Question

What is distance of closest approach?

Answer 1

The minimum distance between the centre of the nucleus and the alpha particle just before it gets reflected back through 180° is defined as the distance of the closest approach r₀ (also known as contact distance).

At this distance, all the kinetic energy of the alpha particle will be converted into electrostatic potential energy

`1/2 mv_0^2 = 1/(4 pi epsilon_0) ((2e)(Ze))/r_0`

⇒ `r_0 = 1/(4 pi epsilon_0) (2Ze^2)/(1/2 mv_0^2)`

= `1/(4 pi epsilon_0) (2Ze^2)/E_k`

where E_k is the kinetic energy of the alpha particle.This is used to estimate the size of the nucleus, but the size of the nucleus is always lesser than the distance of the closest approach.