Question
Knowing that the atomic masses of Al and Mg are respectively 2513Al = 24.990432 u and 2512Mg = 24.985839 u while electron mass is often expressed as me = 0.511 MeV, the Q value (energy liberated) of the β decay nuclear reaction 25Al → 25Mg + e+ + ν in MeV is :
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Solution
[Key Concept: In β+ decay computed with neutral atomic masses, two electron rest energies must be subtracted from the atomic mass difference.]
For $\beta +$ decay process
$$\begin{matrix} & Q = \left\lbrack m_{\text{parent~}} - m_{\text{daughter~}} - 2{\text{ }m}_{e} \right\rbrack \times 931.5MeV \\ & Q = \left\lbrack m_{\text{parent~}} - m_{\text{daughter~}} \right\rbrack \times 931.5 - 2\left\lbrack {\text{ }m}_{e} \times 931.5MeV \right\rbrack \\ & Q = \lbrack 24.990432 - 24.985839\rbrack \times 931.5 - 2\lbrack 0.511\rbrack \\ & Q = 3.256MeV \end{matrix}$$
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