In an exothermic nuclear reaction, the difference in mass between the reactants and the products is m, and the energy released is $Q$. In a separate exothermic nuclear reaction in which the mass difference between reactants and products is $\mathrm{\displaystyle \frac{m}{4}}$, how much energy will be released?
A) $\displaystyle \frac{Q}{4}$
B) $\displaystyle \frac{Q}{2}$
C) $\left(\displaystyle \frac{Q}{4}\right)c^2$
D) $\left(\displaystyle \frac{Q}{2}\right)c^2$
E) $4Q$
A) $\displaystyle \frac{Q}{4}$
B) $\displaystyle \frac{Q}{2}$
C) $\left(\displaystyle \frac{Q}{4}\right)c^2$
D) $\left(\displaystyle \frac{Q}{2}\right)c^2$
E) $4Q$
The equation that relates the mass difference m and the disintegration energy $Q$ is Einstein’s mass‑energy equivalence formula,
$$Q=mc^2$$
Because $c^2$ is a constant, we see that $Q$ is proportional to $m$. Therefore, if $m$ decreases by a factor of $4$, then so will $Q$.