Hydrogen gas emits a strong spectral line of red light with a wavelength of 656.3 nm (the Balmer$\alpha$ line). This emission line is seen in the spectrum of a distant quasar but at a wavelength of 721.9 nm. Applying Doppler's relationship, how fast is this object moving with respect to Earth, in terms of the velocity of light, c?
A) 1/10 c
B) 1.1 c
C) 1/100 c
D) 10 c

Question

Quizplus · Accepted Answer

The Doppler shift formula for light is $\Delta \lambda / \lambda = v / c$, where $\Delta \lambda = 721.9 \, \text{nm} - 656.3 \, \text{nm}$, $\lambda = 656.3 \, \text{nm}$, $v$ is the velocity of the object, and $c$ is the speed of light. Solving for $v/c$ gives a value close to 0.1, or 1/10 of the speed of light.

Hydrogen Gas Emits a Strong Spectral Line of Red Light α\alphaα

Hydrogen Gas Emits a Strong Spectral Line of Red Light $\alpha$