Distance of closest approach:

Estimation of two size of nucleus (by Rutherford experiments or distance of closest approach).

Suppose an  ∝ - particle of mass m and initial velocity u moves directly towards the centre of the nucleus of an atom.

As it approaches the +ve nucleus, it experience a coulombic repulsions and its kinetic energy gets progressively converted in electrical energy.

At a certain distance r_o from the nucleus the alpha particle stops for a moment and then begins to retrace its path. The distance r_o is called the Distance of closest approach.

Initial kinetic energy of ∝ - particle

                K_∝ = ½ mu²

The electrostatic potential energy of alpha particle and nucleus at a distance r_o is given by

                V = K. (q₁q₂/r_o)                  K. (2eZe/r_o)

At a distance of r_o, K_∝ = U therefore

½ mu² = K2Ze²/r_o

r_o = 4KZe²/mu²

Clearly radius of nucleus must be smaller than r_o.