\section{Introduction}

In the blackbody lab, you studied the most basic type of radiation: a
continuous spectrum caused by a hot, dense object.  You also found out
that by studying the blackbody radiation some basic physical
parameters about the emitting source could be derived, most
importantly the $temperature$ of the object.  You should have learned
that when the temperature of the body is increased, the peak of the
blackbody spectrum moves towards bluer light and the whole spectrum
gets brighter.  Continuous spectra however, cannot give us much more
information than that about the object emitting the light.

\medskip

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?  The answers to these and other similar questions
are related to observations of features in the spectra of objects
which we call {\it Spectral Lines}.  This is the topic of this lab exercise.

\begin{itemize}
\item{{\it Goals:}  to discuss the Bohr model of the atom and Kirchoff's Laws; to use these concepts to explain absorption and emission lines; and to be able to identify elements by their spectral lines}
\item{{\it Materials:} Spectrograph, power source, gas filled spark tubes}
\end{itemize} 

\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.

\medskip

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 smashing the little atoms into
each other more often by increasing the 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 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.

\medskip

Now, since each element has a different nucleus make-up 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 time, only one 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}

You have learned about continuous spectra in the Blackbody lab, 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.

\medskip

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}

\medskip

\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}

As you should have learned from the Blackbody lab, 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.

\medskip

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 this lab you will be observing the spectral lines produced by
several different elements when their gaseous forms are heated.  The
goal of this lab is to observe these emission lines and to understand
their formation process.  Follow the instructions below and remember
to answer the questions at the end of the lab.

\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.

\medskip

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 this experiment, you will be using the same spectrographs that you
used in the blackbody lab.  {\bf Remember} to be careful with the
spectrographs; they are fragile instruments.

\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 (25 points)}}

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

\item{Depending on which tubes are available, the TA will show you at least 3 
more elements: Neon, Mercury, Oxygen, Nitrogen, Bromine, or Air.  Draw and label
these spectra on your sheet as well.}

\item{Now the TA will show you one of the elements again, but won't tell
you which one. Try to identify which element it is by comparing the
observed spectrum with the spectra you already recorded.  Draw the
spectrum in the last graph and label it with the element you think it
is.}
\end{itemize}
 

\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}


\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 (10 points)}
\bigspace

\item What causes a spectrum to have more lines than another spectrum
(for example, Helium has more lines than Hydrogen)?  {\it (10 points)}
\bigspace

\item In this lab, what energy source is causing the electrons in the
atoms to become excited? {\it (6 points)} 
\bigspace

\item Which element showed the fewest spectral lines?  Which element
showed the most spectral lines?  Why? {\it (6 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 (8 points)}
\bigspace

\end{enumerate} 
 
\section{Summary}
{\it (35 points)}  Please summarize the important concepts discussed in this lab {\it and} the Blackbody Lab:

\begin{itemize}
\item{What information can you learn about an astronomical object from its spectrum?}
\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.

%\end{document}
