Chapter 11, Problem 11B.8E

Interpretation Introduction

Interpretation:

Ratio of the number of ways of reaching rotational levels with odd and even J for deuterium has to be calculated where $I\text{ = 1}$.

Concept Introduction:

Nuclear statistics for a molecule having nonzero spin can be obtained as follows,

  $\begin{array}{c}\text{Nuclear statistics = }\frac{\text{Number of ways of achieving odd J}}{\text{Number of ways of achieving even J}}\\ \\ where,\\ \frac{\left(I+1\right)}{I}for\text{ half-integral spin nuclei}\\ \frac{I}{\left(I+1\right)}for\text{ integral spin nuclei}\\ \\ J=\text{ Rotational quantum number}\\ I=\text{ Nuclear spin quantum number}\end{array}$

  $\begin{array}{l}\text{Moment of inertia, I = }\mu {\text{R}}^2\\ \\ where,\mu =\frac{m_A{m}_B}{\left(m_A+m_B\right)}\end{array}$