# The Fermi-Dirac Distribution In Physics

A number of people sitting in a room or a number of students sit in a class follow a particular seating arrangement. Similar to this, assume that we put some particles in a closed container. What do we now expect? We assume that those particles will arrange themselves in a manner to reside easily inside the box. Let us call this arrangement of particles as "Distribution". In Today's article, I shall explain a famous distribution in quantum mechanics known as Fermi-Dirac Distribution.

## Distribution Function

The distribution function describes the probability with which one can expect particles to occupy the available energy levels in a given system. A distribution function 'f (E)' refers to the probability of a particle to exist in an energy state E.

In nature, there are three distinct forms of distribution functions. Now, the form of distribution function or the arrangement of particles in a given system depends upon various factors:

• Properties of particles: The choice of distribution depends upon the kind of particles. This refers to whether the particles are Bosons or Fermions.
• Indistinguishability: This means to identify whether the particles in a system are distinguishable of not. In other words, we choose a particular form of distribution for that system depending upon whether in a system of particles each particle can be separately identified.

## Fermi Dirac Distribution

In 1926, physicists Enrico Fermi and Paul Dirac developed the Fermi-Dirac distribution. The Fermi-Dirac (F-D) distribution is a quantum distribution that explains the behavior of a collection of fermions in thermodynamic equilibrium. Fermions are particles having a half-integer spin such as electrons, protons, neutrons, and neutrinos. These particles follow Pauli's Exclusion principle. This principle forbids any two particles to occupy the same energy level. We can say that the Fermi-Dirac distribution is applicable to indistinguishable particles having half-integral spin such that no two particles may stay in the same energy level.

The expression for Fermi-Dirac distribution function that depicts the average number of particles in an energy state 'E' is given as: