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Chapter 19: Problem 4

If you observed a galaxy with an \(\mathrm{H} \alpha\) emission line that had a wavelength of \(756.3 \mathrm{nm}\), what would be the galaxy's redshift? Note that the rest wavelength of the H \(\alpha\) emission line is \(656.3 \mathrm{nm}\). a. 0.01 b. 0.05 c. 0.10 d. 0.15

Short Answer

Expert verified
The redshift is approximately 0.152, closer to 0.15. So, the correct answer is d. 0.15.

Step by step solution

01

Determine Redshift Formula

The formula for redshift (z) is given by: \[ z = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}} \] where \( \lambda_{observed} \) is the observed wavelength and \( \lambda_{rest} \) is the rest wavelength.
02

Identify Given Values

From the problem, the observed wavelength \( \lambda_{observed} = 756.3 \mathrm{nm} \) and the rest wavelength \( \lambda_{rest} = 656.3 \mathrm{nm} \).
03

Substitute Values into Formula

Substitute the given values into the redshift formula: \[ z = \frac{756.3 \mathrm{nm} - 656.3 \mathrm{nm}}{656.3 \mathrm{nm}} \]
04

Calculate the Difference

Calculate the difference in the numerator: \[ 756.3 \mathrm{nm} - 656.3 \mathrm{nm} = 100 \mathrm{nm} \]
05

Calculate the Redshift

Now, substitute this difference back into the formula: \[ z = \frac{100 \mathrm{nm}}{656.3 \mathrm{nm}} \approx 0.152 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

H-alpha emission line
The H-alpha emission line is a specific wavelength of light emitted by hydrogen atoms when an electron falls from the third energy level to the second energy level. This spectral line is significant in astronomy as it helps to identify regions with ionized hydrogen, such as star-forming regions and certain types of galaxies. The rest wavelength of the H-alpha emission line is exactly 656.3 nanometers (nm). Noticing shifts in this wavelength allows us to infer useful astrophysical data.
Wavelength shift
A wavelength shift occurs when the observed wavelength of light from an object differs from its rest wavelength. In the context of observational astronomy, this shift can be due to various phenomena like the Doppler effect or, most commonly, the cosmological redshift. For instance, in the given exercise, the observed H-alpha emission line wavelength is 756.3 nm, while its rest wavelength is 656.3 nm. The difference of 100 nm indicates a redshift, meaning the galaxy is moving away from us.
Cosmological redshift
Cosmological redshift happens because of the expansion of the universe. When light travels through space, which is constantly expanding, the wavelengths of the light stretch, causing a redshift. The further away a galaxy is, the faster it appears to be moving away and the more its light is redshifted. The redshift, denoted as 'z', is calculated using the formula \( z = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}} \). In our specific problem, this formula helps us calculate a redshift value of approximately 0.152.
Observational astronomy
Observational astronomy involves collecting and interpreting data from various celestial objects using telescopes and other instruments. It includes studying light from stars, galaxies, and other astronomical phenomena to deduce their properties and behaviors. One key technique is the analysis of light spectra, including emission and absorption lines like the H-alpha line. Observing wavelength shifts in these lines helps astronomers understand the movement and distances of celestial bodies, contributing to our knowledge of the universe's structure and expansion.

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Most popular questions from this chapter

a. Go to the website for the NASA Swift Gamma-Ray observatory (swift.gsfc.nasa.gov), which studies gamma-ray bursts. Click on "Latest Swift News" and look for a story about supermassive black holes. What has been discovered? b. Go to the website for NuSTAR (Nuclear Spectroscopic Telescope Array- http://www.nustar.caltech.edu), a space telescope launched by NASA in 2012 . This mission is studying active galaxies hosting supermassive black holes. What type of telescope is this (wavelengths observed, general design)? What has been discovered?

As astronomers extend their distance ladder beyond \(30 \mathrm{Mpc}\) they change their measuring standard from Cepheid variable stars to Type Ia supernovae. Why is this change necessary? a. Type Ia supernovae are more luminous than Cepheid variables. b. Type Ia supernovae are less luminous than Cepheid variables. c. Type Ia supernovae vary more slowly than do Cepheid variables. d. Type Ia supernovae vary more quickly than do Cepheid variables.

Suppose the number density of galaxies in the universe is, on average, \(3 \times 10^{-68}\) galaxy \(/ \mathrm{m}^{3} .\) If astronomers could observe all galaxies out to a distance of \(10^{10} \mathrm{pc}\), how many galaxies would they find?

What distinguishes a normal galaxy from one that contains an AGN? It is a principle of science, often attributed to Einstein, that one should make things as simple as possible, but not simpler. Explain how this principle is at work in the distinction between normal galaxies and AGNs.

Suppose that an object with the mass of Earth \(\left(M_{\text {Earth }}=5.97 \times 10^{24} \mathrm{kg}\right)\) fell into a supermassive black hole with a 10 percent energy conversion. a. How much energy (in joules) would be radiated by the black hole? b. Compare your answer with the energy radiated by the Sun each second: \(3.85 \times 10^{26} \mathrm{J}\)
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