Estimate the observed wavelength for the 656 nm line in the spectrum of a star which is 100 million light-years from us.
A)653 nm
B)659 nm
C)661 nm
D)677 nm
E)692 nm

Question

Quizplus · Accepted Answer

The observed wavelength is redshifted due to the expansion of the universe, so it will be longer than the emitted wavelength. The redshift is given by z = (observed wavelength - emitted wavelength) / emitted wavelength. The distance to the star is 100 million light-years, which is 9.46 x 10^22 km. The Hubble constant is 70 km/s/Mpc, which is 2.27 x 10^-18 s^-1/km. The redshift is therefore z = (9.46 x 10^22 km) x (2.27 x 10^-18 s^-1/km) = 0.0214. The observed wavelength is therefore 656 nm x (1 + 0.0214) = 661 nm.

Estimate the Observed Wavelength for the 656 Nm Line in the Spectrum