Wave OpticsEasy
Question
In hydrogen spectrum the wavelength of Hα line is 656 nm; whereas in the spectrum of a distance galaxy Hα line wavelength is 706 nm. Estimated speed of galaxy with respect to earth is
Options
A.2 × 108 m/s
B.2 × 107 m/s
C.2 × 106 m/s
D.2 × 105 m/s
Solution
Since, the wavelength (λ) is increasing, we can say that the galaxy is receding. Doppler can be given by
λ′ = λ
.....(i)
or 706 = 656
or
= 1.16
∴ C + v = 1.16 c - 1.16v
∴
= 0.22 × 108 m/s
v
2.2 × 107 m/s
If we take the approximation then Eq. (i) can be written as
ᐃλ = λ
.....(ii)
From here v =
× (3 × 108)
v = 0.23 × 108 m/s.
λ′ = λ
.....(i)or 706 = 656
or
= 1.16∴ C + v = 1.16 c - 1.16v
∴
= 0.22 × 108 m/s v
2.2 × 107 m/sIf we take the approximation then Eq. (i) can be written as
ᐃλ = λ
.....(ii)From here v =
× (3 × 108) v = 0.23 × 108 m/s.
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