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//81`
B. `8//9`
C. `8//27 `
D. `2//3`

Answer

B

Explanation

`(KE)_(i) =1/2 m_1u_1^2`
`(KE)_f =m_1 [((m_1-m_2)/(m_1+m_2))u_1]^2`
Fraction of KE of neutron –
`= ((KE)_i-(KE)_f)/((KE)_i)implies1-((m_1-m_2)/(m_1+m_2))^2`
`implies1-((1-2)/(1+2))^2 =1-1/9=8/9`
Note: Mass of deutron is 2 unit.