Question

For a finite system of Fermions where the density of states increases with energy, the chemical potential

• A. decreases with temperature
• B. increases with temperature
• C. does not vary with temperature
• D. corresponds to the energy where the occupation probability is 0.5

Hint:

The chemical potential decreases with temperature for Fermionic systems because more states are occupied at higher energies as temperature increases.

Answer 1

The Correct Option is A, D

For a system of Fermions (particles obeying the Pauli exclusion principle, such as electrons), the chemical potential \( \mu \) plays a crucial role in determining the energy distribution of the particles. The density of states increases with energy, and as the temperature increases, the particles are more likely to occupy higher energy states. At absolute zero, the chemical potential is the energy at which the Fermi-Dirac distribution function equals 1/2. As the temperature rises, more particles occupy higher energy states, which causes the chemical potential to decrease with increasing temperature. Therefore, the correct answer is (A).