Problem 51
Calculate the binding energy in J/nucleon for carbon-12 (atomic mass \(=12.0000\) u) and uranium-235 (atomic mass \(=\) 235.0439 u). The atomic mass of \(_{1}^{1} \mathrm{H}\) is 1.00782 \(\mathrm{u}\) and the mass of a neutron is 1.00866 u. The most stable nucleus known is \(^{56}\) Fe \((\text { see Exercise } 50)\) . Would the binding energy per nucleon for \(^{56} \mathrm{Fe}\) be larger or smaller than that of \(^{12} \mathrm{C}\) or \(^{235} \mathrm{U}\) ? Explain.
Problem 52
Calculate the binding energy for \(_{1}^{2} \mathrm{H}\) and \(_{1}^{3} \mathrm{H} .\) The atomic masses are \(_{1}^{2} \mathrm{H}, 2.01410 \mathrm{u} ;\) and \(^{3} \mathrm{H}, 3.01605 \mathrm{u} .\)
Problem 54
The binding energy per nucleon for magnesium- 27 is \(1.326 \times 10^{-12} \mathrm{J} /\) nucleon. Calculate the atomic mass of \(^{27} \mathrm{Mg}\) .
Problem 55
Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are \(_{1}^{1} \mathrm{H}, \quad 1.00782\) u; \(_{1}^{2} \mathrm{H}, \quad 2.01410 \quad \mathrm{u} ;\) and an electron, \(5.4858 \times 10^{-4}\) u. (Hint: Think carefully about how to account for the electron mass.) $$ _{1}^{1} \mathrm{H}+_{1}^{1} \mathrm{H} \longrightarrow_{1}^{2} \mathrm{H}+_{+1}^{0} \mathrm{e} $$
Problem 58
When using a Geiger-Müller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the Geiger-Muller tube to compare different measurements. Why?
Problem 59
Consider the following reaction to produce methyl acetate: When this reaction is carried out with \(\mathrm{CH}_{3} \mathrm{OH}\) containing oxygen- \(18,\) the water produced does not contain oxygen-18. Explain.
Problem 60
A chemist studied the reaction mechanism for the reaction $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ by reacting \(\mathrm{N}^{16} \mathrm{O}\) with \(^{18} \mathrm{O}_{2}\) . If the reaction mechanism is $$ \begin{aligned} \mathrm{NO}+\mathrm{O}_{2} & \rightleftharpoons \mathrm{NO}_{3}(\text { fast equilibrium }) \\ \mathrm{NO}_{3}+\mathrm{NO} & \longrightarrow 2 \mathrm{NO}_{2}(\text { slow }) \end{aligned} $$ what distribution of \(^{18} \mathrm{O}\) would you expect in the NO \(_{2} ?\) Assume that \(\mathrm{N}\) is the central atom in \(\mathrm{NO}_{3},\) assume only \(\mathrm{N}^{16} \mathrm{O}^{16} \mathrm{O}_{2}\) forms, and assume stoichiometric amounts of reactants are combined.
Problem 61
Uranium-235 undergoes many different fission reactions. For one such reaction, when \(^{235} \mathrm{U}\) is struck with a neutron, \(^{144}\mathrm{Ce}\) and \(^{90}\mathrm{Sr}\) are produced along with some neutrons and electrons. How many neutrons and \(\beta\) -particles are produced in this fission reaction?
Problem 62
Breeder reactors are used to convert the nonfissionable nuclide 238 \(\mathrm{U}\) to a fissionable product. Neutron capture of the 238 \(\mathrm{U}\) is followed by two successive beta decays. What is the final fissionable product?
Problem 63
Which do you think would be the greater health hazard: the release of a radioactive nuclide of Sr or a radioactive nuclide of Xe into the environment? Assume the amount of radioactivity is the same in each case. Explain your answer on the basis of the chemical properties of Sr and Xe. Why are the chemical properties of a radioactive substance important in assessing its potential health hazards?
