Problems and Solutions on Thermodynamics and Statistical Mechanics

394 Problem3 d Solutiotu on Thermodynamics €4 Statistical Mechanics

of particles in the beam is lo1'/ cm3. Compare this result with the pressure
from the background gas.
(UC, Berkeley)
collimating slits
small hole

oven

.rm------I

Fig. 2.45.

Soh t ion :

(a) The fractional loss of atoms in the beam is 1 - exp(-z/l), where

1 is the mean free path. If the loss is to be less than l/e after travelling a

distance L, L must be less than 1 In

we require

p = nkT < kTln ( - 1) /h = 0.18N/m2 fcr L = 1 m.

(b) If the velocity in 2-direction is v,, the flying time is L/v,. Since

the distribution of the particle number in the beam is

fdv, cc v,e-*dv, ,

we have

(Note that scattering from background gas atoms has been neglected.)

u, - v, + dv, on the wall is proportional to

(c) The pressure exerted by particles in the velocity interval

v,Amv,fdv,

NA ,