The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy K is ‘r’. Then the distance of closest approach if it is fired with a kinetic energy 2K is 

the distance of closest approach can be obtained by using the conservation of energy principle is 

$$\begin{gathered} \frac{1}{2}{\mathrm{mv}}^2=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{Ze}2\mathrm{e}}{\mathrm{r}} \\ \mathrm{so} \mathrm{r} \mathrm{is} \mathrm{the} \mathrm{distance} \mathrm{of} \mathrm{closest} \mathrm{approach} \\ \mathrm{is} \mathrm{inversely} \mathrm{proportional} \mathrm{to} \mathrm{kinetic} \mathrm{enrergy} \mathrm{of} \mathrm{the} \mathrm{alpha} \mathrm{particle} \end{gathered}$$