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# Principles of Spectroscopy

Star light, star bright.

## Overview

• Learn about continuous spectrum, line emission, and line absorption by viewing examples of each.
• See how this applies to light from the Sun (or any star).

## Introduction

A photon is a small bit of electromagnetic energy sent across space. Photons can be emitted or absorbed by electric charges -- usually an electron.

A hot, dense object contains many "loose" electrons which can emit photons of any energy. However an electron cannot emit a photon with more energy than the electron started with. The light produced by a hot, dense object is called thermal emission and it contains photons of all energies, i.e. light of all colors, or wavelengths. The resulting "rainbow" is called a continuous spectrum. As we heat up an object, we are giving the electrons more kinetic energy, so they become able to emit more energy. The hotter the object becomes,the brighter the continuous spectrum becomes. This is describedby the Stephan-Boltzmann Law:

f = σT4

As the emitting object is heated, the flux, f, of light energy emitted per unit area (the brightness) increases as the temperature, T (measured in Kelvin, K), to the fourth power; σ is called the Stefan-Boltzmann constant, and has the value 5.67x10-8J m-2 K-4. If two hot pokers are the same size, but one is twice as hot as the other, the hotter one will be sixteen times brighter. The same is true of two stars.

As the object heats up and the electrons get more energy, the energy of the typical photon emitted also increases. This means that the continuous spectrum gradually shifts toward shorter wavelengths (higher energies) and therefore looks bluer. This is described by Wien's Law, which says the peak wavelength times the temperature is constant:

λpeak * T = 0.29 cmK

which means that as the temperature, T, of the emitting object increases, the wavelength λpeak where the intensity of the light is the greatest must decrease. A very hot poker will glow with a bluer (shorter wavelength) light while a cooler poker will glow with a redder light.

Any hot, dense, opaque object can and must produce continuous spectrum across all wavelengths, with the total energy and dominant color described by these two laws. This is sometimes called blackbody radiation or thermal radiation. The object has no choice -- if it's hot, the electrons have energy, so they must emit light. Remember, Wien's law and the Stefan-Boltzmann Law apply only to continuous thermal emission.

So far we've talked about processes involving "loose" electrons that lead to thermal radiation. What about electrons that are part of an atom? In the Bohr model of the atom, electrons orbit a nucleus of protons and neutrons. Each orbit has a different potential energy, just like planetary orbits correspond to particular gravitational potential energies. But according to quantum mechanics, the electrons can only orbit in certain places, which means the electrons can only have certain orbital energies -- these allowed energies are called energy levels.

Electrons usually stay in low energy levels, but they can "jump up" to higher energy levels by absorbing a photon or by gaining energy in other ways. If it gains energy by absorbing a photon, it has to have exactly the correct amount of energy -- it has to match the energy difference between the energy levels. Therefore, the atom can only absorb light at a few specific energies, or colors. This is called line absorption. Line absorption occurs when a low-density gas is in front of a hotter, continuous spectrum source. The cooler, low-density gas acts to block the photons which have the right wavelengths, while the other photons travel through the gas unperturbed. This leads to a generally bright spectrum, with dark lines at specific wavelengths. The missing colors are called spectral absorption lines and result in an absorption line spectrum.

The energy-level jumping can also happen in reverse. The electron can "fall down" from a higher energy level to a lower one, emitting a photon with energy equal to the difference between the levels. This is called line emission, because photons are emitted. The spectrum produced is a set of bright emission lines, so it is called an emission line spectrum. This can only occur in a low density gas viewed on its own or in front of a cooler background (if a hot, dense object is in the background, we see line absorption instead of line emission).

Notice that these two processes only involve photons with particular energies that match its energy levels. Since each atom or molecule has a different set of energy levels, each atom or molecule also has a unique set of spectral lines.

Let's summarize what are known as "Kirchoff's Laws." First, a hot, dense gas (or a solid or liquid) has free electrons and will emit a continuous spectrum, with the brightness and typical color described by the Stefan-Boltzmann and Wien Laws. Second, a low-density gas along the line of sight to a hotter continuous radiation source will absorb photons of specific energies, leaving an absorption line spectrum. Third, a low-density gas viewed alone or in front of a cool background will produce an emission line spectrum.

