Chapter 14, Problem 14D.8P

Interpretation Introduction

Interpretation:

The expression for the fundamental vibrational frequency of a one-dimensional randon coil has to be expressed.  The frequency of a sample of polyethene with molar mass $65{\text{ kg mol}}^{-1}$ at $20°\text{C}$ has to be calculated.  The dependence of frequency on the temperature and molar mass has to be stated.

Concept introduction:

A harmonic oscillator consists of a particle of mass $m$ that undergoes a restoring force which is proportional to its amplitude $x$.  The restoring force is represented by $k_{\text{f}}$ which is known as the force constant.  The vibrational frequency is $v$.  It is directly proportional to the force constant.  The vibrational frequency of a bond is given by the expression as shown below.

    $v=\frac{1}{2\text{π}}\sqrt{\frac{k_f}{m}}$