An $\alpha$-particle with a velocity $v$ bombards a heavy stationary nucleus. Then the distance of c

Question

An $\alpha$-particle with a velocity $v$ bombards a heavy stationary nucleus. Then the distance of closest approach depends on the velocity of the $\alpha$-particle as

Professor PC Thomas Classes · Answer

At closest approach, kinetic energy converts to potential energy: $\frac{1}{2}mv^2 \propto \frac{1}{r} \Rightarrow r \propto \frac{1}{v^2}$.