THE QUANTUM PHYSICS OF SOLIDS 



659 



with one spin (the same effect occurs for either spin; the figure shows 

 + spin), these states are depressed in respect to the 2p states with 

 the other spin. The springs must, however, be considered to pull the 



2P 



2S 2S 



?P 



NITROGEN 

 1S2 2S2 2p3 



.ii 



lAi 



lAi iAj 



BERYLLIUM 



OXYGEN 

 1S2 2S2 2P'* 



lAi lA, 



^2 p<i2 



IS*: 2S'= 2p 



FLUORINE 

 1 S2 2S2 2p^ 



CARBON 

 IS2 2S2 2p2 



iL Lil 



NEON 

 ls2 2S2 2p6 



Fig. 4 — Electron configurations illustrating the exchange effect. 



trays up against stops with a force such that a single weight upon a 

 tray will produce no lowering whereas two or three weights will. This 

 effect seems contradictory to the simple idea that adding electrons 

 raises the potential energy and the energy levels; however, it must be 

 remembered that we are here discussing neutral atoms and that with 

 each added electron there is also an added plus charge on the nucleus. 

 These two charges produce the dominant variation in the energy levels 

 and upon this variation the exchange effect is superimposed. 



The reader may verify that so far as the distribution of electrons 

 in the 2p states is concerned, the exchange effect will lead to the con- 

 figurations shown in Fig. 4 for the states of lowest energy for the atoms. 

 Let us consider carbon for example; if the electrons have opposite 

 spins — that is, if there is one weight on each 2p tray — there will be 

 no lowering due to the exchange effect; if the electrons have the same 

 spin, however, then each loses energy because of exchange and the 

 energy of the atom is less than for the case of parallel spins. The 

 fact that one electron is not enough and that two or more electrons 

 are required to produce the exchange effect is a natural consequence 

 of the origin of the exchange energy. 



The exchange energy is due to the electrostatic repulsion between 

 the electrons and results directly from the application of Pauli's prin- 

 ciple to Schroedinger's equation. The exchange effect emerges in a 

 quite straightforward fashion from a consideration of wave functions, 

 but usually no attempt is made to explain it in non-mathematical 



