The spectrum of a distant galaxy shows the H αline of hydrogen(λrest=656.28 nm) at a wavelength

step 1 Hi, everybody. So we want to know what is Redshift in the galaxy? And here we have Redshift star

The spectrum of a distant galaxy shows the H αline of...

The spectrum of a distant galaxy shows the H $\alpha$ line of hydro$\operatorname{gen}\left(\lambda_{\mathrm{rest}}=656.28 \mathrm{nm}\right)$ at a wavelength of $750 \mathrm{nm} .$ Assume that $H_{0}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}$. a. What is the redshift $(z)$ of this galaxy? b. What is its recession velocity $\left(v_{r}\right)$ in kilometers per second? c. What is the distance of the galaxy in megaparsecs?

The spectrum of a distant galaxy shows the H $\alpha$ line of hydro$\operatorname{gen}\left(\lambda_{\mathrm{rest}}=656.28 \mathrm{nm}\right)$ at a wavelength of $750 \mathrm{nm} .$ Assume that $H_{0}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}$.
a. What is the redshift $(z)$ of this galaxy?
b. What is its recession velocity $\left(v_{r}\right)$ in kilometers per second?
c. What is the distance of the galaxy in megaparsecs?

Key Concepts

Cosmological Redshift

Cosmological redshift is the phenomenon where light emitted from a distant astronomical object is stretched to longer, redder wavelengths due to the expansion of the universe. It is quantified by the parameter z, which is calculated using the difference between the observed wavelength and the rest wavelength relative to the rest wavelength. This concept is fundamental in observational cosmology as it provides a measure of how much the universe has expanded since the light left the source.

Recession Velocity

Recession velocity refers to the speed at which a galaxy or other cosmic object is moving away from the observer, primarily due to the expansion of the universe. For objects with relatively small redshift values, the non?relativistic approximation v = cz (where c is the speed of light) can be applied. This concept is key for understanding the dynamics of cosmic expansion and how the motion of galaxies is linked to the redshift of their spectral lines.

Hubble's Law

Hubble's Law is a fundamental principle in cosmology which states that the recession velocity of a galaxy (v) is directly proportional to its distance (d) from the observer, expressed as v = H0 × d, where H0 is the Hubble constant. This law provides a method for estimating the distances to galaxies based on their redshift and plays a crucial role in mapping the expansion of the universe and determining its large-scale structure.

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