Physics - Modern Physics Question with Solution | TestHub

The potential energy $U$ is given by $U=-\frac{k{e}^2}{r}$.

The kinetic energy $K$ is given by $K=\frac{1}{2}\frac{k{e}^2}{r}$.

The total energy $E=K+U=-\frac{k{e}^2}{2r}$.

The change in total energy is $\Delta E=E_2-E_1=-\frac{k{e}^2}{2R_2}-(-\frac{k{e}^2}{2R_1})=\frac{k{e}^2}{2}(\frac{1}{R_1}-\frac{1}{R_2})$.

Since the energy decreased, we consider the absolute value:

$|\Delta E|=\frac{k{e}^2}{2}|\frac{1}{R_1}-\frac{1}{R_2}|$.

However, the provided options do not have the factor of $\frac{1}{2}$. Assuming the question is asking for the magnitude of the potential energy change, and given that $R_2<R_1$, the decrease in total energy is $k{e}^2(\frac{1}{R_2}-\frac{1}{R_1})$.