ƒ■ 



1084 



Cf y^ ^^. ^. jj) ^y. c^T. ;:^:r 



m^-\-m^ vh 



This gives for the eqiiilibrium constant: 



n„ \m,+mj M h 2 |/ 2jr 



§ 13. Zero point energy and chemical binding. 



In the above given formula Planck's later supposition concerning 

 the existence of a zero point energy has not been taken into account. 

 We shall now examine some consequences of this supposition for the 

 chemical phenomena. In the first place we shall show that according to 

 this supposition the entropy of a number of particles does not change 

 at tlie absolute zero joint, when they pass from a binding in which 

 they can vibrate with a definite period into another combined state, 

 in which they have another period. For this purpose we shall make 

 use of Boltzmann's quantity H, which we shall represent as follows : 



/7 ==: j Fli F \m\lxdydz dxdydz. 



:ƒ,.,(. 



So we think here again of a three dimensional vibrator with three 

 equivalent degrees of freedom, though this case probably never 

 occurs in reality. If we had taken a linear vibrator, this would 

 have come to the same thing. But then we should have had to 

 speak besides of vibrations, also of rotations of the molecule, which 

 would have rendered the question somewhat less simple. 



According to Planck's supposition the value of F for 7'=0 is 

 constant for an energy smaller than v h, equal to zero for a larger 

 energy. Let us put: 



m^ dxdydz dxdydz = do), 



and 



then for T = 



j m^ dxdydz dxdydz =z G 



^Fdo> = F fdto = FG = N, 

 when N represents the total number of panicles, and furtiier 

 H=l{F) . Crdio = l[F) .N=N \1{N) - 1{G)]. 

 We may write for G : 



