Explain distance of closest approach and impact parameter with illustrations.

Explanation

Distance of closest approach :
1) Suppose an `alpha`-particle with initial kinetic energy (K.E) is directed towards the centre of the nucleus of an atom.
2) On account of Coulomb's repulsive force between nucleus arid alpha particle, kinetic energy of alpha particle goes on decreasing arid in turn, electric potential energy of the particle goes on increasing.
3) At certain distance 'd' from the nucleus, K. E of `alpha`-particle reduces to zero. The particle stops and it can not go closer to the nucleus. It is repelled by the nucleus and therefore it retraces its path, turning through `180^(@)`.
Therefore, the distance d is known as the distance of closest of approach.

The closets distance of approach,
`d=(1)/(4pi epsi_(0))xx(Ze^(2))/((1)/(2) mv^(2))`
Impact parameter (b) : Impact parameter is defined as the `bot^(r)` distance of the initial velocity vector of the `alph` - particle from the central line of the nucleus, when the particle is far away from the nucleus of the atom.