Definition of distance of closest approach
Finding of distance of closest approach when kinetic energy is doubled
It is the distance of charged particle from the centre of the nucleus, at which the whole of the initial kinetic energy of the (far off) charged particle gets converted into the electric potential energy of the system.
Distance of closest approach(rc) is given by
rc=‌

1

4πε0

⋅‌

2Ze2

K

' K ' is doubled, ∴rc becomes ‌

r

2

[Alternatively: If a candidate writes directly ‌

r

2

without mentioning formula, award the 1 mark forthis part.]
OR
Two important limitations of Rutherford nuclear model
1. According to Rutherford model, electron orbiting around the nucleus, continuously radiates energy due to the acceleration; hence the atom will not remain stable.
2.As electron spirals inwards; its angular velocity and frequency change continuously; therefore it will emit a continuous spectrum.