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Postby TGTS0907129» Free electron quantum theory of conduction

Describe the free electron quantum theory of conduction

1-

Fermi introduced a radically different description of the free electron in a metal. He incorporated the exclusion principle, assuming that the “free electrons in a metal are quantized and that no two can be in precisely the same state.

Moneta is quantized; only two electrons (having opposite spins) can have a given momentum. As the temperature is lowered, electrons settle down by quantized steps to lowest momentum values. But as a consequence of the exclusion principle, some electrons will remain at momentum values considerably above zero; i.e., they will have appreciable energy, even at absolute zero temperature. When the temperature rises, only the electrons of highest momentum values considerer ably above zero; i.e., they will have appreciable energy, event at absolute zero temperature. When the temperature rises, only the electrons of highest momentum can accept thermal energy and move to still higher momentum values.

The Fermi distribution law is expressed by
 


where Em is the maximum energy an electron can have at 0°K. the progressive rounding of the curve as temperature increases represents the shift of some electrons to higher energies. The Fermi distribution curve should be compared with the Maxwell distribution.

The Fermi theory successfully accounts for the slight participation of electrons in specific heats. The Fermi distribution of energy is plotted. At 0°K all energy states are occupied up to a certain maximum. At a higher temperature some electrons in upper levels have been able to accept electrons in upper levels have been able to accept energy and move toss till higher levels. But owing to quantum restriction, relatively few electrons have predicated in the temperature rise. The Fermi theory predicts that electrons in a conductor should contribute roughly 1 percent of the amount predicted by the Maxwell theory, in agreement with experiments in calorimetric.

The fact that all energy levels, up to certain maximum, are filled means that for every electron traveling to the right in a metal there is another electron traveling to the left. Thus all electrical conduction in the metal must be due to the relatively few electrons near the top of the distribution which can be excited easily to an unoccupied quantum level. One concludes that electricity must be conducted b only a small fraction of the free electrons (rather than by all, as assumed in classical theory). In turn, this implies that an electron must be able to travel long distance without being bumped by ions in the crystal lattice. The free –electron quantum theory, like the classical theory, is unable to account for the distinction between conductors and insulators.
 

By TGTT30071258 on 9/22/2015 4:37:07 AM
TGTS0907129 on 9/22/2015 4:21:15 AM
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