# Under what condition the Fermi-Dirac and Bose-Einstein statistics will be equivalent to Maxwell-Boltzmann statistics?

## Under what condition the Fermi-Dirac and Bose-Einstein statistics will be equivalent to Maxwell-Boltzmann statistics?

As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit, unless they also have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration.

What is the difference between Fermi-Dirac and Bose-Einstein statistics?

The Bose-Einstein statistics is applicable to the particles having integer spins called Bosons. The Fermi- Dirac statistics is applicable to the half integer spin particles satisfying the paulis exclusion principle.

### Which can be explained using the Bose-Einstein statistics?

Bose-Einstein statistics is a procedure for counting the possible states of quantum systems composed of identical particles with integer ► spin.

What is the difference between Maxwell distribution and Boltzmann distribution?

The Boltzmann distribution gives the probability that a system will be in a certain state as a function of that state’s energy, while the Maxwell-Boltzmann distributions give the probabilities of particle speeds or energies in ideal gases.

#### What is Boltzmann population ratio?

The Boltzmann distribution law is then given by the expression. This expression states that the natural logrithm of the ratio of the number of particles in the upper state to the number in the lower state is equal to the negative of their energy separation divided by kT.

What is Bose-Einstein statistics in simple words?

In statistical mechanics, Bose-Einstein statistics means the statistics of a system where you can not tell the difference between any of the particles, and the particles are bosons. Bosons are fundamental particles like the photon. The Bose-Einstein distribution tells you how many particles have a certain energy.

## What is Maxwell Boltzmann distribution law?

The Maxwell–Boltzmann distribution concerns the distribution of an amount of energy between identical but distinguishable particles. It represents the probability for the distribution of the states in a system having different energies. A special case is the so-called Maxwell distribution law of molecular velocities.

What is Boltzmann distribution law?

∎ The Boltzmann distribution law states that the. probability of finding the molecule in a particular. energy state varies exponentially as the energy. divided by k. B.

### Which particles obey Bose-Einstein statistics?

Particles with integral spins are said to obey Bose-Einstein statistics; particles with half-integral spins obey Fermi-Dirac statistics. Fortunately, both of these treatments converge to the Boltzmann distribution if the number of quantum states available to the particles is much larger than the number of particles.

What is Maxwell-Boltzmann theory?

The Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, defines the distribution of speeds for a gas at a certain temperature. From this distribution function, the most probable speed, the average speed, and the root-mean-square speed can be derived.

#### What is 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”.

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