The spectral line for a given element , received from a distant star is shifted towards the longer wavelength by `0.028%`. What is the velocity of the star ?

Options

A. a) `5.6 xx 10^(4) m//s `
B. b)`8.4xx10^(4) m//s `
C. c)`4.2xx10^(4) m//s `
D. d)`9.8xx10^(4) m//s `

Answer

B

Explanation

The wavelength of light is increased. This means that the star is moving away from the earth. According to Doppler's principle n light,
`(Delta lambda)/(lambda)=(v)/c" " :. v=c((Delta lambda)/(lambda))`
In this case , `(Delta lambda)/(lambda)=0.028%=(0.028)/(100)`
`=28 xx 10^(-3) xx 10^(-2)=28xx10^(-5)`
`:. v=28xx10^(-5) xx c=28xx10^(-5) xx 3 xx 10^(8)`
`:. v=84 xx 10^(3) =8.4 xx 10^(4) m//s `