If you found a galaxy with a hydrogen emission line,normally found at 656.3 nm,with a measured wavelength of 756.3 nm,what would the galaxy's recessional velocity be if the Hubble constant is 72 km/s/Mpc?
A) 39,700 km/s
B) 45,700 km/s
C) 47,000 km/s
D) 54,500 km/s

Question

Quizplus · Accepted Answer

The recessional velocity of the galaxy can be calculated using the formula for redshift, $ z = \frac{\Delta \lambda}{\lambda_0} = \frac{\lambda - \lambda_0}{\lambda_0} $, where $ \Delta \lambda = \lambda - \lambda_0 $, $ \lambda $ is the observed wavelength, and $ \lambda_0 $ is the rest wavelength. Here, $ \Delta \lambda = 756.3 \, \text{nm} - 656.3 \, \text{nm} = 100 \, \text{nm} $, and $ \lambda_0 = 656.3 \, \text{nm} $, so $ z = \frac{100}{656.3} \approx 0.1524 $. The recessional velocity $ v $ is related to the redshift by $ v = zc $, where $ c $ is the speed of light ($ c = 3 \times 10^5 \, \text{km/s} $). Thus, $ v = 0.1524 \times 3 \times 10^5 \, \text{km/s} = 45,720 \, \text{km/s} $, which rounds to $ 45,700 \, \text{km/s} $.

If You Found a Galaxy with a Hydrogen Emission Line,normally