Rutherford model: The approximate size of the nucleus can be calculated by using energy conservation theorem in Rutherford's `alpha`-scattering experiment. If an `alpha`-particle is projected from infinity with speed v towards the nucleus having Z protons, then the `alpha`-particle which is reflected back or which is deflected by `180^@` must have approached closest to the nucleus .It can be approximated that `alpha` particle collides with the nucleus and gets back. Now if we apply the energy conservation equation at initial point and collision point then:

`(P.E.)_i= 0`, since P.E. of two charge system separated by infinite distance is zero. Finally the particle stops and then starts coming back.
`1/2m_alpha v_alpha^2+0=0+(Kq_1q_2)/Rimplies 1/2m_alphav_alpha^2=K(2exxZe)/R implies R=(4KZe^2)/(m_alphav_alpha^2)`
Thus the radius of nucleus can be calculated using above equation. The nucleus is so small a particle that we can't define a sharp boundary for it
An `alpha`-particle with initial speed `v_0` is projected from infinity and it approaches up to `r_0` distance from a nuclie. Then, the initial speed of `alpha`-particle, which approaches upto `2r_0` distance from the nucleus is :

Options

A. `sqrt2 v_0`
B. `v_0/sqrt2`
C. `2v_0`
D. `v_0/2`