Question

Recall the number of particles in the ground state E₀ = 0 given by

N₀ = (g₀)/(e^αe^E₀/kT − 1) = (1)/(e^α − 1)

Show that N₀ ≈ 1/α for small values of α.

Answer 1

☞Since   , in the question.

→Expanding the exponential term , we get

Because,

Now, for small values of , the terms , ... and all higher orders are very very small and are neglected.( for small value of )

So we are left with only

or

Hence proved.