Example 4.5:
At what temperature is the mean translational K.E. of a molecule equal to that of a singly charged ion of the same mass that has been accelerated from rest through a potential difference of (a) 1 volts, (b) 500 volts? Neglect relativistic effect.

Solution:

Mean translational K.E. of a molecule

Energy of a singly charged ion of the same mass as that of the molecules, accelerated from rest through a potential difference of 1 volt is given by:

Similarly, for (b)