In a lab a hydrogen spectral line is observed to have a wavelength of 656nm. This line is observed in a distance galaxy to have a wavelength of 661nm, what is the recessional velocity of the galaxy?
This question is dealing with phenomena of Redshift, where wavelengths are shifted due to movement between observer and event. The key information to extract from the question is we have a rest wavelength, an observed wavelength and want a velocity of the galaxy (relative to Earth) from where the light has come from. The observed wavelength is larger than the rest wavelength -> wavelength is increased meaning that the galaxy is moving away, hence the question asks for a recessional velocity . So we should expect a positive velocity as our answer.The formula for redshift is given in the higher formula sheet as Z = (λobs - λrest) / λrestAlso given is Z = V/c , where c is the speed of light. We want to solve for V, as this is the recessional velocity, both equations are equal to Z, so we can equate, meaning :V/c = (λobs - λrest) / λrest -> timesing both sides by c, we get an expression for V in terms of everything we know! V = c(λobs - λrest) / λrest -> c = 3 x 108 m/s , λobs = 656nm , λrest = 661nm (as both rest and obs are in nm we don't need to worry about converting to metres as we calculating a ration) V = 3 x 108 (661-656) / 656 ≈ 2.29 x 106 m/s (always remember units are part of the answer too!)
