A neutron strikes a hydrogen atom which is initially at rest and free to move. The initial speed of the neutron is u. After the collision, both neutron and the H-atom move making 30° angle with the initial velocity of the neutron. Also the H-atom is found to get excited to first excited state. If the initial kinetic energy of neutron = p times first excitation energy of the H-atom, the initial kinetic energy of neutron = q times final KE of system of neutron + Hydrogen, the initial momentum of neutron = r times its final momentum in magnitude, the initial magnitude of momentum of system of neutron + Hydrogen is ‘s’ times its final value, then (assume mass of neutron = mass of H-atom)

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p =3

$q = \frac{2}{3}$

$r = \sqrt{3}$

s = 1

answer is A, C, D.

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Detailed Solution

${(P_{i} - P_{f})}_{Y} = O \Rightarrow V_{1} = V_{2} = V {(P_{i} = P_{f})}_{X} \Rightarrow m u = m v_{1} \cos 30 ° + m v_{2} \cos 30 ° u = 2 v \cos 30 ° v = \frac{u}{\sqrt{3}} .... (i) E_{i} = E_{f} K_{i} = K_{f} + I_{E x c i t a t i o n e n e r g y} H e r e K_{f} = (\frac{1}{2} m v^{2}) \times 2 = \frac{2}{3} K_{i} ∴ I_{e x} = \frac{K_{i}}{3}$