As photons travel outwards from the center of the sun, where the density and temperature are high enough to allow fusion, they are constantly absorbed and re-emitted by the atoms in the sun.  Eventually they get to the outer edge of the sun, called the photosphere, which is where the sun changes from being opaque to being transparent. The photospere, then, is the layer where all the photons we see originate. The transparent region above the photosphere is called the atmosphere of the sun and has two major layers. The cooler thin layer abover the photospher is the chromospher. Above that is the increadably hot and thin Corona.

One photon by itself can't tell us much about the photosphere or atmosphere, but by looking at all the photons together, astronomers can gain information about the temperature, density, and chemical composition of the sun. This is done by looking at the spectrum of the light -- the number of photons (i.e. the brightness) at each wavelength.  Similarly, the characteristics of the spectra we will look at in the lab will tell us information about the sources of light we will use.

## Continuous Spectrum

In the photosphere (and regions deeper in the sun), the density is so high that the gas is opaque. This area produces light with a continuous spectrum.  It is radiating simply because it is hot.

For this part of the lab, you will need to get a dispersion grating from your instructor. A dispersion grating does the same thing as a prism: it splits up the light into individual wavelengths so that you can see the spectrum.

Turn on the power supply and the lamp.  Adjust the dial until the light is comfortable to observe.  DO NOT TURN IT OVER 120 V! Hold the grating so the arrow points left and right and look through it toward the light bulb. If you don’t have an arrow on your grating, check with your GSI.  You can see the "first order" spectrum to either side of the filament. If you look further away from the filament, you should see another spectrum similar to the first. This is called a "second order" spectrum. Still further away from the filament will be the third, fourth, fifth and so on. Anything above the first order is considered a higher order spectrum. Note that there is a mirror image of the spectra on the other side of the filament, so there are 2 first order spectra, one to the right and one to the left of the filament. Watch out for spectra from other sources, such as other lights or even reflections inside the light bulb. Once you've figured out which spectra you want to observe, answer the following questions.

1. What kind of light-source are you looking at: thin gas, opaque gas, solid, or liquid (circle one)?  According to Kirchoff’s laws, what type of spectrum should this produce?

2. Observe the first order spectrum with the diffraction grating.  What kind of spectrum is it: continuous, line emission or absorption (circle one)?  How did you identify it as this type of spectrum?

3. How many higher order spectra can you see? List at least two differences between the first order and higher order spectra.

The temperature of the filament can be changed by changing the voltage going to the light bulb. Start with the light on the lowest voltage necessary to see the spectrum, then slowly turn it all the way up to 120 V. Watch the spectrum as you turn it up, especially the relative strengths of the colors. The brightest color is the peak color and is generally the color of the filament. HOWEVER, our eyes and brains adjust quickly to the light, dimming the brightest colors and reacting poorly if the light is bright (so the filament will never look blue-green).  Because of this, you must take your first impression from the spectrum. The best thing to get the peak color is to close your eyes for a few seconds then take your first impression from the spectrum.

Change the voltage a couple times and observe the light, then answer the questions below.

1. Was the bulb hotter at a low voltage or a high voltage (circle one)?

2. At what voltage was the bulb brightest: high or low (circle one)?

3. List the colors you could see at:
1. high voltage

2. low voltage

4. Circle the color in your lists above that appeared to be the peak at high and at low voltage.
5. As you increase the voltage, how do the colors change (overall and the peak color)?

6. Use your observations of the light bulb to explain which would be hotter, a red star or a blue star? You must have at least 2 pieces of evidence.

7. Explain using both Wien's and the Stephan-Boltzmann Laws: if two stars are the same size, which is brighter, a red star or a blue star?

## Line Emission

Now we will look at "discharge tubes," which are each filled with a low-density gas made of a single kind of atom. Running an electric current through the discharge tube gives the electrons energy and kicks them up to a high energy level. The electrons quickly fall back to their original energy level, giving off a photon with a wavelength determined by the difference in energy between the levels. Most of these photons leave the gas without interacting with other atoms allowing us to view them. This is similar to the process that occurs in the low-density, incredibly hot outer most regions of stars called the corona and in low-density, gas clouds in space called emission nebulae.

Fist look at the tube with the power off and note where there are opaque solids.  Then turn on the power and observe where the light is actually emitted.

