\input{labpreamble}
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\subsubsection*{PHSX 222L\hfill Absorption of Gamma Rays\hfill Name:\underline{\hspace*{2in}}}

\underline{Object:} To determine how lead and aluminum absorb gamma rays.

\underline{Theory:} The radioactive source used to provide gamma
radiation for this experiment is a 5.0~$\mu$Ci cesium-137 sample.  This
isotope has a half-life of 30.2 years and emits gamma ($\gamma$)
radiation at an energy of 0.6616 MeV. It also emits a
some beta minus ($\beta^{-}$) radiation which we don't want.

It has been found that gamma radiation interacts with matter in a
manner quite different than alpha or beta rays.  This is due to the
fact that gamma rays consist of high energy electro-magnetic waves,
while alpha and beta rays are made up of high speed charged particles. 
As alpha and beta particles travel through matter they scatter off the
atoms and thus follow a rather zig-zag path through the material,
slowing down as they go.  A gamma ray, being an EM wave or photon, can
travel at only one speed---the speed of light.  The three basic
mechanisms of interaction of photons with matter are the photoelectric
effect (in which the photon delivers all its energy to the charged
particle and disappears), the Compton effect (in which some energy and
momentum is transferred to the charged particle and the balance is
carried away by another photon created in the process), and pair
creation (in which a particle and its antiparticle are created
according to $E=mc^{2}$).  

The greater the distance of travel through
a substance, the greater probability that the photon will be absorbed;
\emph{i.e.}, their number decreases approximately exponentially as
they travel through the absorber.  This means that for large numbers
of photons, the number per minute $N$ that survive a distance $x$ in a
substance is modeled by the formula
\begin{equation}\label{N}
N = N_{o}e^{-\mu x}
\end{equation}
\noindent
where $\mu$ is the linear absorption coefficient of the substance, and $N_{o}$ is the initial
number of photons per minute. The slope of the straight line graph 
of $-\ln(N/N_{o})$ vs.~$x$ should be $\mu$.

A useful number related to this absorption process is the 
\underline{half-value layer} (HVL), also known as the half distance, or 
$x_{1/2}$ of a substance.
This is defined to be the distance through 
the material $x_{1/2}$ for which one half of the original photons will be 
absorbed ($N/N_{o}=1/2$). 

Because the decay process is totally random and predictions can be
made only statistically, it is important to get as many counts as you
have time for---this reduces the uncertainties.  The effect of the air
is negligible in this experiment.

\underline{Apparatus:}  Draw a diagram of the apparatus.
% \vspace{.2in}

\underline{Safety:}  The radioactive sources are of extremely low 
activity and are not hazardous when used as directed.  However, it is 
a good idea to treat all radioactive materials safely.  For example, 
do not put the source in your pocket or bring it too near your body; 
handle it only when necessary, and return it when the experiment is 
over.  For the safety of the equipment, please do not touch the end 
window of the Geiger tube or you will break it and destroy the tube.  
It cannot be repaired and it is expensive to replace.

\newpage
\underline{Procedure:} It would be convenient to make all time 
measurements in minutes for this lab.
\vspace{-.25in}
\begin{enumerate}

\item With the Geiger tube mounted in its stand and with all
radioactive sources placed well away, measure the background
radiation.  Place one aluminum plate in the stand in the top slot and
leave it there for the rest of the experiment.  This is done to block
out the alpha and beta radiation that may be part of the background
(and also emitted by the source).  These alpha and beta particles are
easily blocked by a single plate of aluminum, whereas most of the
gamma radiation (which is what you want to count) passes through. 
Simultaneously press the reset button on the counter and start your
stop watch.  Allow the counts to go to at least 200 and record the
time.  Compute the background rate (in counts per minute or cpm).

\item Place the $^{137}$Cs source, printed side up, in the depression
at the bottom of the plastic stand.  

Measure $N_{o}$ in cpm (let the counter reach at least 2500 counts for
statistical purposes; more is better).  Correct for background
radiation by subtracting the background rate computed above.  Remember
that $x=0$ for $N=N_{o}$.

\item By adding additional aluminum plates one at a time compute $N$
for successive values of $x$, the metal thickness.  Do not count the
beta-shield in your cumulative plate thickness computations.  Correct
for background each time and assume the linear absorption coefficient
is 0 for air.

\item Plot $-\ln(N/N_{o})$ vs.~$x$ and compute $\mu$ (the least
squares slope).  Then compute the HVL ($x_{1/2}$) for Al.  You might also average 
your value with those from the other groups in the class.

\item Interpolate the accepted value of $x_{1/2}$ from the chart on
the web at
\newline\verb=<http://www.safety.queensu.ca/safety/radiation/course/hvlchart.pdf>=\ 
and compare your value to it.

\item Either repeat for lead (assume the same background rate and 
continue to use the single sheet of aluminum to filter out alphas and 
betas) or verify the inverse square law for intensity as a function of 
distance from the source, (or both) as you have time.  If time 
permits, play with alpha and beta sources and note their lack of 
penetrating power.

\end{enumerate}

\underline{Questions:} 
\vspace{-.25in}
\begin{enumerate}
	\item Explain why if your data points do not lie well on a straight line.

	\item Average your value of $x_{1/2} $ with those of the other 
	groups in the class.  How much closer is the average to the accepted 
	value?  Discuss systematic vs. random errors.

	\item In first-year physics we have gone to great lengths to
	make our graphs linear.  This is because the math of straight
	lines is straight forward.  You linearized your graph today by
	taking logarithms.  Qualitatively sketch a graph of your data
	\emph{without} linearizing it, {\it i.e.,} a graph of $N/N_{o}$
	vs.~$x$.  No numbers are necessary.

\end{enumerate}

\underline{Conclusions:} 
\vspace{-.25in}




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