660 BELL SYSTEM TECHNICAL JOURNAL 



terms. It seems to the writer, however, that the explanation given 

 below does contain the mathematical essence in physical language.^* 

 Pauli's principle, we have said, is the quantum mechanical analogue 

 for electrons of the classical law that two bodies may not occupy the 

 same place at the same time; it is, however, more general in the sense 

 that it does not apply alone to location but rather to a combination of 

 location and velocity and spin, and it requires that any two electrons 

 differ essentially in one or more of these. Now a difference in the 

 values for the spin quantum numbers of two electrons is a sufficiently 

 great difference to permit them to have the same velocity and the 

 same location (i.e., be very near together compared to atomic dimen- 

 sions). If the spin quantum numbers are the same, however, there 

 must be a difference in location or in velocity. Now two electrons 

 having the same values of n and /, as for example two 2p electrons, 

 move in similar orbits and have much the same velocities; hence, if 

 their spins are the same they must differ in location — that is, they will 

 satisfy Pauli's principle by keeping away from each other. If, how- 

 ever, their spins are different, then they need not keep away from each 

 other, and in their motion about the nucleus they are, on the average, 

 closer together than for the case of the same spin. Since the energy 

 of repulsion between the two electrons decreases as they move farther 

 apart, the average energy of the electrons is less for the case of parallel 

 spins, for which Pauli's principle requires most difference in location; 

 and this is just the effect shown in Fig. 4. Furthermore, if the elec- 

 trons differ in their values of n and /, then their velocities are quite 

 different and the restriction upon location is not so important and 

 their electrostatic energy of repulsion for parallel spins is nearly the 

 same as for opposite spins. There is, however, a small exchange effect 

 between electrons of different n and / values as may be appreciated 

 in Fig. 4 for boron, for example, by noting that one 2s level i de- 

 pressed compared to the other owing to the presence of the 2p electron. 

 We see that helium and neon correspond to electron configurations 

 which fill all the levels below w = 2 and w = 3 respectively. One 

 sometimes refers to the states with w = 1 as the K shell, and to those 

 with w = 2, 3, 4, etc. as L, M, N, etc., shells. The rare gases helium 

 and neon then correspond to electron configurations consisting of 

 "closed shells "^ — that is, to shells all of whose states are occupied. 



3a As the aspects of exchange energy needed for the exposition are those discussed 

 above in connection with Fig. 4, this explanation is not essential to the later argu- 

 ment of this article and is given in the hope that it may invest the concept of ex- 

 change energy with the appearance of a little more physical reality. If it fails in 

 this, the reader is requested to disregard it. 



