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 ∘ ?

Question

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 ∘ ?, 306 km sec - 1, 322 km sec - 1, 296 km sec - 1, 336 km sec - 1

MARKS App · Accepted Answer

f = f 0 1 + β 1 - β ; β = v c f f 0 1 + β 1 - β 1 + Δ f f 0 2 = 1 + β ( 1 - β ) - 1 β is small compared to 1 1 + 2 Δ f f 0 = 1 + 2 β β = Δ f f 0 = v c v = 6 × c 5890 = 305 . 6 km sec - 1

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