The spectral line of wavelength `lambda=5000 Å` in the light coming from a distant star is observed as 5200 Å.Determine the recession velocity of the star.

Options

A. Receding , `1.2 xx 10^(7) m//s `
B. Approaching , ` 1.2 xx 10^(7) m//s `
C. Receding , `2.4 xx 10^(7) m//s `
D. Approaching, `1.8 xx 10^(7) m//s `

Answer

A

Explanation

Since the wavelength of light is increased, the star is moving away (receding ) from the earth.
In this case , `lambda=5000 Å and lambda'=5200Å`
`:. Delta lambda= lambda'-lambda=200Å`
Using Doppler's formula in light , viz. ,
`(Delta lambda)/(lambda)=(v)/(c)` we get
`v=(Delta lambda)/(lambda) xx c=(( 200 xx 10^(-10))/(5000 xx 10^(-10)))xx 3 xx 10^8`
`:. ""v=(2)/(50) xx 3 xx 10^(8) = 1.2 xx 10^(7) m//s `