Closest Approach of Alpha Particles

Rutherford fired alpha particles at gold atoms in a piece of foil. They approach the nucleus but slow down as the electromagnetic repulsive force become stronger. Eventually they stop moving, all the kinetic energy has been converted into potential energy as the particles come to rest at a distance r from the centre of the nucleus.

where V is the electric potential at a distance of r from the centre

This gives us the upper limit of the radius of a nucleus.

Calculating the nuclear radius this way gives us a value of r = 4.55 x 10^-14 m or 45.5 fm (where 1 fm = 1 x 10^-15 m)

Modern measurements give us values of approximately r = 6.5 fm

(Remember that 1 eV of energy is equal to 1.6 x 10^-19 J)