A nucleus desintegrated into two nucleus which have their velocities in the ratio of `2 : 1 ` . The ratio of their nuiclear sizes will be

Options

A. `2^(1//3) : 1`
B. `1 : 3^(1//2)`
C. `3^(1//2) : 1`
D. `1 : 2^(1//3)`

Answer

D

Explanation

By conservation of momentum,
`m_(1) v_(1) = m_(2) v_(2)`
`therefore" "(m_(1))/(m_(2)) = (v_(2))/(v_(1)) = (1)/(2) [because "given", v_(1) : v_(2) = 2 : 1]" "...(i)`
Again, `R = R_(0) xx A^(1//3)` where A is mass number.
`therefore" "(R_(1))/(R_(2)) = ((A_(1))/(A_(2)))^(1//3) = ((m_(1))/(m_(2)))^(1//3) = ((1)/(2))^(1//3)`
`rArr" "(R_(1))/(R_(2)) = (1)/(2^(1//3)) rArr R_(1) : R_(2) = 1 : 2^(1//3)`