A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which perfactly inelastic collision will take place is :

Step-by-step solution

Let velocity before collision v from momentum conservation m v = ( m + m ) v 1 v 1 = v 2 Loss in K.E. = 1 2 m v 2 - 1 2 2 m v 2 2 = 1 4 m v 2 K.E. lost is used to jump from 1 s t orbit to 2 n d orbit ∆ K . E . = 10.2 e V ⇒ 1 4 m v 2 = 10.2 1 2 m v 2 = 2 × 10.2 = 20.4 e V