In hydrogen spectrum the wavelength of `H_(a)` line is `656nm, ` where in the spectrum of a distance galaxy `H_(a)` line wavelength is `706 nm` . Estimated speed of the galaxy with respect to earth is ,

Options

A. `2 x 10^8 m//s`
B. `2 xx 10^7 m//s`
C. `2 xx 10^6 m//s`
D. `2 xx 10^5 m//s`

Answer

B

Explanation

`1/ lamda ,(1)/( lamda) sqrt((c-v)/(c+v))`
here ` lamda = 706 nm , lamda = 656 nm`
` therefore (c-v )/(c +v ) = (lamda / lamda)^2 =(656/(706 )^2 = 0.86 implies (v )/(c ) = 0.14 )/( 1.86 )`
`implies v= 0.075 xx 3 xx 10^8 = 2.25 xx 10^7 m//s`