A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio `8 : 1`. The ratio of radii of the fragments is.

Options

A. `2:1`
B. `1:2`
C. `1:4`
D. `4:1`

Answer

D

Explanation

By the principle of conservation of linear momentum
`m_1v_1 = m_2 v_2 ` ( in magnitude)
`therefore m_1/m_2 = v_2/v_1 = 1/8`
But `m prop A` where A is the mass number and the nuclear radius is proportional to `A^(1//3) " i.e. " R prop A^(1//3)`
`therefore R_1/R_2 = (A_1/A_2)^(1//3) = (1/8)^(1//3) = 1/2`