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. 16/82
B. `8//9`
C. `8//27`
D. `2/3`

Answer

B

Explanation

`u=v_(1)=2v_(2)` . . . (i)
`e=1-(-(v_(1)-v_(2)))/(u)`
`therefore u=v_(2)-v_(1)` . .. (2)
solving `v_(1)=(-u)/(3),v_(2)=(2u)/(3)`
fraction energy loss of neutron
`((1)/(2)m u^(2)-(1)/(2)m(-(u)/(3))^(2))/((1)/(2)m u^(2))=(8)/(9)` .