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%\chapter{The Power of Light: Understanding Spectroscopy}
%
\section{Introduction}


For most celestial objects, light is the astronomer's only subject for
study. Light from celestial objects is packed with amazingly large
amounts of information. Studying the distribution of brightness for each
wavelength (color) which makes up the light provides the temperature of a
source. A simple example of this comes from flame color comparison. Think
of the color of a flame from a candle (yellow) and a flame from a
chemistry class Bunson burner (blue). Which is hotter? The flame from
the Bunson burner is hotter. By observing which color is dominant in
the flame, we can determine which flame is hotter or cooler.  The same
is true for stars; by observing the color of stars, we can determine
which stars are hot and which stars are cool. If we know the temperature
of a star, and how far away it is (see the ``Measuring Distances Using 
Parallax'' lab), we can determine how big a star is.

We can also use a device, called a spectroscope, to break-up the light
from an object into smaller segments and explore the chemical composition
of the source of light. For example, if you light a match, you know that
the predominant color of the light from the match is yellow. This is partly
due to the temperature of the match flame, but it is also due to very strong
{\it emission lines} from sodium. When the sodium atoms are excited (heated
in the flame) they emit yellow light. 

In this lab, you will learn how astronomers can use the light from celestial 
objects to discover their nature. You will see just how much information
can be packed into light! The close-up study of light is called 
{\it spectroscopy}.

This lab is split into three main parts: 
\begin{itemize}
\item Experimentation with actual blackbody light sources to learn about the 
qualitative behavior of blackbody radiation. 
\item Computer simulations of the quantitative behavior of blackbody 
radiation.
\item Experimentation with emission line sources to show you how the spectra
of each element is unique, just like the fingerprints of human beings.
\end{itemize}

Thus there are three main components to this lab, and they can be performed in 
any order. So one third of the groups can work on the computers, while the 
other groups work with the spectrographs and various light sources.

\begin{itemize}
\item{{\it Goals:} to discuss the properties of blackbody radiation, filters, 
and see the relationship between temperature and color by observing light 
bulbs and the spectra of elements by looking at emission line sources through a spectrograph. Using a computer to simulate blackbody.
radiation}
\item{{\it Materials:} spectrograph, adjustable light source, gas tubes and
power source, computers, calculators}
\end{itemize}

\section{Blackbody Radiation}

{\it Blackbody radiation (light) is produced by any hot, dense object.}
By ``hot'' we mean any object with a temperature above absolute zero.
All things in the Universe emit radiation, since all things in the
Universe have temperatures above absolute zero.   Astronomers {\it
idealize} a perfect absorber and perfect emitter of radiation and call it
a ``blackbody''.  This does not mean it is black in color, simply that it
absorbs and emits light at all wavelengths, so no light is reflected.
A blackbody is an object which is a perfect absorber (absorbs at all
wavelengths) and a perfect emitter (emits at all wavelengths) and does
not reflect any light from its surface. Astronomical objects are not
perfect blackbodies, but some, in particular, stars, are fairly well
approximated by blackbodies.

The light emitted by a blackbody object is called blackbody radiation.
This radiation is characterized simply by the $temperature$ of the
blackbody object.  Thus, if we can study the blackbody radiation from
an object, we can determine the temperature of the object.

To study light, astronomers often split the light up into a spectrum.
A spectrum shows the distribution of brightness at many different
wavelengths.  Thus, a spectrum can be shown using a graph of brightness
vs. wavelength.  A simple example of this is if you were to look at a
rainbow and record how bright each of the separate colors were.  Figure
\ref{fig:rainbow} shows what the brightness of the colors in a hot flame
or hot star might look like.  At each separate color, a brightness is 
measured. By fitting a curve to the data points, and finding the peak in 
the curve,  we can determine the temperature of the blackbody source.

\begin{figure}[h] 
\centering 
\leavevmode 
\epsfxsize=0.9\textwidth
\epsfbox{Spectroscopy/newastrophot.ps} 
\caption{Astronomers measure the amount of light at a number of different
wavelengths (or colors) to determine the temperature of a blackbody source.
Every blackbody has the same shape, but the peak moves to the violet/blue
for hot sources, and to the red for cool sources. Thus we can determine the
temperature of a blackbody source by figuring out where the most
light is emitted.} 
\label{fig:rainbow}
\end{figure}

\section{Absorption and Emission Lines}

One question which you may have considered is: how do astronomers know
what elements and molecules make up astronomical objects?  How do they
know that the Universe is made up mostly of hydrogen with a little bit of 
helium and a tiny bit of all the other elements we have discovered on
Earth?  How do astronomers know the chemical make up of the planets in
our Solar System? They do this by examining the absorption or emission
lines in the spectra of astronomical sources. [Note that the plural of
{\it spectrum} is {\it spectra}.]

