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Chapter 5: Problem 32

A spectral line that appears at a wavelength of \(321 \mathrm{nm}\) in the laboratory appears at a wavelength of \(328 \mathrm{nm}\) in the spectrum of a distant object. We say that the object's spectrum is (a) redshifted. (b) blueshifted. (c) whiteshifted.

Short Answer

Expert verified
The object's spectrum is redshifted.

Step by step solution

01

Understanding Redshift and Blueshift

Redshift and blueshift relate to the change in wavelength of light due to motion of an object. If an object is moving away, its light stretches to longer wavelengths, a phenomenon known as redshift. Conversely, blueshift occurs when light shifts to shorter wavelengths because the object is moving closer.
02

Identify Initial and Observed Wavelengths

In the laboratory, the wavelength is given as \(321 \mathrm{nm}\), and for the distant object, it is \(328 \mathrm{nm}\). Compare these values to determine the shift type.
03

Determine the Type of Shift

The observed wavelength (\(328 \mathrm{nm}\)) is longer than the laboratory wavelength (\(321 \mathrm{nm}\)). Since longer wavelengths indicate that the object is moving away, this is a redshift.

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Key Concepts

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

Spectral Lines
Spectral lines are unique patterns of light emitted or absorbed by substances, acting like fingerprints for different elements and molecules. Each element has its own set of spectral lines that make it distinguishable. You can find them in the visible, ultraviolet, or infrared light spectrum.
  • Emission lines occur when atoms or molecules release energy, resulting in light being emitted at specific wavelengths.
  • Absorption lines appear when light passes through a gas or a liquid, and certain wavelengths are absorbed by the substance, leaving dark lines in the spectrum.
These lines are crucial for identifying the chemical composition of stars, galaxies, and other celestial bodies. By analyzing spectral lines, scientists can determine not only what a distant object is made of but also how it behaves in terms of its motion and characteristics.
Doppler Effect
The Doppler Effect is the change in frequency or wavelength of light or sound due to the motion of the source relative to an observer. It is a common phenomenon that can be experienced in everyday life. For instance, you might notice how a siren sounds higher in pitch as it approaches you and lower as it moves away.
  • In terms of light, when an object is moving toward you, the light waves it emits or reflects are compressed, leading to shorter wavelengths (blueshift).
  • Conversely, if the object is moving away, the light stretches to longer wavelengths (redshift).
This concept is pivotal in astronomy for determining the motion and velocity of celestial bodies. The Doppler Effect aids in calculating the speed at which galaxies and stars are moving either toward or away from the Earth.
Wavelength Shift
Wavelength shift refers to the alteration in the observed wavelength of light from a source compared to its known value in a laboratory setting. This shift is a fundamental way scientists measure the velocity and direction of an object's motion through space.
  • The shift can be quantified using the relationship: \( \Delta \lambda = \lambda_{observed} - \lambda_{rest} \)
  • In the redshift scenario, the observed wavelength is longer than the rest wavelength, indicating the source is receding.
  • In blueshift, the opposite occurs, with a shorter observed wavelength showing the source is approaching.
In our exercise example, a spectral line observed at \(328 \mathrm{nm}\) compared to its \(321 \mathrm{nm}\) laboratory measurement signifies a shift towards the red part of the spectrum. This implies that the object is moving away from the observer.

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Most popular questions from this chapter

The Changing Limitations of Science. In \(1835,\) French philosopher Auguste Comte stated that science would never allow us to learn the composition of stars. Although spectral lines had been seen in the Sun's spectrum at that time, it wasn't until the mid- 19 th century that scientists recognized (primarily through the work of Foucault and Kirchhoff) that spectral lines give clear information about chemical composition. Why might our present knowledge have seemed unattainable in \(1835 ?\) Discuss how new discoveries can change the apparent limitations of science. Today, other questions seem beyond the reach of science, such as the question of how life began on Earth. Do you think such questions will ever be answerable through science? Defend your opinion.

Telescope Technology. Suppose you were building a space-based observatory consisting of five individual telescopes. Which would be the best way to use these telescopes: as five individual telescopes with adaptive optics, or as five telescopes linked together for interferometry but without adaptive optics? Explain your reasoning clearly.

If a distant galaxy has a substantial redshift (as viewed from our galaxy), then anyone living in that galaxy would see a substantial redshift in a spectrum of the Milky Way Galaxy.

If you could see infrared light, you would see a glow from the backs of your eyelids when you closed your eyes.

Define wavelength, frequency, and speed for light waves. If light has a long wavelength, what can you say about its frequency? Explain.
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