Chapter 7, Problem 7E.3E

Interpretation Introduction

Interpretation:

The force constant for oscillation of hydrogen atom in $\text{C-H}$ bond with vibrational period of $9.12ps$ has to be calculated.

Concept Introduction:

The energies are quantized in harmonic oscillator and are generally expressed as follows,

$\begin{array}{c}{\text{E}}_{\text{v}}=\left(\upsilon +\frac{1}{2}\right)h\nu \\ \upsilon =0,1,2,\mathrm{...}\\ \nu =\frac{1}{2\pi }{\left(\frac{k_f}{m}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ here,k_f=\text{force}\text{constant}\\ \upsilon =\text{vibrational quantum number}\\ m=mass\\ \nu =vibrationalfrequency\\ \end{array}$

The force constant, ${\text{k}}_{\text{f}}$ is used to characterize the particle that under harmonic motion subjected to Hooke’s law restoring force.

The vibrational quantum number is used to denote the energy levels of harmonic oscillator.