The star recedes from the earth at the speed a `100 kms^(-1)` Find the doppler shift of spectrur line `3xx 10^(8)ms^(-1)` ms having wavelength `5700Å`

Options

A. `0.63Å`
B. `1.90Å`
C. `3.80Å`
D. `5.70Å`

Answer

B

Explanation

As per Dopper effect,
`(Deltaf)/(fs)=(v_(s))/(c) ....(1) and f=(c)/(lambda)`
Taking derivative w.r.t. `lambda`
Putting `Deltaf=(-c)/(lambda^(2))Delta and f_(s)=(c)/(lambda)`
`:.` From equation (1)
`(c)/(lambda^(2)xx(c)/(lambda)) delta lambda=(v_(s))/(c)`
`:. delta lambda=(v_(s))/(c)xxlambda`
`=(100xx10^(3)xx 5.7xx10^(-7))/(3xx10^(8))`
`=1.90Å`