If you measure the spectrum emitted by a cloud of gas that orbits a nearby spiral galaxy and the observed wavelength of a hydrogen emission line is 658.4 nm while the rest wavelength of that line is 656.3 nm, what is the velocity of this gas cloud along your line of sight (i.e., the radial velocity)? Note that the speed of light is 3 *10⁵ km/s. A) 960 km/s B) 1,200 km/s C) 2,300 km/s D) 3,800 km/s E) 4,400 km/s

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Quizplus · Accepted Answer

The radial velocity can be calculated using the formula for redshift: $ v = c \times \frac{\Delta \lambda}{\lambda_0} $, where $ \Delta \lambda = 658.4 \, \text{nm} - 656.3 \, \text{nm} = 2.1 \, \text{nm} $ and $ \lambda_0 = 656.3 \, \text{nm} $. Plugging in the values, $ v = 300,000 \, \text{km/s} \times \frac{2.1}{656.3} \approx 960 \, \text{km/s} $.

If You Measure the Spectrum Emitted by a Cloud of Gas