1. What kind of light-source are you looking at: thin gas, opaque gas, solid, or liquid (circle one)?  According to Kirchoff’s laws, what type of spectrum should this produce?

There should be a spectroscope set up to observe the spectrum.  A slit is aligned with the light source that allows light to travel down to the diffraction grating at the eyepiece.  The spectrum is projected onto a scale to the left of the light source. Observe the spectrum through the spectroscope.

1. What kind of spectrum is it: continuous, line emission or absorption (circle one)?  How did you identify it as this type of spectrum?

2. Observe the spectrum of at least four of the discharge tubes, including hydrogen and the sodium lamp. Roughly sketch what you see, labeling the element's name and the colors of the brightest lines. Compare these to the chart of emission lines in the classroom.  PLEASE TURN OFF THE DISCHARGE TUBES WHEN NOT IN USE (but leave the sodium lamp on)

element: Hydrogen H

element: Sodium Na

element:

element:

1. Observe the unknown element.  Sketch its spectrum, then use the chart to identify it.
element:

2. How could astronomers use emission lines from an object?

3. The hydrogen atom has only one electron, but when you look through the spectroscope, you see several emission lines.  Explain how this is possible (how are several lines generated and why can you see all of them if there is only one electron per atom)

Note that you can adjust the width of the slit with a screw on the front of the spectroscope.  Observe the neon, argon or unknown discharge tubes through the grey spectroscope.  Open the slit wide (but don’t take the screw out!), and then begin to close it slowly while looking at the spectrum.

1. How does the resolution of crowded emission lines change as you close the slit?

2. How does the overall intensity of the spectrum change as you close the slit?

3. Suppose you are observing a bright star and a faint star with your spectroscope. How would you set the slit to obtain high-resolution spectra of these stars? What would happen to the intensity? Knowing this, would it be easier to obtain a high-resolution spectrum of a bright star or a faint star? Explain.

4. Find an image of an emission nebula and compare it to the discharge tubes. What is the primary gas in an emission nebula? How can you tell just from the picture?

## Line Absorption

The chromosphere of the Sun and other stars is cooler than the photosphere (which produces a continuous spectrum), and has a lower density, so this is where line absorption occurs.  We cannot observe the star without looking through the chromosphere, so we can always observe absorption lines if our spectroscope has enough resolution.

Normally in astronomy, absorption is caused by a thin transparent gas according to Kirchoff’s law: thin absorption lines are produced in the same pattern as the emission lines when you view a cool gas against a continuous background source.  However, it is difficult to replicate a cold thin gas with sufficient density for visible absorption lines in the lab.  Translucent objects like the solid filters for this part also absorb light, so we will use them to observe an absorption spectrum.  Since these are solids, they produce very broad absorption bands, not quite the same as the absorption lines from Kirchoff’s law.

There are several filters for you to use including the Skyglow filter, the Skyglow Ultrablock filter, an H-alpha filter and several colored filters. To use the filters, hold a filter in one hand and the diffraction grating in the other.  Look through the diffraction grating at the spectrum, then place the filter between the grating and your eye.

1. What kind of material is the light source: transparent gas, opaque gas, solid or liquid (circle one)?  What kind of spectrum will it produce.

2. You are looking at it through air, which is a thin transparent gas.  What kind of spectrum should you see?  Why don’t you see it?

3. Look at the light source through one of the colored filters. What kind of spectrum do you see?  Explain how you determined it must be this type.

4. Observe the spectrum with at least 5 different colored filters.  Fill out table 1 below with the color of the filter (the plastic ones are primaries, the ones in the slide holders have their names printed on them) and what color(s) it blocked.
5. Observe the spectrum through the skyglow, ultrablock, and H-alpha filters.  Complete table 1 for these filters.

 Filter Color Color(s) Blocked skyglow ultrablock H-alpha
1. Looking at the emission line chart, which element(s) have very strong lines that would be blocked by the skyglow filter?

2. Look through the skyglow filter at the discharge tubes and sodium lamp.  Which light(s) have the greatest decrease in brightness when viewed through the filter (note that the lights have different intensities: you are looking for the biggest overall change, not the dimmest light).  Does this confirm your answer to the previous question? Explain.

3. What might this filter be useful for? (Hint: where do you see lights the same color as the one this filter blocks?)

4. Look through the H-alpha filter at the discharge tubes and sodium lamp.  Which light is NOT significantly blocked by the filter?

