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With what speed should a galaxy move out...

With what speed should a galaxy move outward, with respect to earth so that the sodium-D line at wavelength 5890 Å is observed at 5896 Å ?

A

296 km/sec

B

322 km/sec

C

336 km/sec

D

306 km/sec

Text Solution

Verified by Experts

The correct Answer is:
D
`f=f_0sqrt((1+beta)/(1-beta))" " { :. beta=v/c}`
`f/(f_0)=sqrt((1+beta)/(1-beta))`
`(1+(Deltaf)/f_0)^2 =(1+beta)(1-beta)^(-1)`
`beta ` is small compared to 1,
`(1+(2Deltaf)/f_0)=(1+2beta)implies beta=(Deltaf)/(f_0)=v/c`
`v = 6 xx c/(5890)=305.6 km//s`
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