Respuesta :
Answer:
Explanation:
It is given that,
Wavelength of hydrogen line, [tex]\lambda=656.28\ nm=656.28\times 10^{-9}\ m[/tex]
Shift in wavelength, [tex]\lambda'=656.08\ nm=656.08\times 10^{-9}\ m[/tex]
According to Relativistic Doppler Effect, the shift in wavelength is given by :
[tex]\dfrac{\lambda'}{\lambda}=\sqrt{\dfrac{1+v/c}{1-v/c}}[/tex]
v is the speed of star
c is the speed of light
[tex](\dfrac{\lambda'}{\lambda})^2=\dfrac{c+v}{c-v}[/tex]
[tex]v=c-\dfrac{2c}{(\dfrac{\lambda'}{\lambda})^2+1}[/tex]
[tex]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}[/tex]
[tex]v=91438.32\ m/s[/tex]
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.
