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In the hydrogen spectrum, the Hα emission line has a wavelength of 656 nm. In the spectrum of a faraway galaxy, the same Hα line is observed at 706 nm. The approximate speed of the galaxy relative to the Earth is

1. 2 × 10⁸ m/s
2. 2 × 10⁷ m/s
3. 2 × 10⁶ m/s
4. 2 × 10⁵ m/s

Correct answer: 2 × 10⁷ m/s

Solution

Redshift delta lambda = 706 - 656 = 50 nm. v = c (delta lambda / lambda) = 3 x 10^8 x (50/656) = 2.3 x 10^7 m/s ~ 2 x 10^7 m/s.

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