Question

The mathematical form of Maxwell Boltzmann Law is
1. \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}-1}\)
2. \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}+1}\)
3. \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}}\)
4. \(n_i=\frac{e^{\alpha+\beta\epsilon_i}}{g_i}\)

Answer 1

Correct Answer - Option 3 : \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}}\)

CONCEPT:

Bose-Einstein Statistics	Fermi-Dirac Statistics	Maxwell Boltzmann distribution
This statistics is obeyed by identical, indistinguishable particles of integral spin (bosons) that have symmetrical wave functions and is so named as it was devised by Bose for light quanta and generalized by Einstein and don’t obey the Pauli exclusion principle	These statistics are obeyed by indistinguishable particles of half-integral spin that have anti-symmetric wave function and obey the Pauli exclusion principle.	According to Maxwell distribution of velocities, a very small fraction of the molecules has either very high or very low velocities. The major fraction has a velocity close to the average velocity. It is known as probable velocity.
The mathematical form of Bose-Einstein Distribution Law is \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}-1}\)	The mathematical form of Fermi Dirac Distribution Law is \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}+1}\)	The mathematical form of Maxwell Boltzmann Law is \(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}}\)

EXPLANATION:

• From the above, it is clear that the mathematical form of Maxwell Boltzmann Law is 

\(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}}\)

• Hence, option 3 is correct.