Question

Hydrogen gas emits a strong spectral line of red light with a wavelength of 656.3 nm (Balmer a line). This emission line is seen in the spectrum of a distant quasar but at a wavelength of 721.9 nm. Applying Doppler's relation, how fast is this object moving with respect to Earth, in terms of the velocity of light, c?

Answer 1

The quasar is moving at approximately 30.25% the speed of light relative to Earth.

Step-by-step explanation:

The observed redshift of a spectral line can be used to determine the speed at which an object is moving relative to Earth using Doppler's relation. In this case, the spectral line of hydrogen emitted by a quasar has a wavelength of 721.9 nm, while its rest wavelength is 656.3 nm. The redshift can be calculated using the formula = (−)/, where is the observed wavelength and is the rest wavelength.

After finding the value of , we can use the formula = , where is the velocity of the object relative to Earth and is the speed of light. So, = × . In this case, the quasar is moving at approximately 30.25% the speed of light.