- #1

xago

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## Homework Statement

The spectral lines of the light from distant galaxies exhibit a Doppler redshift due to

the motion of the galaxy away from our own. For a particular galaxy, three spectral

absorption lines are observed from the Earth to have wavelengths of 164.4 nm 168.4 nm

and 177.5 nm. Assuming that these lines are from hydrogen gas in the outer regions

of the stars in the galaxy, answer the following:

(a) Identify the initial and final quantum numbers for the states involved in these

three transitions.

(b) Determine the speed with which the galaxy is receding from our own.

## Homework Equations

a)Rydberg Equation: [tex]\frac{1}{\lambda}[/tex] = R*([tex]\frac{1}{nf^2}[/tex] - [tex]\frac{1}{ni^2}[/tex])

b)Relativistic Doppler Shift: f

_{obs}= [tex]\frac{\sqrt{1 + \frac{v}{c}}}{\sqrt{1 - \frac{v}{c}}}[/tex] * f

_{source}

## The Attempt at a Solution

For a) since were given 3 wavelengths I've simplified it down to 1/[tex]\lambda[/tex]/R = ([tex]\frac{1}{nf^2}[/tex] - [tex]\frac{1}{ni^2}[/tex]). The probelm is, when I plug in the wavelength of 164.3nm, it simplifies to 0.5543 = ([tex]\frac{1}{nf^2}[/tex] - [tex]\frac{1}{ni^2}[/tex]). Now I've got 2 unknowns and 1 equation. If i just sub in whole integers for ni and nf to try and find the best combination, I still can't come close to 0.5543.

For b) I was thinking just to use the realativistic Doppler Shift equation, but I'm only given the observed wavelength and not the wavelength of the source or the velocity between the two. Once again, 2 unknowns, 1 equation.

If anyone could tell me what I'm missing for the 2 questions I'd be forever grateful