Doppler shifted hydrogen absorption lines are seen in the spectrum of a star. The hydrogen line at 656.28 nm is seen to be shifted to 656.08 nm. How fast is the star moving (Note: The speed of light is approximately 300,000 km/s, or 3 × 105 km/s.)?

Question

Quizplus · Accepted Answer

The Doppler shift formula for velocity is $v = c \times \frac{\Delta \lambda}{\lambda}$, where $c$ is the speed of light, $\Delta \lambda$ is the change in wavelength, and $\lambda$ is the original wavelength. Here, $\Delta \lambda = 656.28 - 656.08 = 0.20$ nm, and $\lambda = 656.28$ nm. Plugging in the values, $v = 3 \times 10^5 \times \frac{0.20}{656.28}$ km/s, which gives approximately 91 km/s, rounding to the nearest order of magnitude gives about 100 km/s.

Doppler Shifted Hydrogen Absorption Lines Are Seen in the Spectrum