31.4 Exercise 23

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation $e^{+ } + e^{- } \rightarrow \gamma + \gamma$ conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each $\gamma$ ray, assuming the electron and positron are initially nearly at rest. (c) Explain why the two $\gamma$ rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.