Observing M87's spectral of light

[bobo1455]

The galaxy M87, shown in Figure 15.5, was discovered by Charles Messier in 1781. Located
54 million light-years from Earth, it is one of the most massive galaxies in the Universe,
including a black hole at its centre that is 4 billion times more massive than the Sun. Observing
the spectrum of M87’s light, we detect the spectral pattern of hydrogen. Use this information
to determine the wavelength at which we observe the red spectral line of hydrogen. Show how
you got your answer.

(A) 650 nm
(B) 654 nm
(C) 656 nm
(D) 659 nm
(E) 662 nm

I got 656 nm. My reasoning for picking (C) is that I looked up the wavelength spectrum for Hydrogen in my textbook and for red spectral line in Hydrogen is approximately 656.3 nm, so I assume it is 656 nm for the final answer.

I don't think it has anything to do with redshift and blueshift so I believe my answer is correct, but please correct me if I am missing something.

 

[Chronum]

Now, from the data given, strictly speaking, the hydrogen-red line is at 656.2/656.3, so 656 nm is correct.

However, if we take redshift into account, it's 659 nm.

Now, the question says, "to determine the wavelength at which we observe the red spectral line of hydrogen". There's that word there "observe", which creates complications.

 

[bobo1455]

How did you get 659 nm? Are you using some form of the Doppler shift formula? I'll try using a re-arranged version of the Doppler Shift formula to solve for one of the wavelengths and maybe that will make more sense to me.

 

[bobo1455]

I got it. I re-arranged the doppler shift formula to solve for λ_shift.

The known variables I need for the formula were λ_rest, speed of light (c) and the radial velocity of the object.

I got the radial velocity for M87 in my textbook under the Appendix. Then I just plugged in the values and got 659 nm as my final answer.

Thanks for the help!