Atomic Structure: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Atomic Structure. Understanding the underlying formula is key to arriving at the correct answer below:

At the distance of closest approach $r_0$, kinetic energy is converted to potential energy. $\frac{1}{2} m v^2 = \frac{1}{4\pi\epsilon_0} \frac{(2e)(Ze)}{r_0}$. Rearranging gives $r_0 = \frac{4 Z e^2}{4\pi\epsilon_0 m v^2}$, which shows $r_0 \propto \frac{1}{m}$.