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 \({ }^{90} \mathrm{Sr}\) \((89.907738
\mathrm{amu})\)
$$
{ }_{38}^{90} \mathrm{Sr} \longrightarrow{ }_{39}^{90} \mathrm{Y}+{ }_{-1}^{0}
\beta \quad t_{\frac{1}{2}}=28.1 \mathrm{yr}
$$
The \({ }^{90} \mathrm{Y}(89.907152 \mathrm{amu})\) further decays as follows:
$$
{ }_{39}^{90} \mathrm{Y} \longrightarrow{ }_{40}^{90} \mathrm{Zr}+{ }_{-1}^{0}
\beta \quad t_{\frac{1}{2}}=64 \mathrm{~h}
$$
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 preceding two decays. (The mass of the electron is \(5.4857 \times\)
\(10^{-4}\) amu. ( b) Starting with 1 mole of \({ }^{90}\) Sr, calculate the
number of moles of \(9^{9}\) 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
\((\mathrm{b})\)
