Problems and Solutions on Thermodynamics and Statistical Mechanics

378 Problems d Solutions on Thermodynamics d Statistical Mechanics

Fig. 2.41.

Solution:
aH
Putting 22 = 0 and - = 0, we obtain b = p/fi corresponding to

the peak of potential barrier. Assume b >> 1, where 1 is the mean free path
of the particles, so that even near the peak the particles are in thermal
equilibrium. We need consider only the escape rate near the peak:

?Xl

I/ fdv

N = 2rbv,n(b) f dv

m ma

v,e-mus dv,

J

where n(b) is the number density at the peak. To find n(b) we note that

where r2 = xf + 52, and c is a normalizing factor defined by the following
equation:

As the majority of the particles reside within the quadratic part of the