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.
According to http://hyperphysics.phy-astr.gsu.edu, for the Gaussian form of line
Δλλ0=22ln2⋅kTc2=22ln2⋅1.38⋅10−23⋅6⋅105(3⋅108)2=5.5⋅10−4.\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}.λ0Δλ=22ln2⋅c2kT=22ln2⋅(3⋅108)21.38⋅10−23⋅6⋅105=5.5⋅10−4.
Therefore, Δλ=5.5⋅10−4⋅5500A˚=3A˚.\Delta\lambda = 5.5\cdot10^{-4}\cdot5500\text{\AA} = 3\text{\AA} .Δλ=5.5⋅10−4⋅5500A˚=3A˚.
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments