\section*{Problem 5}
\subsection*{Part A}

Xenon-135 is primarily produced in a reactor as a fission product or by the
decay of Iodine-135, which is a direct product of uranium fission. Xenon-135
decays naturally over time or can absorb neutrons to become other isotopes with
a much smaller neutron cross section.



\subsection*{Part B}

Xenon-135:

The second reactor will have a lower concentration of xenon-135 in the reactor
core. Xenon-135 will be generated by the decay of iodine-135, but will also
decay naturally to other elements over time as well as being removed through
neutron absorption. If the reactors are shut down after a year, the xenon-135 in
both will spike with the full power reactor having a larger spike, and it will
take longer for the 100\% power reactor to be able to be restarted until the
extra xenon-135 has had time to decay away.

Samarium-149:

The second reactor will also have a lower concentration of samarium-149 for a
similar reason as the xenon-135 case. There will be less fissile products to
decay into samarium-149 in the low power reactor. If the reactors are powered
off, however, both reactors will develop additional samarium-149 concentrations
that will not decay away naturally as samarium-149 is stable. It will take more reactivity
to restart the full power reactor from shutdown as the samarium-149
concentration will be much higher than the low power reactor. 

\subsection*{Part C}

Xenon is the more challenging poison to deal with. First, xenon has a much
larger cross section and has a more significant effect on reactivity than
samarium. Second, xenon-135 is not a stable element, and thus has decay effects
when the reactor is shut down. As such, the amount of time since shutdown is an
important factor to consider when restarting a reactor with consideration to
xenon. A miscalculation on xenon concentration can lead to a too-large insertion
of reactivity on start-up, which doesn't exist in the same way with samarium as
samarium doesn't decay during shutdown. Finally, xenon is a much faster response
dynamically compared to samarium. Xenon-135 can quickly change concentrations
in hours, while samarium-149 concentrations can take weeks to change
significantly. Human operators are much more likely to be able to cope with the
longer time constant poison versus misjudging the small time constant effects of
xenon.
