A) 7400 m/s
B) \[32.\,4\times {{10}^{2}}m/s\]
C) 6480 km/s
D) none of these
Correct Answer: C
Solution :
From Hubbles law, the red shift (Z) is directly proportional to the distance (r) of the galaxy from us that is \[Z\propto r\] Also, \[Z=\frac{d\lambda }{\lambda }=\frac{v}{c}=\frac{\text{speed}\,\text{of}\,\text{galaxy}}{\text{speed}\,\text{of}\,\text{light}}\] Given, \[d\lambda =401.8-393.3=8.5\,nm,\] \[\lambda =393.3\,nm.\] \[\therefore \] \[Z=\frac{8.5}{393.3}=0.0216\] Also \[v=cZ\] \[=3\times {{10}^{8}}\times 0.0216\] \[=64.8\times {{10}^{8}}\,m/s\] Since, \[1\,km={{10}^{3}}m,\]therefore \[v=6480\,km/s\]
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