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Chapter 21: Problem 72
Assume that Bismuth- 213 decays to a stable nucleus by a series of two alpha and two beta emissions. What is the stable nucleus that is formed?
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A radioactive decay series that begins with 90 Th ends with formation of the stable nuclide \({ }^{208} \mathrm{~Pb} .\) How many alpha-particle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?
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 \(10^{7} \mathrm{~K}\). Use the mass of the helium-4 nucleus given in Table 21.7 to determine how much energy is released per mol of hydrogen atoms.
Write balanced equations for each of the following nuclear reactions: $(\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\( (c) \){ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}$.
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 -mg sample of the \(\mathrm{CaCO}_{3}\) had a radioactivity of $1.5 \times 10^{-2}$ 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, 5700 yr, calculate the age of the charcoal sample.
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 \(1 \mathrm{~J} / \mathrm{s}\).
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