**eV**and here I will explain the following topic:

# Fermi Distribution: The Occupation Probability of Fermions

## Formula

## What do the formula symbols mean?

## Probability

`$$ P(W) $$`Unit

`$$ - $$`

## Energy

`$$ W $$`Unit

`$$ \mathrm{J} = \mathrm{Nm} = \frac{ \mathrm{kg} \, \mathrm{m^2} }{ \mathrm{s}^2 } $$`

## Chemical potential

`$$ \mu $$`Unit

`$$ \mathrm{J} $$`

## Temperature

`$$ T $$`Unit

`$$ \mathrm{K} $$`

## Boltzmann Constant

`$$ k_{\text B} $$`Unit

`$$ \frac{\mathrm J}{\mathrm K} = \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$`

`$$ k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} $$`

**Explanation**

## Video

The Fermi distribution (also known as the Fermi-Dirac distribution) is particularly important in the description of electrons in solids, especially in metals.

The Fermi distribution indicates the occupation probability \( P(W) \) that a fermion in a system acquires the energy \( W \). The occupation probability depends on the temperature \( T \) of the system.

In contrast to the Bose distribution, the Fermi distribution contains a positive term in the denominator, which ensures that the probability of occupying a state does not approach zero when the temperature approaches zero. This means that fermions cannot occupy the same quantum mechanical state according to the Pauli principle.