Question
Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for $\beta^-$ decay given in the equation $^A_Z\textrm{X}_N \to ^A_{Z+1}\textrm{Y}_{N-1} + \beta^- + \bar{\nu_\textrm{e}}$. To do this, identify the values of each before and after the decay.
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# OpenStax College Physics Solution, Chapter 31, Problem 31 (Problems & Exercises) (1:38)

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This is College Physics Answers with Shaun Dychko. We have <i>β</i>-decay of this nuclide <i>X</i> with atomic number <i>Z<i/>, mass number <i>A</i> and number of neutrons <i>N</i>. <i>β</i>-decay means that a neutron turns into a proton and so there is a additional proton here in this daughter nuclide and in order to conserve charge, an electron is also produced. So a neutron turns into a proton and an electron; it splits up into these two. And in order to conserve electron family number, an electron anti-neutrino is produced. Ok but let's go step-by-step through each of those conservation rules. We have conservation of charge so on the left side, we have a charge of <i>Z</i> and on the right hand side, we have a charge of <i>Z</i> plus 1 from this daughter nuclide and we have a charge of negative 1 from the electron produced for a total of <i>Z</i> so that checks out. Considering electron family number on the left side, there are no electrons or other particles that have an electron family number and so that's zero. On the right hand side, we have an electron family number of negative 1 for this <i>β</i>-particle and then we have a compensating positive 1 electron family number for the electron anti-neutrino and so this total is zero also. And the number of nucleons on the left-side is <i>A</i> and on the right hand side, it's also <i>A</i> and then there are no nucleons in a <i>β</i>-particle or in a neutrino and so it's <i>A</i> on each side and so that conservation rule checks out also.