\subsection{The Bohr Model of the Atom}

In the early part of this century, a group of physicists developed the
{\it Quantum Theory of the Atom}.  Among these scientists was a Danish
physicist named Niels Bohr.  His model of the atom, shown in the
figure below, is the easiest to understand.  In the Bohr model, we
have a nucleus at the center of the atom, which is really much much
smaller relative to the electron orbits than is illustrated in our
figure.  Almost all of the atom's mass is located in the nucleus.  For
Hydrogen, the simplest element known, the nucleus consists of just one
proton.  A proton has an atomic mass unit of 1 and a positive electric
charge.  In Helium, the nucleus has two protons and two other
particles called neutrons which do not have any charge but do have
mass.  An electron cloud surrounds the nucleus.  For Hydrogen there is
only one electron.  For Helium there are two electrons and in a larger
atom like Oxygen, there are 8.  The electron has about
$\frac{1}{2000}$ the mass of the proton but an equal and opposite
electric charge.  So protons have positive charge and electrons have
negative charge.  Because of this, the electron is attracted to the
nucleus and will thus stay as close to the nucleus as possible.

In the Bohr model, the electron is allowed to exist only at $certain$
distances from the nucleus.  This also means the electron is allowed
to have {\it only certain orbital energies}.  Often the terms {\it orbits},
{\it levels}, and {\it energies} are used interchangeably so try not
to get confused.  They all mean the same thing and all refer to the
electrons in the Bohr model of the atom.

\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.8\textwidth
\epsfbox{SPECTRAL/spectralfig1.eps}
\end{figure}
Now that our model is set up let's look at some situations of
interest. When scientists studied simple atoms in their normal, or
average state, they found that the electron was found in the lowest
level. They named this level the ground level.  When an atom is
exposed to conditions other than average, say for example, putting it
in a very strong electric field, or by increasing its temperature, the electron will
jump from inner levels toward outer levels.  Once the abnormal
conditions are taken away, the electron jumps downward towards the
ground level and emits some light as it does so.  The interesting
thing about this light is that it comes out at only $particular$
wavelengths. It does not come out in a continuous spectrum, but at
solitary wavelengths.  What has happened here?

After much study, the physicists found out that the atom had taken-in
energy from the collision or from the surrounding environment and that as
it jumps downward in levels, it re-emits the energy as light.  The
light is a particular color because the electron really is allowed
only to be in certain discrete levels or orbits.  It cannot be halfway
in between two energy levels.  This is not the same situation for
large scale objects like ourselves.  Picture a person in an elevator
moving up and down between floors in a building.  The person can use
the emergency stop button to stop in between any floor if they want
to.  An electron cannot.  It can only exist in certain energy levels
around a nucleus.

Now, since each element has a different number of protons and neutrons in
its nucleus and a
different number of electrons, you may think that studying ``electron
gymnastics'' would get very complicated.  Actually, nature has been
kind to us because at any one time, only a single electron in a given atom
jumps around.  This means that each element, when it is
excited, gives off certain colors or wavelengths.  This allows
scientists to develop a color $fingerprint$ for each element.  This even
works for molecules.  These fingerprints are sometimes referred to as
spectral lines.  The light coming from these atoms does not take the
shape of lines.  Rather, each atom produces its own set of distinct
colors.  Scientists then use lenses and slits to produce an image in
the shape of a line so that they can measure the exact wavelength
accurately.  This is why spectral lines get their name, because they
are generally studied in a linear shape, but they are actually just
different wavelengths of light.

\subsection{Kirchoff's Laws}

Continuous spectra are the same as blackbody spectra, and
now you know about spectral lines. But there are two types of spectral
lines: $absorption$ lines and $emission$ lines. Emission lines occur when
the electron is moving down to a lower level, and emits some light in
the process. An electron can also move up to a higher level by
absorbing the right wavelength of light. If the atom is exposed to a
continuous spectrum, it will absorb only the right wavelength of light
to move the electron up. Think about how that would affect the
continuous spectrum. One wavelength of light would be absorbed, but
nothing would happen to the other colors. If you looked at the source
of the continuous spectrum (light bulb, core of a star) through a 
spectrograph, it would have the familiar Blackbody spectrum, with a dark 
line where the light had been absorbed. This is an absorption line.

