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In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Drude formula is derived in a limited way, namely by assuming that the charge carriers form a classical ideal gas. When quantum theory is considered, the Drude model can be extended to the free electron model, where the carriers follow Fermi–Dirac distribution. The conductivity predicted is the same as in the Drude model because it does not ...
The alkali metals are expected to have the best agreement with the free electron model since these metals only one s-electron outside a closed shell. However even sodium, which is considered to be the closest to a free electron metal, is determined to have a more than 25 per cent higher than expected from the theory.
The original classical Marcus theory for outer sphere electron transfer reactions demonstrates the importance of the solvent and leads the way to the calculation of the Gibbs free energy of activation, using the polarization properties of the solvent, the size of the reactants, the transfer distance and the Gibbs free energy of the redox reaction.
Thomson scattering is a model for the effect of electromagnetic fields on electrons when the field energy is much less than the rest mass of the electron .In the model the electric field of the incident wave accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered.
The electron emerges from under the barrier at = . is the ionization potential of the atom. When the intensity of the laser is strong, the lowest-order perturbation theory is not sufficient to describe the MPI process. In this case, the laser field on larger distances from the nucleus is more important than the Coulomb potential and the ...
Free electron model [ edit ] After taking into account the quantum effects, as in the free electron model , the heat capacity, mean free path and average speed of electrons are modified and the proportionality constant is then corrected to π 2 3 ≈ 3.29 {\displaystyle {\frac {\pi ^{2}}{3}}\approx 3.29} , which agrees with experimental values.
is the classical continuous partition function of a single particle as given in the previous section. The reason for the factorial factor N ! is discussed below . The extra constant factor introduced in the denominator was introduced because, unlike the discrete form, the continuous form shown above is not dimensionless .