Irodov Problem 1.177

As with the last few problems, momentum will be conserved before and after collision of the molecules and so we have,























In case the collision is elastic no energy will be lost and so we have,









Here is the angle of divergence. One trivial solution to (6) is . This corresponds to a perfectly head on collision, in this case the angle of divergence will be 0. Now let us consider the non-trivial case when .









Now (7) can only be true if . This demonstrates part a) of the question.

In case of an inelastic collision we will have,





Clearly then and this demonstrates part b).