The absorption process is basically the reverse of the emission
process. The electron must acquire energy (by absorbing some light) to
move to a higher level, and it must get rid of energy (by emitting
some light) to move to a lower level. If you're having a hard time
keeping all this straight, don't worry. Gustav Kirchoff made it simple
in 1860, when he came up with three laws describing the processes
behind the three types of spectra.  The laws are usually stated as
follows:

\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.8\textwidth
\epsfbox{SPECTRAL/spectralfig2.eps}
\end{figure}

\begin{itemize}
\item{{\bf I.} A dense object will produce a continuous spectrum when heated.}
\\
\item{{\bf II.} A low-density, gas that is excited (meaning that the atoms 
have electrons in higher levels than normal) will produce an
emission-line spectrum.}
\\
\item{{\bf III.} If a source emitting a continuous spectrum is observed 
through a cooler, low-density gas, an absorption-line spectrum will
result.}
\end{itemize}

A blackbody
produces a continuous spectrum.  This is in agreement with Kirchoff's
first law.  When the light from this blackbody passes through a cloud
of cooler gas, certain wavelengths are absorbed by the atoms in that
gas.  This produces an absorption spectrum according to Kichoff's
third law.  However, if you observe the cloud of gas from a different
angle, so you cannot see the blackbody, you will see the light emitted
from the atoms when the excited electrons move to lower levels.  This
is the emission spectrum described by Kirchoff's second law.

Kirchoff's laws describe the conditions that produce each type of
spectrum, and they are a helpful way to remember them, but a real
understanding of what is happening comes from the Bohr model.

\medskip
     
In the second half of this lab you will be observing the spectral lines 
produced by several different elements when their gaseous forms are 
heated.  The goal of this section of the lab is to observe these emission 
lines and to understand their formation process. 

\section{Creating a Spectrum}

Light which has been split up to create a spectrum is called dispersed
light.  By dispersing light, one can see how pure white light is really
made up of all possible colors.  If we disperse light from astronomical
sources, we can learn a lot about that object.  To split up the light
so you can see the spectrum, one has to have some kind of tool which
disperses the light.  In the case of the rainbow mentioned above, the
dispersing element is actually the raindrops which are in the sky. Another
common dispersing element is a prism.

We will be using an optical element called a {\it diffraction grating} to
split a source of white light into its component colors.  A diffraction
grating is a bunch of really, really, small rectangular openings called
slits packed close together on a single sheet of material (usually
plastic or glass).  They are usually made by first etching a piece of
glass with a diamond and a computer driven etching machine and then
taking either casts of the original or a picture of the original.

The diffraction grating we will be using is located at the optical
entrance of an instrument called a $spectroscope$.  The image screen
inside the spectroscope is where the dispersed light ends up.  Instead of
having all the colors land on the same spot, they are dispersed across
the screen when the light is split up into its component wavelengths.
The resultant dispersed light image is called a spectrum.

\section{Observing Blackbody Sources with the Spectrograph}

In part one of this lab, we will study a common blackbody in
everyday use:  a simple white light bulb.  Your Lab TA
will show you a regular light bulb at two different brightnesses (which
correspond to two different temperatures).  The light bulb emits at all
wavelengths, even ones that we can't see with our human eyes. You will
also use a spectroscope to observe emission line sources

\begin{enumerate}
\item{First, get a spectroscope from your lab instructor.  Study 
Figure \ref{fig:spectrograph}
figure out which way the entrance slit
should line up with the light source.  {\bf DO NOT TOUCH THE ENTRANCE
SLIT OR DIFFRACTION GRATING!}   Touching the plastic ends degrades the
effectiveness and quality of the spectroscope.}
  
\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.9\textwidth
\epsfbox{BLACKBODY/bb_fig2.eps}
\caption{}
\label{fig:spectrograph}
\end{figure}

\item Observe the light source at the brighter (hotter) setting. 

\item Do you see light at all different wavelengths/colors or only a
few discrete wavelengths? (\textit{2 points})
\smallspace

\item Of all of the colors which you see in the spectrographs, which color
appears the brightest?(\textit{3 points})
\smallspace

\item Observe the light source at the fainter (cooler) setting. 

\item Do you see light at all different wavelengths/colors or only a
few discrete wavelengths? 
Of all of the colors which you see in the spectrographs, which color
appears the brightest?
(\textit{3 points})
\smallspace

\item Describe the changes between the two light bulb observations. What
happened to the spectrum as the brightness and temperature of the
light bulb increased?  Specifically, what happened to the relative amount
of light at different wavelengths?(\textit{5 points})

\smallspace

\item Betelguese is a Red Giant Star found in the constellation
Orion. Sirius, the brightest star in the sky, is much hotter and
brighter than Betelguese. Describe how you might expect the colors of these 
two stars to differ. (\textit{4 points})

\smallspace
\end{enumerate}

\section{Quantitative Behavior of Blackbody Radiation}

This section, which your TA may make optional (or done as one big group), should be done outside of class on a computer with
network access, we will investigate how changing the temperature of
a source changes the characteristics of the radiation which is emitted
by the source. We will see how the measurement of the \textit{color}
of an object can be used to determine the object's temperature. We
will also see how changing the temperature of a source also affects
the source's \textit{brightness}.

