Find the speed of a galaxy

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1. Feb 28, 2015

HaLAA

1. The problem statement, all variables and given/known data
Taking light collected by the telescope and shine it through a diffraction grating with a 765.5 lines/mm. Using the filter that just the brightest Helium II line. you cast the diffraction grating's diffracted pattern on a screen is 22.000cm away and there are 3 dots, m=-1, m=0 amd m=1. the distances between m=-1 and m=1 is 10.7314.

find the speed of the galaxy moving away from us?

2. Relevant equations

d sin theta =m lambda
y_m=Ltan lambda
Doppler effect
3. The attempt at a solution

At first, I think I need to find the angel by using: y_m=Ltan lambda
then I have: 0.22 tan theta _1 =0.107314/2 → theta=47.3972 degrees

Since I have the angel, I can find the wavelength of the light by using: d sin theta =m lambda
then I have: 1mm/765.5 sin (47.3972)= 1*lambda → lambda = 962 nm

I get stuck at this step, can anyone give me a hit to get the answer?

Thanks

2. Feb 28, 2015

TSny

You set this up correctly, but your answer for the angle θ is not correct.

Think about how to use the Doppler effect to get the speed of the galaxy.

3. Feb 28, 2015

HaLAA

θ=13.7ο,
λ=309nm, this is the initial wavelength.

the equation of the Doppler effect is λ=λ'√(1+v_s/c)/(1-v_s/c)

309nm is λ' , I dont't see how to get λ with the information I have.

4. Feb 28, 2015

TSny

What is the normal wavelength for the brightest He II line?

5. Feb 28, 2015

HaLAA

I don't know, the question doesn't give me any information about that

6. Feb 28, 2015

Staff: Mentor

Your text or notes will likely contain the value. If not it can be looked up online. The NIST site should have a table.