A star is moving away from the earth with a velocity of `100 km//s`. If the velocity of light is `3 xx 10^(8) m//s` then the shift of its spectral line of wavelength `5700 A` due to Doppler effect is

Options

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

Answer

B

Explanation

`c = 3 xx 10^(8)m//s, v = 100 km//s, lambda = 5700 A^(@), lambda' = ?`
`lambda' = sqrt((1+(v)/(c))/(1-(v)/(c)))lambda`
`= sqrt((1+(100 xx 10^(3))/(3 xx 10^(8)))/(1-(100 xx 10^(3))/(3 xx 10^(8)))) xx 5700 xx 10^(-10)`
`= 1.9 xx 10^(-10)m = 1.9 A^(@)`