Question #202938

 Calculate the half-width of a spectral line of wavelength of λ= 550 nm when the 

temperature of the gas is 6 × 105 K. Assume H atoms to be emitters.


1
Expert's answer
2021-06-07T09:30:37-0400

According to http://hyperphysics.phy-astr.gsu.edu, for the Gaussian form of line

Δλλ0=22ln2kTc2=22ln21.3810236105(3108)2=5.5104.\dfrac{\Delta\lambda}{\lambda_0} = 2\sqrt{2\ln2\cdot\dfrac{kT}{c^2}} = 2\sqrt{2\ln2\cdot\dfrac{1.38\cdot10^{-23}\cdot6\cdot10^5}{(3\cdot10^8)^2}} = 5.5\cdot10^{-4}.

Therefore, Δλ=5.51045500A˚=3A˚.\Delta\lambda = 5.5\cdot10^{-4}\cdot5500\text{\AA} = 3\text{\AA} .


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