For free electrons in a solid with Fermi energy EF and temperature T, find the energy for which the probability that a state at that energy is occupied is 0.90.
For free electrons in a solid with Fermi energy EF and temperature T, find the energy for which the probability that a state at that energy is occupied is 0.90.
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Question
For free electrons in a solid with Fermi energy EF and temperature T, find the energy for which the probability that a state at that energy is occupied is 0.90.
Expert Solution
Step 1
The free electron gas behaves as a system of Fermi particles, Therefore they obey Fermi-Dirac statistics.
At the finite temperature T, the probability of occupation of F(E) of a state with energy E and with fermi energy EF is given by the Fermi-Dirac distribution function is given by;
# NOTE:
As the value of Fermi energy EF and the value of temperature is not given in the problem, So these values are kept in the final equation as it is. And the general form of the energy equation is solved.
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