In the hydrogen spectrum the wavelength of H λ line is 656 nm whereas, in the spectrum of a distant galaxy the H λ line has a wavelength of 706 nm . The estimated speed of the galaxy with respect to the earth is

Question

In the hydrogen spectrum the wavelength of H λ line is 656 nm whereas, in the spectrum of a distant galaxy the H λ line has a wavelength of 706 nm . The estimated speed of the galaxy with respect to the earth is, 1.2 × 10 7 m s - 1, 2.2 × 10 7 m s - 1, 3 × 10 7 m s - 1, 1.9 × 10 7 m s - 1

MARKS App · Accepted Answer

Since, the wavelength observed is more than the true wavelength, we can say that the galaxy is receding. Doppler effect in this case gives us λ ' = λ c + v c - v 706 = 656 c + v c - v or, c + v c - v = 706 656 2 = 1.16 or, c + v = 1 . 16 c - 1 . 16 v v = 0 .16 c 2 .16 = 0 .16 × 3 .0 × 10 8 2 .16 = 0 .22 × 10 8 m s - 1 v = 2 .2 × 10 7 m s - 1

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