The Fermi energy of silver is 5.5 eV. (a) At , we have to calculate the probabilities that states at the following energies are occupied: 4.4 eV, 5.4 eV, 5.5 eV, 5.6 eV, 6.4 eV. (b) We have to find the temperature at which the probability that a state at 5.6 eV is occupied be 0.16.

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For a gas of fermions the probability for occupation of a state of energy E at temperature T is given by the function

where is the Fermi energy.

At the temperature in Kelvin is 273 K. We calculate for . It is

The Fermi energy of silver is 5.5 eV. We calculate the probability for occupation of states at the following energies: 4.4 eV, 5.4 eV, 5.5 eV, 5.6 eV, 6.4 eV.

(b)

We have to find the temperature at which the probability that a state at 5.6 eV is occupied will be 0.16. As

we have