Chapter 11, Problem 11B.12E

Interpretation Introduction

Interpretation:

Wavenumber of $J\text{ = 1 }\leftarrow \text{ 0}$ transition whether moves to higher or lower wavenumber when deuterium replaces hydrogen in ${}^1{\text{H}}^{\text{35}}\text{C}$ has to be determined.

Concept Introduction:

Rotational constant of a molecule can be determined using the given formula.

  $\begin{array}{c}\text{Rotational constant, B = }\frac{\hslash }{\text{4πI}}\\ \\ \text{where,}\\ \text{I = moment of inertia }\end{array}$

Moment of inertia of diatomic molecules is given by,

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

Rotational transition frequency of the radiation that is absorbed during a transition that starts from the level J is given by,

  ${\nu }_J\text{ = 2B}\left(J+1\right)$

Wavenumber is the total number of wavelengths observed at a unit distance. Equation for wavenumber can be given as,

  $\begin{array}{c}\text{Wavenumber, }\overline{\text{ν}}\text{ =}\frac{\text{1}}{\text{λ}}\text{ = }\frac{\text{ν}}{\text{c}}\\ \\ \text{where, }\\ \text{λ}\text{=}\text{wavelength}\\ \text{ν}=\text{frequency}\\ \text{c = speed of light}\end{array}$