To do this, we will use an online computer program which simulates the
spectrum for objects at a given temperature. This
program is located here:\\
\begin{verbatim}
http://www.mhhe.com/physsci/astronomy/applets/Blackbody/ 
applet_files/BlackBody.html
\end{verbatim}

The program just produces a graph
of wavelength on the x-axis vs. brightness on the y-axis; you are
looking at the relative brightness of this source at different wavelengths.

The program is simple to use. There is a sliding bar on the bottom of the
``applet'' that allows you to set the temperature of the star.  Play around
with it a bit to get the idea. Be aware that the y-axis scale of the plot will
change to make sure that none of the spectrum goes off the top of the
plot; thus if you are looking at objects of different temperature,
the y-scale can be different.

Note that the temperature of the objects are measured in units called
degrees Kelvin (K). These are very similar to degrees Centigrade/Celsius (C);
the only difference is that: $K = C + 273$. So if the outdoor temperature
is about 20 C (68 Fahrenheit), then it is 293 K. Temperatures of stars
are measured in \textit{thousands} of degrees Kelvin; they are much hotter than
it is on Earth!

\begin{enumerate}
\item Set the object to a temperature of around 6000 degrees, which is
the temperature of the Sun. Note the wavelength, and the color of the spectrum
at the peak of the blackbody curve.

\item Now set the temperature to 3000 K, much cooler than the Sun.
How do the spectra differ? Consider both the \textit{relative}
amount of light at different wavelengths as well as the overall
\textit{brightness}. Now set the temperature to 12,000 K, hotter than Sun.
How do the spectra differ?  (\textit{5 points})

\smallspace

\item You can see that each blackbody spectrum has a wavelength where the
emission is the brightest (the ``top'' of the curve). Note that this wavelength
changes as the temperature is changed. Fill in the following small
table of the wavelength (in ``nanometers'') of the peak of the curve for
objects of several different temperatures. You should read the wavelengths at
the peak of the curve by looking at the x-axis value of the peak.
(\textit{5 points})

\begin{table}[h]
\begin{center}
\bigskip
\begin{tabular}{c|c}
\hline
Temperature & Peak Wavelength  \\
\hline
\hline
3000  &  \\
6000  &  \\
12000  &  \\
24000  &  \\
\hline
\end{tabular}
\end{center}
\end{table}

\item Can you see a pattern from your table? For example, consider how the
peak wavelength changes as the temperature increases by a factor of 2, a
factor of 3, a factor of 4, etc. Can you come up with a mathematical expression
which relates the peak wavelength to the temperature?(\textit{3 points})

\smallspace

\item Where do you think the peak wavelength would be for objects on
Earth, at a temperature of about 300 degrees K?(\textit{2 points})

\smallspace
\end{enumerate}

\section{Spectral Lines Experiment}

\subsection{Spark Tubes}
In space, atoms in a gas can get excited when light from a continuous
source heats the gas.  We cannot do this easily because it requires
extreme temperatures, but we do have special equipment which allows us
to excite the atoms in a gas in another way.  When two atoms collide
they can exchange kinetic energy (energy of motion) and one of the
atoms can become excited.  This same process can occur if an atom
collides with a high speed electron.  We can generate high speed
electrons simply - it's called electricity!  Thus we can excite the
atoms in a gas by running electricity through the gas.

The instrument we will be using is called a spark tube.  It is very
similar to the equipment used to make neon signs.  Each tube is filled
with gas of a particular element.  The tube is placed in a circuit and
electricity is run through the circuit.  When the electrons pass
through the gas they collide with the atoms causing them to become
excited.  So the electrons in the atoms jump to higher levels.  When
these excited electrons cascade back down to the lower levels, they
emit light which we can record as a spectrum.

