Answer to Question #116991 in Physics for Maya Elena

Question

Atoms of CO2 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 is Gaussian. The distribution of the frequencies of the absorbed radiation is

$$L=\frac{1}{\sigma\sqrt{2\pi}}\text{exp}\bigg(-\frac{(f-f_0)^2}{2\sigma^2}\bigg),\\ \sigma=\frac{f_0}{c}\sqrt{\frac{2kT\text{ ln}2}{m}}.$$

In the equation above m is the mass of molecules and T - absolute temperature of gas.