In the hydrogen spectrum the wavelength of textHλ line is 656 nm whereas, in the spectrum of a distant galaxy the textHλ 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 textHλ line is 656 nm whereas, in the spectrum of a distant galaxy the textHλ line has a wavelength of 706 nm . The estimated speed of the galaxy with respect to the earth is (A) 1.2× 107m s- 1 (B) 2.2× 107m s- 1 (C) 3× 107m s- 1 (D) 1.9× 107m s- 1

Tardigrade Admin · 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 \frac{c + v}{c - v}

706 = 656 \frac{c + v}{c - v}

or, \frac{c + v}{c - v} = (\frac{706}{656})^{2} = 1.16

or, c + v = 1.16 c - 1.16 v

v = \frac{0.16 c}{2.16} = \frac{0.16 \times 3.0 \times 1 0 ^{8}}{2.16} = 0.22 \times 1 0^{8} m s^{- 1}

v = 2.2 \times 1 0^{7} m s^{- 1}

Q. 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

$1.2 \times 1 0^{7} m s^{- 1}$

$2.2 \times 1 0^{7} m s^{- 1}$

$3 \times 1 0^{7} m s^{- 1}$

$1.9 \times 1 0^{7} m s^{- 1}$

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

1.2×107ms−1

2.2×107ms−1

3×107ms−1

1.9×107ms−1

Q. 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

$1.2 \times 1 0^{7} m s^{- 1}$

$2.2 \times 1 0^{7} m s^{- 1}$

$3 \times 1 0^{7} m s^{- 1}$

$1.9 \times 1 0^{7} m s^{- 1}$