# What is the Bose-Einstein distribution law?

Table of Contents

- 1 What is the Bose-Einstein distribution law?
- 2 What is the application of Fermi-Dirac statistics?
- 3 What is the role of Fermi-Dirac function to find the number of electrons in valence and conduction bands?
- 4 What is meant by Fermi energy level explain the Fermi-Dirac distribution function for the intrinsic and extrinsic semiconductor?
- 5 Is it possible to derive Bose-Einstein statistics in the canonical ensemble?

## What is the Bose-Einstein distribution law?

The Bose-Einstein distribution describes the statistical behavior of integer spin particles (bosons). At low temperatures, bosons can behave very differently than fermions because an unlimited number of them can collect into the same energy state, a phenomenon called “condensation”.

**What do you mean by Fermi-Dirac function?**

The Fermi-Dirac distribution applies to fermions, particles with half-integer spin which must obey the Pauli exclusion principle. Each type of distribution function has a normalization term multiplying the exponential in the denominator which may be temperature dependent.

**Is Bose-Einstein statistics?**

Bose-Einstein statistics is a procedure for counting the possible states of quantum systems composed of identical particles with integer ► spin. The usual statistical assumption is that all possible states of the many-particle system (i.e. all configurations) are equally probable.

### What is the application of Fermi-Dirac statistics?

Fermi–Dirac statistics has many applications in studying electrical and thermal conductivities, thermoelectricity, thermionic and photoelectric effects, specific heat of metals, etc. on the assumption that metals contain free electrons constituting like a perfect gas known as electron gas.

**Which of the following can be explained using the Bose-Einstein statistics?**

Explanation: Bose-Einstein Statistics can be applied to particles having integral spin number and do not obey Pauli’s principle. Photon comes under this category. 6. In Bose-Einstein Statistics, one energy state can be occupied by more than one particle.

**What are the basic postulates used in Bose-Einstein statistics?**

The basic postulates of MB statistics are:- ( i)The associated particles are distinguishable. (ii)Each energy state can contain any number of particles. (iii)Total number of particles in the entire system is constant.

#### What is the role of Fermi-Dirac function to find the number of electrons in valence and conduction bands?

The Fermi function gives the probability of occupying an available energy state, but this must be factored by the number of available energy states to determine how many electrons would reach the conduction band.

**Which of the following can be explained using Bose-Einstein statistics Mcq?**

Explanation: The Bose-Einstein statistics is for the indistinguishable particles with integral spin.

**What do you understand by Fermi gas?**

An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. The model is named after the Italian physicist Enrico Fermi.

## What is meant by Fermi energy level explain the Fermi-Dirac distribution function for the intrinsic and extrinsic semiconductor?

Fermi level is the energy state which has probability ½ of being occupied by an electron. At absolute zero temperature, half of the Fermi level will be filled with electrons. In energy band diagram of semiconductor, Fermi level lies in the middle of conduction and valence band for an intrinsic semiconductor.

**What is the difference between Fermi-Dirac and Maxwell-Boltzmann statistics?**

Both Fermi-Dirac and Bose-Einstein become Maxwell-Boltzmann statistics at high temperatures or low concentrations. Maxwell-Boltzmann statistics are often described as the statistics of “distinguishable” classical particles.

**What is Bose-Einstein statistics?**

In statistical mechanics, Bose -Einstein statistics (or more colloquially B-E statistics) determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium .

### Is it possible to derive Bose-Einstein statistics in the canonical ensemble?

Derivation in the canonical approach. It is also possible to derive approximate Bose–Einstein statistics in the canonical ensemble. These derivations are lengthy and only yield the above results in the asymptotic limit of a large number of particles. The reason is that the total number of bosons is fixed in the canonical ensemble.

**Why is the Bose-Einstein distribution a fixed number of bosons?**

The reason is that the total number of bosons is fixed in the canonical ensemble. The Bose–Einstein distribution in this case can be derived as in most texts by maximization, but the mathematically best derivation is by the Darwin–Fowler method of mean values as emphasized by Dingle.