Question

atoms of carbondioxide 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

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

With

ν₀=10⁴ Hz,

T=300 K,

c=300 000 000 m/s,

m=7.308x10^-26 kg, or 44.01 amu,

we get

$$\sigma=9.34\cdot10^{-3},\\ \space\\G(\nu)=42.7\text{ exp}\bigg(-\frac{(\nu-10^4)^2}{1.74\cdot10^{-4}}\bigg):$$