A molecule collides with another, stationary, molecule of the same mass. Demonstrate that the angle of divergence
(a) equals `90^@` when the collision is ideally elastic,
(b) differs from `90^@` when the collision is inelastic.

Explanation

(a) Let a molecule comes with velocity `vecv_1` to strike another stationary molecule and just after collision their velocities become `overset(rarr')v_1` and `overset(rarr')v_2` respectively. As the mass of the each molecule is same, conservation of linear momentum nad conservation of kinetic energy for the system (both molecules) respectively gives:
`vecv_1=overset(rarr')v_1+overset(rarr')v_2`
and `v_1^2=v'_1^2+v'_2^2`
From the property of vector addition it is obvious from the obtained Eqs. that
`overset(rarr')v_1_|_overset(rarr')v_2` or `overset(rarr')v_1*overset(rarr')v_2=0`
(b) Due to the loss of kinetic energy in inelastic collision `v_1^2 gt v'_1^2+v'_2^2`
so, `overset(rarr')v_1*overset(rarr')v_2gt0` and therefore angle of divergence `lt 90^@`.