A neutron collides head-on and elasticity with an atom of mass number `A`, which is initially at rest. The fraction of kinetic energy retained by neutron is

Options

A. `((A)/(A + 1))^(2)`
B. `((A - 1)/(A + 1))^(2)`
C. `((A - 1)/(A))^(2)`
D. `((A + 1)/(A - 1))^(2)`

Answer

B

Explanation

`mu = mv_(1) + mA v_(2)` (i)
`v_(1) + u = v_(2) + 0` (ii)
`v_(1) = ((1 - A)/( 1 + A)) u`
Fraction of energy retained by neutron is
`(((1)/(2) mv_(1)^(2))/((1)/(2) mu^(2))) = ((v_(1))/(u))^(2) = ((1 - A)/(1 + A))^(2) = ((A - 1)/(A + 1))^(2)`