With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 A is observed at 5896 A? (a) 306 km/sec (b) 322 km/sec (c) 296 km/sec (d) 336 km/sec

Answer: (a). Doppler shift: v = c(Δλ)/(λ), with Δλ = 5896 - 5890 = 6 Å. v = 3×10⁸ × 6/5890 ≈ 3.06×10⁵ m/s v ≈ 306 km/s So the answer is (a) 306 km/s.

With what speed should a galaxy move outward with respect to earth so… | JEE Main 2021 (20 Jul, Shift 2)

Q18JEE Main 2021 · 20 JUL · SHIFT 2Medium

Wave Theory, Wavefronts & Doppler Effect

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $\mathring{A}$ is observed at 5896 $\mathring{A}$ ?

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Answer: (a)

Doppler shift: $v = c\dfrac{\Delta\lambda}{\lambda}$ , with $\Delta\lambda = 5896 - 5890 = 6$ Å.
$v = 3\times10^{8} \times \dfrac{6}{5890} \approx 3.06\times10^{5}$ m/s
$v \approx 306$ km/s
So the answer is (a) 306 km/s.

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