You observe a distant quasar in which a spectral line of hydrogen with rest wavelength \(\lambda_{\text {rest }}=121.6 \mathrm{nm}\) is found at a wavelength of \(547.2 \mathrm{nm}\). What is its redshift? When the light from this quasar was emitted, how large was the universe compared to its current size?

Cosmology is the scientific study of the large scale properties of the universe as a whole. It involves understanding the origins, evolution, and large-scale structures of the universe. Cosmologists examine various phenomena such as the cosmic microwave background, galaxy formation, and the rate of universe expansion.
One of the key observations in cosmology is the redshift of light from distant galaxies and quasars. Redshift provides evidence that the universe is expanding. When studying the cosmos, astronomers rely heavily on this concept to draw conclusions about the age, size, and overall behavior of the universe.
The study of cosmology helps us understand where the universe is heading and its ultimate fate. Key tools in this field include telescopes, satellites, and theoretical models.

The universe expansion refers to the idea that the universe has been growing since the Big Bang. This concept was first discovered by observing that distant galaxies are moving away from us, which is evidenced by the redshift of their spectral lines. As light from these galaxies travels to us, the space through which it travels is expanding, stretching the light to longer wavelengths.
Key points to understand about universe expansion:

• Hubble's Law: This states that the speed at which a galaxy moves away is proportional to its distance from us.
• The Scale Factor: This represents the size of the universe at any given time compared to its current size.
• Redshift and Scale Factor Relationship: Redshift can be used to determine how much the universe has expanded since the light left the galaxy or quasar.

By measuring redshift, we can derive the rate at which the universe is expanding and gain insights into the constants and parameters that govern cosmic evolution.

Hydrogen, the most abundant element in the universe, emits light at specific wavelengths when its electrons change energy levels. These specific wavelengths are known as spectral lines. The most familiar hydrogen line is the 121.6 nm wavelength, also known as the Lyman-alpha line.
When studying distant cosmic objects like quasars, astronomers observe these hydrogen spectral lines to determine their redshift. By comparing the observed wavelength of the spectral line with its rest wavelength, they can calculate how much the light has been stretched.
Key points about hydrogen spectral lines:

• Rest Wavelength: The original wavelength of the light emitted by hydrogen.
• Observed Wavelength: The wavelength detected by telescopes, shifted due to the expansion of the universe.
• Redshift Calculation: Using the difference between the observed and rest wavelengths, astronomers calculate the redshift to understand the object's distance and the rate of universe expansion.

Understanding hydrogen spectral lines is crucial for astronomers because it helps to map the large-scale structure of the universe and trace its evolutionary history.