\) 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.