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Question

A particle is moving along x-axis back and forth in a box of length L. Assuming de-broglie hypothesis applicable for the particle, and it is moving with constant speed in the box making perfectly elastic collisions to the walls. The possible value of momentum of the particle is : (Note : h is plank constant, n is principal quantum number)

(A) 2 nh/ L                 (B) nh /L                           (C) 4 nh /L                       (D) 2 /3 nh /L

Answer 1

The necessary conditions on the de Broglie wave are that the wave itself must vanish at the ends of the box (in order to satisfy the first postulate, since the particle can never escape the box.) This will happen for very specific wavelengths which are dependent on the length of the box itself.

Here a=L, 

So final answer is momentum = nh/2L