Charge Is Conserved — Question 4

Question 4

Charge balance constrains reaction products without identifying a reaction

Consider a proposed nuclear transformation with initial nuclear charge $+12e$. A daughter nucleus has charge $+13e$, and all unlisted products are stated to be neutral except for an unknown charged product X. Only electric-charge conservation is to be tested; no claim about energy or other particle quantum numbers is supplied.

1. Find the charge of X. Test whether an electron or a positron could satisfy this charge requirement, using charges $-e$ and $+e$, respectively.

2. If the daughter instead has charge $+11e$, find the required X charge. Explain why either successful charge balance is only a necessary condition for a physical transformation.

Question 4 - Solution

Charge balance constrains reaction products without identifying a reaction

(a) Method and calculation

$$12e=13e+Q_X\Rightarrow Q_X=-e.$$$$13e+(-e)=12e,\quad13e+(+e)=14e\ne12e.$$An electron has the required charge in the first proposal; a positron does not.

(b) Interpretation and further calculation

$$12e=11e+Q_X\Rightarrow Q_X=+e.$$$$\sum Q_{\mathrm{before}}=\sum Q_{\mathrm{after}}.$$A positron meets the second charge condition. Energy, momentum and other applicable conservation laws must also be satisfied before the process is physically allowed.

Physical check

A change in nuclear proton count can be compatible with conserved total charge when charged products are included.