320 



PHENOMENA, ATOMS, AND MOLECULES 



TABLE IV 



with it. Thus from the table we see that if a molecule of hydrogen (A) 

 starts from rest (oi = o) and is attracted towards the metal surface, it 

 will only be reflected if the metal atom which it strikes is moving towards 

 it with a velocity numerically in excess of that corresponding to a2 = 0.34. 

 If, however, the hydrogen molecule starts with an initial velocity (normal 

 to the surface) corresponding to ai = o.i we see that it may be reflected 

 even if it strikes a metal atom moving away from it with a velocity as 

 large as that corresponding to a2 = 0.15. 



The probability that a molecule striking the surface should have a 

 velocity greater than ai is given by 



Pi = e 



— ^-i<^i' 



(36) 



On the other hand, the probability Po that a molecule on the surface 

 should have a velocity component less than that corresponding to ao may 

 be readily calculated by means of equation (30). The probabilities Pi and 

 Po have been entered in Table TV. From these data we see for example, 

 that 87 per cent, of all the incident molecules have velocities towards the 

 surface greater than that corresponding to a, = 0.3. In order that these 

 molecules may be reflected it is necessary that ao shall not exceed T.14, but 

 according to the fourth column we see that 98 per cent, of the metal atoms 

 have a value of a^ less than 1.14. 



From these data by approximate integration of / PodP], it can be 

 shown that of all molecules striking the surface 97.3 per cent, would be 

 reflected if we could assume all motions and forces to have directions 

 normal to the surface. This figure gives us an upper limit for the amount 

 of reflection. This result is not greatly difi^erent if we take other values 

 for X or n. Thus if we take 1 or n (or botli) equal to zero, we obtain in a 

 similar manner to that used above, the value 98.7 per cent, for the maxi- 

 mum possible reflectivity. On the other hand if we take « = co and 

 "k = 40,000 we find 95.1 per cent. 



