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distrib.xls - distrib.gif
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| bet | 3/57 | | Sana | 09.05.2021 | | Hajmi | 0,62 Mb. | | #14427 |
distrib.xls - distrib.gif
Fig. 2.4.1 Occupancy probability versus energy of the Fermi-Dirac (red curve), the Bose-Einstein (green curve) and the Maxwell-Boltzman (blue curve) distribution.
All three distribution functions are almost equal for large energies (more than a few kT beyond the Fermi energy). The Fermi-Dirac distribution reaches a maximum of 1 for energies which are a few kT below the Fermi energy, while the Bose-Einstein distribution diverges at the Fermi energy and has no validity for energies below the Fermi energy.
An Example
To better understand the general derivation without going through it, we now consider a system with equidistant energy levels at 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, .... eV, which each can contain two electrons. The electrons are Fermions so that they are indistinguishable from each other and no more than two electrons (with opposite spin) can occupy a given energy level. This system contains 20 electrons and we arbitrarily set the total energy at 106 eV, which is 6 eV more than the minimum possible energy of this system. There are 24 possible and different configurations, which satisfy these particular constraints. Six of those configurations are shown in the figure below, where the red dots represent the electrons:
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