Question

Doppler shifted hydrogen absorption lines are seen in the spectrum of a star.

Answer 1

Answer:

Explanation:

It is given that,

Wavelength of hydrogen line, $\lambda=656.28\ nm=656.28\times 10^{-9}\ m$

Shift in wavelength, $\lambda'=656.08\ nm=656.08\times 10^{-9}\ m$

According to Relativistic Doppler Effect, the shift in wavelength is given by :

$\dfrac{\lambda'}{\lambda}=\sqrt{\dfrac{1+v/c}{1-v/c}}$

v is the speed of star

c is the speed of light

$(\dfrac{\lambda'}{\lambda})^2=\dfrac{c+v}{c-v}$

$v=c-\dfrac{2c}{(\dfrac{\lambda'}{\lambda})^2+1}$

$v=3\times 10^8-\dfrac{2\times 3\times 10^8}{(\dfrac{656.08\times 10^{-9}}{656.28\times 10^{-9}})^2+1}$

$v=91438.32\ m/s$

or

v = 91.43 km/s

So, the star is moving with a speed of about 100 km/s. Hence, this is the required solution.