If the spectrum of a distant galaxy is observed to have a calcium K absorption line that occurs at a wavelength of 500.4 nm, what is this galaxy's distance if the rest wavelength of this absorption line is 393.4 nm? Assume the Hubble constant is 70 km/s/Mpc.
A) 720 Mpc
B) 950 Mpc
C) 1,200 Mpc
D) 2,500 Mpc
E) 3,700 Mpc

Question

Quizplus · Accepted Answer

The redshift z is calculated using the formula z = (observed wavelength - rest wavelength) / rest wavelength = (500.4 nm - 393.4 nm) / 393.4 nm = 0.272. The velocity v is then v = z * c = 0.272 * 300,000 km/s = 81,600 km/s. Using Hubble's law, distance = velocity / Hubble constant = 81,600 km/s / 70 km/s/Mpc = 1,165.71 Mpc, which is closest to 1,200 Mpc.

If the Spectrum of a Distant Galaxy Is Observed to Have