Chapter 3, Problem 14P

(a)

To determine

The expression of Maxwell-Boltzmann distribution as $A=N\left(1-e^{-\epsilon /kT}\right)$.

(b)

To determine

The expression ${\displaystyle \sum _{n=0}^{\infty }n{e}^{nx}}=e^x/{\left(1-e^x\right)}^2$ with the help of derivation with respect to $x$.

(c)

To determine

The expression $E_{avg}=\frac{hc/\lambda }{e^{\epsilon /kT}-1}$.

(d)

To determine

The value of $E_{av}\cong kT$ at large $\lambda$ and $E_{avg}\to 0$ for small $\lambda$.