A spectral line = 5000 Å in the light coming from a distant star … - Vidyadip

MCQ

A spectral line $\lambda = 5000 Å$ in the light coming from a distant star is observed as a $5200 Å.$ What will be recession velocity of the star

A
$1.15 \times {10^7}cm/\sec $
✓
$1.15 \times {10^7}m/\sec $
C
$1.15 \times {10^7}km/\sec $
D
$1.15 \,km/sec$

✓

Answer

Correct option: B.

$1.15 \times {10^7}m/\sec $

b
(b)$\Delta \lambda = 5200 - 5000 = 200Å$
Now $\frac{{\Delta \lambda }}{{\lambda '}} = \frac{v}{c} \Rightarrow v = \frac{{c\Delta \lambda }}{{\lambda '}} = \frac{{3 \times {{10}^8} \times 200}}{{5000}}$
$ = 1.2 \times {10^7}m/\sec \approx 1.15 \times {10^7}m/\sec $

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