Chapter 11, Problem 11C.3E

Interpretation Introduction

Interpretation:

Force constant of the bond in ${}^{35}C{l}_2$ has to be determined where the wavenumber of its fundamental vibrational transition is $565{\text{ cm}}^{-1}$.

Concept Introduction:

Vibrational frequency of a molecule can be determined using the given formula.

  $\begin{array}{c}Vibrationalfrequency,\nu \text{ = }\frac{1}{2\pi }{\left(\frac{k_f}{\mu }\right)}^{\text{1/2}}\\ \\ \text{where,}\\ \text{μ = Effective mass}\\ {\text{k}}_{\text{f}}\text{= Force constant}\end{array}$

Effective mass of a diatomic molecule is given by,

  $\mu =\frac{m_A{m}_B}{\left(m_A+m_B\right)}$

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

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