Question

Atoms of CO 2 gas decay from upper to lower level with a spread in frequency is about

10kHz. Calculate the line shape if the broadening mechanism is found Doppler

broadening?

Answer 1

The line shape will be Gaussian, it is expressed as

$$G=\frac{1}{σ\sqrt{2π}}\text{exp}\bigg(−\frac{(ν-ν_0)^2}{2σ^2}\bigg),\\\space\\ σ = \frac{ν_0}{c}\sqrt{\frac{2kT\text{ ln}2}{m}}.$$

Here m - mass of the molecule,

c - the speed of light,

T - absolute temperature of gas,

v - frequency.

Substituting the numerical values, at the temperature of 300 K, the line shape will be