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Montserrat Natural World Cluster -- November 13, 2017\\
Technical FAQ for the film ``Containment''
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\begin{enumerate}
\item[(a)] {\it What is a half-life?} Radioactive materials, such as the 
isotope \emph{Plutonium-239} used in nuclear weapons 
and mentioned prominently in ``Containment,'' decay over time.  This process
takes place at a \emph{characteristic rate}, usually described by giving 
what is known as the \emph{half-life}.  The half-life is, by definition, 
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\emph{the time necessary
for a sample of a given mass originally to decay to one-half of its original mass}.
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As a formula, if $Q_0$ is the amount originally present, and the half life is 
$T_{1/2}$ then the amount present at time $t$ is given by:
$$Q(t) = Q_0 \cdot \left(\frac{1}{2}\right)^{t/T_{1/2}}.$$
Many of you have probably done problems in precalculus or calculus classes
based on this sort of formula.  But what does this \emph{really mean} in more intuitive 
terms?  
The half-life of Plutonium-239 is approxmimately
$$24,100\ {\rm years}.$$
The graph on the back of this sheet shows how a 100 kg sample of Plutonium-239
(this would be enough to create about 5 nuclear bombs)
decays over time.  
\begin{itemize}
\item At $t = 24,100$ years (1 half-life), one half of the original, or 50 kg are left
\item At $t = 48,200$ years (2 half-lives), one half of the 50 kg, or 25 kg are left
\item At $t = 72,300$ years (3 half-lives), one half of the 25 kg, or 12.5 kg are left
\item and so on ... 
\end{itemize}
\item[(b)]  {\it Why is this of concern?} 
It has been estimated that a pound (454 grams) of Plutonium inhaled as 
Plutonium Oxide dust could give cancer to two million people.\footnote{Bernard L. Cohen. 
The Nuclear Energy Option. Plenum Press, 1990.}
\item[(c)]  {\it Why can't we just launch all this waste into space and let it
fall into the sun?}  Well, the main reason is that there is \emph{so much of it, now}.
As of 2010, the WIPP facility highlighted in ``Containment'' had already accepted
about $7.2 \times 10^4$ cubic meters of waste and stored it.  With current rocket
technology, we would need thousands of rockets to launch what was already stored.
If each launch has a probability of success of $.999$ and we launch a thousand times, 
the probability that there is {\it at least one launch accident} 
would be $1 - (.999)^{1000} = .6323$, 
or about $62\%$.  Even one launch accident could have catastrophic results (see (b) above).  
\item[(d)] {\it Isn't this just an engineering problem?}  In a sense, maybe.  But 
the time scales involved and the difficulty of even thinking about communicating
with people thousands of years in the future (if there are any of us left) is what ``Containment''
is about.  
\end{enumerate}
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