For Rutherford scattering, at the closest approach all kinetic energy converts to electrostatic potential energy.
For alpha particle-nucleus collision:
K.E.=4πε01rminZ1Z2e2
Where: Z1=2 (alpha), Z2=79 (gold), K.E.=7.9 MeV
rmin=7.9×106×1.6×10−199×109×2×79×(1.6×10−19)2
rmin=2.88×10−14 m
The estimated nuclear diameter is approximately:
d=2×rmin=5.76×10−14 m