Chapter 11, Problem 11A.2ST

Interpretation Introduction

Interpretation:

Doppler with of the transition of the molecule ${}^{\text{12}}{\text{C}}^{\text{16}}\text{O}$ has to be determined where at $\text{400K}$, its transition is detected at $\text{461}\text{.0 MHz}$.

Concept Introduction:

Doppler effect is the broadening of spectral lines of gases where the frequency of radiation changes as the sources moves towards or away from an observer.

The line that is detected in spectroscopy is the emission or absorption profile of a certain gas arising as a result of the Doppler effect and the width of the line detected at half its maximum height $\left(\delta \nu \right)$ can be determined using the given formula,

$\begin{array}{c}Doppler\text{ width, }\delta \nu \text{ = }\frac{2\nu }{c}{\left(\frac{2RT\text{ ln 2}}{M}\right)}^{\text{1/2}}\\ \\ where,\\ \nu \text{ = frequency}\\ M\text{ = Molar mass}\\ \text{T = Temperature}\end{array}$