A galaxy is moving away from the earth at a speed of 286 km s^(-1). The shift in the wavelength of a red line at 630 nm is x×10^(-10) m. The value of x, to the nearest integer, is ___ . [Take the value of the speed of the light c, as 3×10^8 m s^(-1)]

Correct answer: 6. ⇒(Δλ)/(λ)c=v, ⇒Δλ=v/c×λ=286/(3×10^5)×630×10^(-9)=6×10^(-10) m

Q90 / 90 · JEE Main 2021 (18 Mar Shift 2) · Physics

A galaxy is moving away from the earth at a speed of $286 km s^{- 1}$ . The shift in the wavelength of a red line at $630 nm$ is $x \times 10^{- 10} m$ . The value of $x$ , to the nearest integer, is ___ .
[Take the value of the speed of the light $c$ , as $3 \times 10^{8} m s^{- 1}$ ]

Correct answer: 6

$\Rightarrow \frac{Δ λ}{λ} c = v$ ,

$\Rightarrow Δ λ = \frac{v}{c} \times λ = \frac{286}{3 \times 10^{5}} \times 630 \times 10^{- 9} = 6 \times 10^{- 10} m$

Hence, the correct answer is 6.