Beta Decay $($Similar to Problem $12\mathrm{.}26$ ns $12\mathrm{.}27)$ a$.$ Show explicitly that for each of the three beta decay processes $($equations$)$: negative beta decay $12\mathrm{.}29,$ positive beta decay $(12\mathrm{.}33),$ and electron capture $(12\mathrm{.}36),$ that the masses of the electrons cancel. b$.$ Using the negative beta decay equation, calculate the maximum kinetic energy of the electron. c$.$ Why is this a maximum? Under what conditions is this achieved? Is this what is true in nature?