The wavelength of light coming from a star is found to be 0.6% more than that coming from a source on earth. What is the velocity of the star ? `[c=3xx 10^(8)m//s]`

Options

A. A. `1.2xx10^(6) m//s `
B. B. `1.5xx10^(6) m//s `
C. C.`1.8 xx 10^(6) m//s `
D. D. `1.6xx10^(6) m//s `

Answer

C

Explanation

In the case of Doppler effect for light, the shift of wavelength `(Delta lambda)` is given by `Delta lambda=((v)/(c)) lambda `.
` :. ""v=((Delta lambda)/(lambda))c ` ............... (1)
If ` lambda and lambda'` are the wavelength of light from a source on the earth and from the star , then it is given that
`(lambda'- lamdba)/(lambda)=0.6%=(0.6)/(100)=6 xx 10^(-3)`
`:. (Delta lambda)/(lambda)=6 xx 10^(-3)` ................ (2)
`:.` from (1) and (2),
`v=6 xx 10(-3) xx 3 xx 10^(8) =18 xx 10^(5)=1.8 xx 10^(6) m//s `