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Complete Question
Evaluate the Fermi function for an energy kT above the Fermi energy. Find the temperature at which there is a 1% probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron.
Answer:
a
The Fermi function for the energy KT is
b
The temperature is
Step-by-step explanation:
From the question we are told that
The energy considered is
Generally the Fermi function is mathematically represented as
Here K is the Boltzmann constant with value
is the Fermi energy
is the initial energy level which is mathematically represented as
So
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Generally the probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron is mathematically represented by the Fermi function as
Here is that energy level that is 0.5 ev above the Fermi energy
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Taking natural log of both sides
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Note eV is electron volt and the equivalence in Joule is
So
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