Spectroscopy and Doppler Shift

Introduction

Light can act as a wave. A light wave has three main characteristics: (1) speed, which is a constant (299,793 km/sec), (2) wavelength, which is the distance from one peak of the wave to the next, and (3) frequency, which is the number of times a wavelength passes a given point per second (unit = Hertz). All three are related in the following equation: c = wavelength/frequency. As you will notice, there is an inverse relationship between wavelength and frequency.

The Doppler shift is a change in both the wavelength and frequency of light emitted from a body in motion. You may be familiar with Doppler shift when you hear an ambulance siren race past you. As it approaches, the pitch becomes very high and then becomes lower as the siren moves away from you. The Doppler shift of light works the same way. As an object gets closer, the wavelengths get shorter (frequency is greater). This is called a blue shift. If an object is moving away, light is said to be redshifted.

In astronomy, we can use this phenomenon to tell if objects are moving toward us or away. We can also determine how far away an object is and its velocity. This begs the question: How can we be sure how far a wavelength has been red (or blue) shifted if we don’t know what it was originally? This can be answered using the field of spectroscopy.

Spectroscopy studies the emission and/or absorption of radiation from atoms and molecules. An electron in its orbital around an atom is said to be at its lowest energy level (called the ground state). When light photons carrying a specific amount of energy hits the electron, the electron will become excited and jump into a higher orbit. Eventually the electron will come back to the ground state orbital, but it must get rid of the excess energy. The electron releases a photon of light with the same energy it absorbed from the light. This photon corresponds to a specific wavelength and frequency. An electron in an atom has to be hit by a photon carrying a very specific amount of energy to do this. Any more or less than this specific energy, and the electron will not become excited. This gives different atoms unique emission patterns that can be observed. Molecules also have unique patterns that involve their rotation. Photons will cause molecules to rotate, and this causes the molecule to emit energy as described above.

It is this emission pattern of atoms and molecules that allow us to calculate red and blueshifts. If you recognize a pattern from a molecule and know where it should be with regard to its wavelength, you could match that pattern to an observation that shows the same pattern, but at different a different wavelength due to the Doppler shifting. By comparing the two, you could tell where the object is, where it is going, and how fast it is going.

Using SRT to give hydrogen spectral lines???

Activity – Using spectra to calculate Doppler shift

1. Obtain a spectra pattern.

a. What are you looking at?

b. Record the emission wavelengths of each peak

2. Obtain an observed spectral pattern of an extragalactic object

a. Describe what you are looking at

3. Look for patterns from first spectra in the extragalactic spectra

a. Where is the pattern in the extragalactic object in relation to the pattern you received?

4. Calculation of Doppler shift

a. Is object moving toward or away from us?

5. Using the following formulas, to calculate the shift, distance, and speed of the object. Remember to conserve units.

a. To calculate the redshift (z)

z = Dl/l_o

b. To calculate distance

zc = Hr

H = Hubble constant (50km/sec·Mpc) c = speed of light

r = distance of object

c. To calculate velocity,

velocity = Hr

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