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`
Deteron constains `1` neutron and `1` proton.
`mass = 2m`

In elastic collision both momentum and `KE` are conserved `P_(i) = P_(f)`
`mv = m_(1)v_(2) + m_(2)v_(2) implies mv = 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`
`:' v_(1) = (m_(1) + 2m)/(3m) = - (v)/(3) K_(i) = (1)/(2) mv^(2)`
`K_(f) = (1)/(2) mv_(1)^(2) implies (K_(i) - K_(f))/(K_(i)) = 1 - (v_(1)^(2))/(v^(2))`
`= 1 - (1)/(9) = (8)/(9)` (Fractional change in `KE`)