Answer: Nuclear waste disposal is one of the major

Chapter 19, Problem 76P

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Nuclear waste disposal is one of the major concerns of the nuclear industry. In choosing a safe and stable environment to store nuclear wastes, consideration must be given to the heat released during nuclear decay. As an example, consider the \(\beta\) decay of \({ }^{90} \mathrm{Sr}\) (89.907738 amu):

            \(_{38}^{90}\mathrm{Sr}\ \longrightarrow\ _{39}^{90}\mathrm{Y}+_{-1}^{\ \ 0}\beta\)         \(t_\frac{1}{2}\) = 28.1 yr

The \({ }^{90} \mathrm{Y}\) (89.907152 amu) further decays as follows:

               \(_{39}^{90}\mathrm{Y}\ \longrightarrow\ _{40}^{90}\mathrm{Zr}+_{-1}^{\ \ 0}\beta\)         \(t_\frac{1}{2}\) = 64 h

Zirconium-90 (89.904703 amu) is a stable isotope. (a) Use the mass defect to calculate the energy released (in joules) in each of the above two decays. (The mass of the electron is \(5.4857\times10^{-4}\mathrm{\ amu}\).) (b) Starting with one mole of \({ }^{90} \mathrm{Sr}\), calculate the number of moles of \({ }^{90} \mathrm{Sr}\) that will decay in a year. (c) Calculate the amount of heat released (in kilojoules) corresponding to the number of moles of \({ }^{90} \mathrm{Sr}\) decayed to \({ }^{90} \mathrm{Zr}\) in (b).