Question

Imagine that you have obtained spectra for several galaxies and have measured the observed wavelength of a hydrogen emission line that has a rest wavelength of 656.3 nanometers. Here are your results:Galaxy 1: Observed wavelength of hydrogen line is 660.0 nanometers.Galaxy 2: Observed wavelength of hydrogen line is 665.8 nanometers.Galaxy 3: Observed wavelength of hydrogen line is 682.7 nanometers.Calculate the redshift, z, for each of these galaxies.

Answer 1

Answer:

Galaxy 1:

z = 0.0056

Galaxy 2:

z = 0.014

Galaxy 3:

z = 0.040

Explanation:

Spectral lines will be shifted to the blue part of the spectrum¹ if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect). The source in this particular case is represented for each of the galaxies of interest.

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. That is a direct confirmation of how the universe is in an expanding accelerated motion.

The redshift can be defined in analytic way by means of the Doppler velocity:

$v = c\frac{\Delta \lambda}{\lambda_{0}}$  (1)

Where $\Delta \lambda$ is the wavelength shift, $\lambda_{0}$ is the wavelength at rest, v is the velocity of the source and c is the speed of light.

$v = c(\frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}})$

$\frac{v}{c} = \frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}}$  

$z = \frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}}$  (2)

Where z is the redshift.

For the case of Galaxy 1:

Where $\lambda_{measured} = 660.0 nm$ and $\lambda_{0} = 656.3 nm$.

$z = \frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}}$

$z = (\frac{660.0 nm - 656.3 nm}{656.3 nm})$

$z = 0.0056$

For the case of Galaxy 2:

Where $\lambda_{measured} = 665.8 nm$ and $\lambda_{0} = 656.3 nm$.

$z = \frac{665.8 nm - 656.3 nm}{656.3 nm}$

$z = 0.014$

For the case of Galaxy 3:

       

Where $\lambda_{measured} = 682.7 nm$ and $\lambda_{0} = 656.3 nm$.

$z = \frac{682.7 nm - 656.3 nm}{656.3 nm}$

$z = 0.040$

Key terms:

¹Spectrum: Decomposition of light in its characteristic colors (wavelengths).