(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The hydrogen atoms in a star are also moving at high velocity because of the random motions caused by their high temperature. As a result, each atom is Doppler shifted a little bit differently, leading to a finite width of each spectral line, such as the 656.46-nm line we were just discussing. For a star like our sun, this leads to a finite width of the spectral lines of roughly %Delta lambda = 0.04 nm. If our instruments can only resolve to this accuracy, what is the lowest speed V, greater than 0, that we can measure a star to be moving?

2. Relevant equations

Lambda_o = Lamba_s*sqrt((c+v)/(c-v))

where lambda_o is the observed wavelength and lambda_s is the wavelength in the rest frame of the source.

3. The attempt at a solution

All I could try for a solution was to rearrange that equation to get an expression for the change in wavelength over the wavelength in the source's rest frame in terms of c and v, then set lambda_s=656.46-nm and the change=0.04nm and solve for v. But frankly this method seems daft and nonsensical to me. My main problem with the question is that I don't really understand what it means. I don't really see how the width of the spectral lines can be the same as the change in wavelength, I don't see how that relationship can hold or where it comes from. It seems to be a bunch of dissimilar things to me...

Also to clarify, when they say "finite lengths" it refers to the lines having a clear stopping and starting point, yes?

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# Astronomy and the Relativistic Doppler Shift

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