5. Observe the tube you listed through the spectroscope, then place the filter between you and the spectroscope.  Why would this filter be useful to astronomers? (hint, where does the filter get its name?)

## Two types at once?

Just for curiosity, let's look at a peculiar man-made object, the fluorescent light bulb. Observe it with the diffraction grating. To make this part of the lab work, it is best to look at a single fluorescent light and turn off all the other lights in the room.

1. Look at the tube with the light off.  What kind of material does it appear to be: transparent gas, opaque gas, solid, or liquid?  What kind of spectrum would you expect from this?

2. What do you see through the spectroscope (or grating)? Draw a sketch if you think that will be useful. What type(s) of spectra does this appear to be?

3. Inside the fluorescent light bulb, a discharge tube produces line emission light. However the light we see is more like white light (continuous).  How might you explain this?

4. What kind of spectrum would you expect to see from the Moon? Explain. You can use one of the blue hand-held spectroscopes to check this if the Moon is out and the Sun has set.

## Light Questions

1. Describe two ways astronomers could determine the composition of a planet’s atmosphere without leaving Earth (hint, emission and absorption lines are not restricted to the visible spectrum.)

2. Notice that the discharge tubes have different colors to our eyes. Can we use Wien's Law to tell the relative temperatures of the gas within the tubes? Explain.

3. Calculate λpeak for the following stars, and estimate which color dominates the visible light.

 Star Temperature λpeak Color Sirius 10,000 K Sun 5,800 K Betelgeuse 3,000 K

4. The interior of the Sun is opaque, so none of the light emitted inside makes it directly to us. The region where the Sun changes from opaque to transparent is the photosphere. This is the visible surface of the Sun. Above that is the solar atmosphere, which has two layers, the chromosphere and the corona. The density and temperature of each of theses regions is given below. Use that information and Kirchoff's laws to label the diagram below with the type of spectrum that corresponds to each region, and explain how you know which type of spectrum applies to that region.
Bottom of Photosphere: temp: 5800 K; density: 2x10-4 kg/m3
Bottom of Chromosphere: temp: 4500 K; density: 5x10 -6 kg/m3
Corona (average): temp: 106 K; density: 10-12 kg/m3

## Random Walk (optional according to your GSI)

A photon's path out of the sun, through the inner continuous spectrum region particularly, is not as straight forward as you might think. Photons travel at the speed of light -- they are light after all -- and would take only a few seconds to travel straight out of the Sun, but their actual journey can take up to a million years. The problem is that the interior of the sun is a thick, hot soup of hydrogen and free electrons (along with a few other elements in small amounts). Photons inside the sun can't travel very far through the 'soup' before they run into an atom or electron and are absorbed. Once an atom absorbs a photon it quickly gives off a new photon (with the same energy), but it does so in a random direction. After all, the atom doesn't "remember" which way the photon was trying to go. The photon is like a drunk who keeps banging into streetlights, then stepping out in a totally new, random direction. This is called a random walk. The laws of probability require that after many bounces, the photon will eventually leave the center of the sun.

A simple probablity game can duplicate the random walk. Your instructor will give you a sheet of paper with circles drawn on it and a die. You will need a marker of some sort (a small coin works well). Place the marker somewhere in the first column of circles near the middle. In the upper corner of the page is a circle marked with directions numbered 1 - 6. Roll the die and move your marker in the direction indicated by the die. Count this as your first interaction. If you get a number that would force you to move out of the circles, count it as an interaction, but do not move your marker. Repeat the process until your marker exits the right side. Record the total number of die rolls you had to make to get out, and the number of columns of circles in the table below.

Do a second run just like you did the first one.

Do a third run using a different number of columns. You must use at least three columns, or you may add another sheet of paper to get more columns.

 Run No. of Interactions No. of columns 1. 2. 3.

Compare your results with other groups, especially run 3.

1. What happens if you change the number of layers?

2. In the Sun, the average path length is about 1 cm and roughly 10 interactions can occur per second. Based on the number of interactions it took to travel the few steps in our model, what can you say about the time it takes for light to escape the Sun? What is the most apropriate unit to use to measure this time (e.g. seconds, days, years, Myrs, etc)?

updated: 8/30/07 by SAM

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