Chapter 30, Problem 30.11NP

(a)

Interpretation Introduction

Interpretation:The sets have the same energy should be demonstrated.

Concept Introduction:

The formula for calculation total energy is given as:

  $\text{E =}{\displaystyle \sum }_{\text{n}}{\text{ε}}_{\text{n}}{\text{ a}}_{\text{n}}\mathrm{....}$

Whereas ${\text{ε}}_{\text{n}}$ is the energy of the n^th energy state level.

(b)

Interpretation Introduction

Interpretation:The set which is most probable should be determined

Concept Introduction:Stirling's approximation is an approximate formula, for  $\text{n! = 1×2×3× … ×n }\left(\text{n factorial}\right)$ with weight configuration formula.

Those sets having large value of weight configuration of mass such set is most probable set among all sets.

  $\begin{array}{l}\text{W=}\frac{\text{N!}}{{\text{a}}_{\text{a}}{\text{! a}}_{\text{1}}\text{! }\mathrm{.....}{\text{a}}_{\text{n}}\text{! }}\\ \text{whereas W is the weight configuration of mass of set,}\\ \text{N is total numbers of oscilator for components and a is occupation number of set configuration}\text{.}\end{array}$

(c)

Interpretation Introduction

Interpretation: For the most probable set whether the distribution of energy is consistent with the Boltzmann distribution should be determined.

Concept Introduction:

The occupation gap between the energy levels of set C.

  $\begin{array}{l}\text{The occupation number is as follows,}\\ {\text{a}}_{\text{n}}\text{=}\frac{{\text{e}}^{{\text{-P}}_{\text{n}}}}{\text{q}}\\ \text{Whereas q is the partition function ,}\\ {\text{a}}_{\text{n}}\text{ is the occupation number,}\\ {\text{P}}_{\text{n}}\text{ Probablity of energy levels}\text{.}\end{array}$