Question

The distance of closest approach of an alpha paricle reaching a nucleus with momentum p is r0 when the alpha particle travels towards the same nucleus with momentum p/2 the distance of closest approach will be

Answer 1

Initial momentum P= mv, where m= mass of the alpha particle and

r₀= closest approach of alpha particle to nucleus  

v= velocity with which it travels towards the nucleus.

The closest path to approach nucleus is r₀, if the alpha particle is moving with momentum P.

We also know, P=mv= m(r/t)

If the particle is moving momentum P/2= (mv)/2= m(v/2)= m(r₀/2t)

Since mass is constant. So definitely speed will be halved. Thus the closest approach would be r₀/2