Occupation of the Electron-Energy Levels

Equation (34.32) is remarkable in the relation that it shows that (1) the observable symmetry factor is determined by occupation of the electron energy level in the metal, giving the major contribution to the current, and (2) that the observable symmetry factor does not leave the interval of values between 0 and 1. The latter means that one cannot observe the inverted region in a traditional electrochemical experiment. Equation (34.32) shows that in the normal region (where a bs is close to ) the energy levels near the Fermi level provide the main contribution to the current, whereas in the activationless (a bs 0) and barrierless (a bs 1) regions, the energy levels below and above the Fermi level, respectively, play the major role. 

The occupation of the electron energy levels under thermal equilibrium at T > 0 K can be derived from statistical thermodynamics [11]. The reasoning results in the well-known Fermi-Dirac occupation function. The probability that an electron energy level at E is occupied by an electron is given by... 

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