Question

The Fermi distribution f(E):

a)Gives the probability that an available quantum state is occupied with an electron at a given temperature T.
b)Can be used to calculate that an available quantum state is unoccupied with an electron at a given temperature T by calculating 1-f(E).
c)Has a value between 0 and 1.
d)All of the above.

Answer 1

The Fermi distribution f(E) describes the probability that an available quantum state is occupied or unoccupied by an electron at a given temperature T. It has a value between 0 and 1.

Step-by-step explanation:

The Fermi distribution, or the Fermi-Dirac distribution, describes the probability that an available quantum state is occupied by an electron at a given temperature T. It is denoted by f(E), where E is the energy of the state. This distribution allows us to understand the filling of electron states in a solid material, where the lowest energy states are occupied first, and higher energy states are filled subsequently. For T = 0 K, the Fermi distribution becomes a step function, with a value of 1 for states below the Fermi energy (EF) and 0 for states above EF.

The Fermi distribution can also be used to calculate the probability that an available quantum state is unoccupied by an electron at a given temperature T. This is done by subtracting the Fermi distribution from 1, i.e., calculating 1-f(E).

The Fermi distribution has a value between 0 and 1, representing the probability of occupancy for an electron state. Therefore, option d) 'All of the above' is correct.