312 PHENOMENA, ATOMS, AND MOLECULES 



If n = o, this gives /5 = — i, so that the atom A has its velocity re 

 versed. Thus when n — o the existence of attractive forces between the 

 atoms does not change the conditions from those of elastic collisions. If, 

 however, n = i we find 



T 



/3 = - 



I + 7' 



so that the velocity after collision is much less than we would calculate 

 according to the laws of elastic collision. 



This loss in velocity, which Baule has failed to take into account, would 

 result in a very great decrease in the number of atoms reflected from the 

 surface. In order to estimate the effect on the reflectivity we need to con- 

 sider the initial velocity of the atom A, due to its thermal energy. 



We may calculate this effect approximately by considering two atoms 

 A and C having given initial velocities, but without attractive force 

 between them. Let the initial velocities of A and C be Vi and V2 respectively. 

 Let Vq be the velocity of the common center of gravity of A and C and let 

 Vi be the velocity of A after collision. 



Then 



_ niiVi + m^Vj 7z;i + V2 



^mi -\- mi ~ 7+1 (^^) 



The velocity of A towards the center of gravity is Vi — Vq before col- 

 lision. After collision this velocity is reversed. The actual velocity of A 

 after collision Vi is thus equal to —{vx — Vo)-\-Vo. This gives, with 



7z;i + 2V2 - vi (22) 



Let us now return to the consideration of an atom striking a surface 

 toward which it is attracted. We have seen that the work done by the 

 attractive forces in bringing the atom to an equilibrium position is "k/N. 

 This appears as kinetic energy of the atom \m.iVi^. If Mi is the molecular 

 weight of the atom or molecule A, then since Mi = Nmi 



After collision with the atom C the velocity of A will be 

 But because of the initial velocities of A and C the velocity V\ should 



