Answer to Question #87865 in Quantum Mechanics for Sridhar

Question

At temperature T Kelvin (K), the value of the Fermi function at an energy 0.5 eV above the Fermi energy is 0.01. Then T, to the nearest integer, is_____________
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Answer 1

The Fermi function f(E) gives the probability that a given available electron energy state will be occupied at a given temperature.

The Fermi function f(E) is given by formula

$$f(E)= \frac {1} {1+e^{\frac {E-E_F}{kT}}} (1)$$

where E_F is the Fermi energy or Fermi level, k is the Boltzmann constant (k=8.6 10^-5 eV/K), T is the absolute temperature in K

In our case, f(E)= 0.01 eV, E-E_F=0.5 eV

Using (1) we got:

$$1+e^{\frac {E-E_F}{kT}}=100$$

$$T=\frac {0.5}{8.6\times 10^{-5}}=5814 K$$

Answer:

5814 K