Question

For all the quantum states with energy greater than Fermi energy to be empty in a Fermi-Dirac system, the temperature should be ______

(a) 273 K

(b) 373 K

(c) 0 K

(d) 100 K

This question was addressed to me in a job interview.

The query is from Fermi-Dirac Distribution topic in chapter Quantum Physics of Engineering Physics I

Answer 1

Right option is (c) 0 K

To elaborate: We know that the Fermi-Dirac distribution is given by:

FFD(E) = \( \frac{1}{e\frac{E-E_F}{nT}+1}\)

For all the quantum states with energy greater than Fermi energy to be empty,

FFD(E) = 0, for E > EF and FFD(E) = 1, for E < EF

Therefore, for E < EF  \( \frac{1}{e\frac{E-E_F}{nT}+1}=1\)

\(e\frac{E-E_F}{nT}= 0\)

As, E < EF, E- EF < 0.  Therefore, to satisfy the given statement,

T = 0 K

Thus, we can define Fermi energy as the energy of the uppermost occupied level at 0 K.