316 PHENOMENA, ATOMS, AND MOLECULES 



1. That the forces and motions involved are all normal to the surface. 



2. That the collisions are perfectly elastic and that the work done on 

 the incident particle by the attractive forces all appears as kinetic energy 

 of this particle. 



It is certain that the first assumption cannot correspond to the facts. 

 The directions of motion of the incident particles after the collisions are 

 probably distributed uniformly in all directions so that the chance of an 

 atom being reflected is very vnuch less than that given by P. 



It is also probable that the second condition is not fulfilled, which must 

 result in a still further decrease in the amount of reflectivity. Some idea 

 of the rapidity with which adjacent atoms in a solid reach thermal equi- 

 librium may be obtained from a consideration of the heat conductivity. 



The problem is similar to that of a calculation of the "time of relaxa- 

 tion" for a gas. The distribution of velocities among the molecules of a gas 

 in the steady state is given by Maxwell's distribution law. If a deviation 

 from this law is brought about in some manner, and the gas is then left 

 to itself, the distribution will rapidly return to that of Maxwell. The time 

 required for the abnormal condition to subside is measured by the "time 

 of relaxation," which Maxwell defines as the time needed for the deviation 

 (measured in terms of kinetic energy) to fall to i/rth of its original value. 



The following roughly approximate method will enable us to estimate 

 the order of magnitude of the time of relaxation in a solid body. 



Let us imagine that a single layer of atoms on the surface of a solid is 

 at a temperature T , while the underlying layers of atoms are at zero tem- 

 perature. If h is the heat conductivity of the solid, and a is the distance 

 between adjacent atoms, then the heat flowing between the first and 

 second layers will be /zT/o per sq. cm. if we neglect the change in tem- 

 perature of the second layer. The number of atoms in the surface layer 

 will be i/o^ per sq. cm. and the heat capacity of each atom is3^, where h 

 is the Boltzmann gas constant 1.37 X 10"^'^ erg./deg. We thus obtain 



hT _ _3k dT C^j^) 



•T a" dt 



or 



, To h(x 



If we let To/T equal e, then t will become equal to the time of relaxa- 

 tion, which we may represent by tr, thus 



'-=!-!• (33) 



