How does the distance of closest approach ($d$) for an alpha particle directed towards a nucleus var

Question

How does the distance of closest approach ($d$) for an alpha particle directed towards a nucleus vary with its initial kinetic energy ($K$)?

Professor PC Thomas Classes · Answer

From the conservation of energy, $K = \frac{1}{4\pi\epsilon_0} \frac{2Ze^2}{d}$, showing that the distance of closest approach is inversely proportional to $K$.