The distance of closest approach of an `alpha`-particle fired towards a nucleus with momentum p, is r. If the momentum of the `alpha`-particle is 2p, the corresponding distance of closest approach is

Options

A. `(r)/(2)`
B. 2r
C. 4r
D. `(r)/(4)`

Answer

D

Explanation

`p prop (1)/(sqrt(r))`
`r prop (1)/(p^(2))`
Hence, `(r_(1))/(r_(2)) = ((p_(2))/(p_(1)))^(2)`
`= ((p)/(2p))^(2) = (1)/(4)`
`r_(1) = (r_(2))/(4)`