Answer:
[tex]\lambda_x=5.019858nm[/tex]
Explanation:
From the question we are told that
Speed of star [tex]S=8.46km/s[/tex]
Distance of spectral line [tex]\lambda_0= 5.02nm[/tex]
Generally the equation for wavelength with respect to spectral lines is mathematically given by
[tex]\lambda=\lambda _0 *\frac{v}{c}[/tex]
where
[tex]\lambda_0= length\ of\ spectral\ line[/tex]
[tex]c=The\ speed\ of\ light[/tex]
[tex]v= speed\ of\ moving\ object[/tex]
therefore
[tex]\lambda=5.02*10^{-9} *\frac{8.46*10^{12}}{299 792 458*10^9}[/tex]
[tex]\lambda=1.42*10^{-4} nm[/tex]
Generally the equation for new wavelength is mathematically given as
[tex]\lambda_x=\lambda _0-\lambda[/tex]
[tex]\lambda_x=5.02 nm-1.42*10^{-4} nm[/tex]
[tex]\lambda_x=5.02-1.42*10^{-4}[/tex]
Therefore
[tex]\lambda_x=5.019858nm[/tex]
