The wavelength of Hα line in the hydrogen spectrum is found to be 6563 Å in the laboratory. If the velocity of the milky way is 1.05× 106 m s- 1 , then the wavelength of Hα line in the spectrum of milky way will be

Question

The wavelength of Hα line in the hydrogen spectrum is found to be 6563 Å in the laboratory. If the velocity of the milky way is 1.05× 106 m s- 1 , then the wavelength of Hα line in the spectrum of milky way will be (A) 6457 Å (B) 6586 Å (C) 7123 Å (D) 7349 Å

Tardigrade Admin · Accepted Answer

As λ =Δ λ × (c/v) or Δ λ =λ × (v/c) Δ λ =(6563 × 1.05 × 106/3 × 108)â«=2297× 10- 2 =22.97 â«≈ 23 â« ∴ New wavelength is (6563 + 23) â« =6586 â«

Q. The wavelength of $H_{α}$ line in the hydrogen spectrum is found to be $6563 Å$ in the laboratory. If the velocity of the milky way is $1.05 \times 1 0^{6} m s^{- 1}$ , then the wavelength of $H_{α}$ line in the spectrum of milky way will be

$6457 Å$

$6586 Å$

$7123 Å$

$7349 Å$

As $λ = Δ λ \times \frac{c}{v}$ or $Δ λ = λ \times \frac{v}{c}$
$Δ λ = \frac{6563 \times 1.05 \times 1 0 ^{6}}{3 \times 1 0 ^{8}} Å = 2297 \times 1 0^{- 2}$
$= 22.97 Å \approx 23 Å$
$∴$ New wavelength is $(6563 + 23) Å$
$= 6586 Å$

Q. The wavelength of Hα​ line in the hydrogen spectrum is found to be 6563Å in the laboratory. If the velocity of the milky way is 1.05×106ms−1 , then the wavelength of Hα​ line in the spectrum of milky way will be

6457Å

6586Å

7123Å

7349Å