A neutron makes a head-on elastic collision with a stationary deuteron. The fraction energy loss of the neutron in the collision is

Options

A. `16//18`
B. `8//9`
C. `8//27`
D. `2//3`

Answer

B

Explanation

`mu = mv_(1) +2mv_(2) rArr v_(1) + 2 v_(2) = u` (i)
`v_(1) + u = v_(2) + 0 rArr v_(1) - v_(2) = -u` (ii)
`v_(1) = -(u)/(3)`
Fractional loss of `K.E.` of neuton is
`((1)/(2) m u^(2) - (1)/(2) mv_(1)^(2))/((1)/(2) m u^(2)) = 1 - ((v_(1))/(u))^(2) = 1 - (1)/(9) = (8)/(9)`