Answer:
The observed wavelength of the line of hydrogen originating from the galaxy is 23cm.
Explanation:
The speed of the galaxies using the shifted of the spectral lines can be known by using the Doppler speed:
[tex]v = c\frac{\Delta \lambda}{\lambda_{0}}[/tex] (1)
Where [tex]\Delta \lambda[/tex] is the wavelength shift, [tex]\lambda_{0}[/tex] is the wavelength at rest, v is the velocity of the source and c is the speed of light.
Therefore, from equation 1 it can be deduce the equation for the redshift
[tex]v = c(\frac{\lambda_{observed}-\lambda_{0}}{\lambda_{0}})[/tex]
[tex]\frac{v}{c} = \frac{\lambda_{observed}-\lambda_{0}}{\lambda_{0}}[/tex]
[tex]z = \frac{\lambda_{observed}-\lambda_{0}}{\lambda_{0}}[/tex] (2)
Where z is the redshift.
Hence, the redshift represents this shift of the spectral lines to red part in the spectrum of a galaxy or any object which is moving away.
Then, [tex]\lambda_{observed}[/tex] can be isolated from equation 2.
[tex]\lambda_{observed} = (z \cdot \lambda_{0})+\lambda_{0}[/tex] (3)
For this particular case [tex]\lambda_{0} = 21cm[/tex] and [tex]z = 2[/tex]
[tex]\lambda_{observed} = (2)(21cm)+21cm[/tex] (3)
[tex]\lambda_{observed} = 23cm[/tex] (3)
Hence, the observed wavelength of the line of hydrogen originating from the galaxy is 23cm.
