Modern Physics 1 Question 26

23. In hydrogen spectrum, the wavelength of Hα line is 656nm; whereas in the spectrum of a distant galaxy Hα line wavelength is 706nm. Estimated speed of galaxy with respect to earth is

(1999,2M)

(a) 2×108m/s

(b) 2×107m/s

(c) 2×106m/s

(d) 2×105m/s

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Solution:

  1. Since, the wavelength (λ) is increasing, we can say that the galaxy is receding. Doppler effect can be given by

λ=λc+vcv

 or 706=656c+vcv or c+vcv=7066562=1.16c+v=1.16c1.16vv=0.16c2.16=0.16×3.0×1082.16=0.22×108m/sv2.2×107m/s

If we take the approximation then Eq. (i) can be written as

Δλ=λvc

From here v=Δλλc=706656656(3×108)

v=0.23×108m/s

which is almost equal to the previous answer. So, we may use Eq. (ii) also.



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