91影视

According to the Doppler effect or Doppler shift, the frequency of a source changes if the observer is in relative motion w.r.t source.

Given, the expression of relative variation of wavelength due to the Doppler effect is given by,

$\frac{\mathbf{鈭�}\mathbf{位}}{\mathbf{位}}\mathbf{=}\frac{\sqrt{\mathbf{3}{\mathbf{k}}_{\mathbf{B}}\mathbf{T}\mathbf{/}\mathbf{m}}}{\mathbf{c}}$

Where,${\mathbf{k}}_{\mathbf{B}}$is theBoltzmann constant,$\mathbf{位}$is the Wavelength of the light, is the temperature (in K), is the mass of hydrogen atom,and c is the speed of light.

Now,

$$\begin{gathered} \frac{鈭�\mathrm{位}}{\mathrm{位}}=\frac{\sqrt{3{\mathrm{k}}_{\mathrm{B}}\mathrm{T}/\mathrm{m}}}{\mathrm{c}} \\ =\frac{\sqrt{3\left(1.38脳{10}^{-23}\mathrm{J}/\mathrm{K}\right)\left(5脳{10}^4\mathrm{K}\right)/\left(1.67脳{10}^{-27}\mathrm{kg}\right)}}{3脳{10}^8\mathrm{m}/\mathrm{s}} \\ =1.74脳{10}^{-8} \end{gathered}$$

Hence, wavelength is varied by a fraction of $1.74脳{10}^{-8}$for Doppler.

Given,variation in wavelength due to uncertainty principle

$$\begin{gathered} \frac{鈭�\mathrm{位}}{\mathrm{位}}=\frac{\mathrm{位}}{4\mathrm{蟺肠}鈭�\mathrm{t}} \\ =\frac{656脳{10}^{-9}\mathrm{m}}{4\mathrm{蟺}\left(3脳{10}^8\mathrm{m}/\mathrm{s}\right)\left({10}^{-8}\mathrm{s}\right)} \\ =1.74脳{10}^{-8} \end{gathered}$$

Hence, wavelength is varied by a fraction of $1.74脳{10}^{-8}$for uncertainty principle.

It can be clearly observed from Step 1 and 2 that, the Doppler broadening is more important. ([Doppler:$1.17脳{10}^4$] [Uncertainty:$1.17脳{10}^{-8}$ ])

As you know that, variation in wavelength due to uncertainty principle is given by,

$\frac{鈭�位}{位}=\frac{位}{4\mathrm{蟺肠}鈭�\mathrm{t}}$

It increases when wavelength $位$is higher. And according to Doppler effect,

$\frac{鈭�\mathrm{位}}{\mathrm{位}}=\frac{\sqrt{3{\mathrm{k}}_{\mathrm{B}}\mathrm{T}/\mathrm{m}}}{\mathrm{c}}$

It lowers when the temperature lowers.

Hence, the Uncertainty principle broadening can predominate the Doppler effect if wavelength increases or temperature decreases.