Answer:
The wavelength of that line in the spectrum of a planet is [tex]5000.5\ \AA[/tex].
Explanation:
Given that,
Wavelength [tex]\lambda= 5000\ \AA[/tex]
Velocity = 30 km/s
We need to calculate the wavelength of that line in the spectrum of a planet
Using formula of wavelength
[tex]\lambda=\lambda'\sqrt{\dfrac{1-\dfrac{v}{c}}{1+\dfrac{v}{c}}}[/tex]
Where, v = velocity of planet
c = speed of light
Put the value into the formula
[tex]5000=\lambda'\sqrt{\dfrac{1-\dfrac{30\times10^{3}}{3\times10^{8}}}{1+\dfrac{30\times10^{3}}{3\times10^{8}}}}[/tex]
[tex]\lambda'=\dfrac{5000\times10^{-10}}{\sqrt{\dfrac{1-\dfrac{30\times10^{3}}{3\times10^{8}}}{1+\dfrac{30\times10^{3}}{3\times10^{8}}}}}[/tex]
[tex]\lambda'=5000.5\ \AA[/tex]
Hence, The wavelength of that line in the spectrum of a planet is [tex]5000.5\ \AA[/tex].