A neutron with velocity `V` strikes a stationary deuterium atom, its kinetic energy changes by a factor of

Options

A. `(15)/(16)`
B. `(1)/(2)`
C. `(2)/(1)`
D. None of these

Answer

D

Explanation

Neutron velocity `= v`, mass `= m`
Deuteron contains `1` neutron and `1` proton, mass `= 2m`

In elastic collison both momentum and `K.E.` are conserved `p_(i) = p_(f)`
`mv = m_(1)v_(2) + m_(2)v_(2) rArr mv_(1) + 2mv_(2) .......(i)`
By conservation of kinetic energy
`(1)/(2) mv^(2) = (1)/(2)mv_(1)^(2) + (1)/(2) (2m)v_(2)^(2)........(ii)`
By solving (i) and (ii) we get
`v_(1) = (m_(1) - m_(2))/(m_(1) + m_(2))v + (2m_(2))/((m_(1) + m_(2)))v rArr v_(1) = (m_(1) + 2m)/(3m) = -(v)/(3)`
`K_(i) = (1)/(2)mv^(2), K_(f) = (1)/(2)mv_(1)^(2) rArr (K_(i) - K_(f))/(K_(i)) = 1 - (v_(1)^(2))/(v^(2))`
`= 1- (1)/(9) = (8)/(9)` (Fractional change in `K.E.`)