\subsection{Emission-line Spectra Experiment}

For the third, and final section of this lab you will be using the spectrographs to look at
the spark tubes that are emission line sources.

\begin{itemize}
\item{The TA will first show you the emission from hot Hydrogen gas.  Notice 
how simple this spectrum is.  On the attached graphs, make a drawing
of the lines you see in the spectrum of hydrogen.  Be sure to label
the graph so you remember which element the spectrum corresponds
to. {\it (4 points)}}

\item{Next the TA will show you Helium.  Notice that this spectrum is more 
complicated.  Draw its spectrum on the attached sheet.{\it (4 points)}}

\item{Depending on which tubes are available, the TA will show you at least 3 
more elements.  Draw and label
these spectra on your sheet as well.{\it (4 points)}}
\end{itemize}

\subsection{The Unknown Element}

Now your TA will show you one of the elements again, but won't tell
you which one. This time you will be using a higher quality spectroscope
(the large gray instrument) to try to identify which element it is by 
comparing the wavelengths of the spectral lines with those in a data  
table. The gray, table-mounted spectrograph is identical in nature to
the handheld spectrographs, except it is heavier, and has a more stable
wavelength calibration. When you look through the gray spectroscope you will 
see that there is a number scale at the bottom of the spectrum. These
are the wavelengths of the light in ``nanometers'' (1 nm = 10$^{\rm -9}$ meter).
Look through this spectrograph at the unknown element and write down
the wavelengths of the spectral lines that you can see in the
table below, and note their color. 

\begin{table}[ht]
\caption{Unknown Emission Line Source}
\begin{center}
\begin{tabular}{|c|c|}\hline
Observed Wavelength (nm) & Color of Line \\
\hline
 & \\
\hline
 & \\
\hline
 & \\
\hline
 & \\
\hline
 & \\
\hline
 & \\
\hline
\end{tabular}
\end{center}
\end{table}

Now, compare the wavelengths of the lines in your data table to each of
the three elements listed below. In this next table we list the wavelengths
(in nanometers) of the brightest emission lines for hydrogen, helium and argon. Note that
most humans cannot see light with a wavelength shorter than 400 nm or
with a wavelength longer than 700 nm. 

\begin{table}[ht]
\caption{Emission Line Wavelengths}
\begin{center}
\begin{tabular}{|c|c|c|}\hline
Hydrogen & Helium & Argon \\
\hline
656.3 & 728.1 & 714.7 \\
\hline
486.1 & 667.8 & 687.1 \\
\hline
434.0 & 587.5 & 675.2 \\
\hline
410.2 & 501.5 & 560.6 \\
\hline
397.0 & 492.1 & 557.2 \\
\hline
388.9 & 471.3 & 549.5 \\
\hline
\end{tabular}
\end{center}
\end{table}

\noindent
Which element is the unknown element? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
{\it (5 points)}

\section{Questions}

\begin{enumerate}
\item Describe in detail why the emission or absorption from a particular
electron would produce lines only at specific wavelengths rather than
at all wavelengths like a blackbody.  (Use the Bohr model to help you
answer this question.)  {\it (6 points)}
\bigspace

\item What causes a spectrum to have more lines than another spectrum
(for example, Helium has more lines than Hydrogen)?  {\it (5 points)}
\bigspace

\item In this lab, what energy source is causing the electrons in the
atoms to become excited? {\it (3 points)} 
\bigspace

\item Which element showed the fewest spectral lines?  Which element
showed the most spectral lines?  Why? {\it (3 points)} 
\bigspace

\item Using your knowledge of spectral lines from 
elements, how do you think all those bright colors in ``neon'' signs are
made? {\it (4 points)}
\bigspace

\end{enumerate} 



\section{Summary}

({\it 35 points})  Summarize the important ideas covered in this lab.
Some questions to answer are:

\begin{itemize}
\item{What information you can learn about a celestial object just
by measuring the peak of its blackbody spectrum?} 
\item{What  does a
blackbody spectrum look like?} 
\item{How does the peak wavelength change
as the temperature of a blackbody changes?} 
\item{How can you \textit{quantitatively} measure the color of an object?}
\item{Do the color of items you see around you on Earth (e.g. a red and
blue shirt) tell you something about the temperature of the object? Why
or why not?}
\item{What information can you learn about an astronomical object from its spectrum
rum?}
\item{Explain how you would get this information from a spectrum.}
\end{itemize}

\noindent
Use complete sentences, and proofread your summary before handing in the lab.

\section{Possible Quiz Questions}

\begin{enumerate}
\item What is meant by the term ``blackbody''?
\item What type of sources emit a blackbody spectrum?
\item How is an emission line spectrum produced?
\item How is an absorption line spectrum produced?
\item What type of instrument is used to produce a spectrum?
\end{enumerate}

\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.8\textwidth
\epsfbox{SPECTRAL/spectralfig3.eps}
\end{figure}

\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.8\textwidth
\epsfbox{SPECTRAL/spectralfig3.eps}
\end{figure}
%\end{document}
