*You* are the nuclear scientist

It's the early 1940s

    • 1938 Hahn finds fission. Lise Meitner calculates huge energy release when fission happens. Szilard verifies that more than one neutron is produced when ${}^{235}U$ splits.
    • 1939 Germany invades Poland
    • 1941 Surprise Japanese attack on Pearl Harbor. U.S. declares war on Japan. Germany & Italy declare war on U.S. U.S. declares war back on them.

    U.S. scientists suspect a chain reaction is possible but no one has ever seen it in action, and it's surprisingly hard to get going (luckily for Otto Hahn).

    Why no chain reaction?


    • $n+{}^{235}U\to$ pieces (fission)
    • But $n+{}^{238}U\to {}^{239}U$ (neutron absorption)

    So, one possibility we discussed to make a chain reaction is to enrich uranium, increasing the percentage of ${}^{235}U$.

    • But you can't do it chemically: That means it's *really hard*.
    • Your boss tells you that before you can get the money (convince the government) to do enrichment, you had better show *any way you can* that a chain reaction is possible.

    How else to make a chain reaction happen??!!

    Experiments with bombarding U-235 nuclei continue...

    Other scientists have been continuing to do experiments with U-235 and fission. One day, your assistant hands you something like this graph:

    • On the vertical axis- The fission "cross section" is proportional to the probability that a neutron hitting a U-235 nucleus will cause it to split.
    • On the horizontal axis- is graphed the kinetic energy of a neutron. (1 MeV=1.6$\times 10^{-13}J$
    • When a U-235 neutron splits, on average 2 neutrons are produced. They can have a range of kinetic energies. But a typical energy is 1 MeV per neutron. (Range shown schematically in blue).
    • A neutron with a kinetic energy of 1 MeV is moving at 10% the speed of light!
    • Also shown on the graph is the cross section ($\propto probability$) for U-238 to capture a neutron. What do you notice?
    • Temperature is proportional to the RMS kinetic energy of particles. Kinetic energies of room temperature particles (called 'thermal' particles) are shown towards the left.

    What does this suggest that you should do to make a chain reaction more likely to happen??

    Temperature and kinetic energy

    Atoms/molecules in a liquid or gas are moving all the time.

    • Some individual atoms are slow (low KE).
    • Some are fast.
    • But (energy conservation after each collision) the total amount of kinetic energy of this collection of atoms in a box is not changing very much.
    • Temperature is exactly proportional to the RMS (average) kinetic energy of a collection of atoms.
    • What happens to the average kinetic energy if you heat up such a liquid of particles? If you cool it?
    • Now, imagine that you open a hatch and throw a very slow particle (KE much smaller than average KE in the box) in. After a while, will the particle be more likely slower or faster than it started out?
    • Imagine if you open a hatch and throw a very fast particle in. What is likely to happen?

    "Moderation" - how to slow down neutrons

    If an initially fast (or very slow) particle bounces off enough other room-temperature particles, it will, on average, eventually end up with a kinetic energy in the range of the other room temperature particles.

    But for neutrons, there is also a chance with each collision that the neutron could be absorbed instead of "scattered" (bouncing off).

    How to slow down a neutron with as *few* collisions as possible? Think about:

    • Throwing a bowling ball into a liquid made of ping pong balls.
    • Throwing a ping pong ball into a liquid made of bowling balls.
    • Throwing a ping pong ball into a liquid made of ping pong balls.

    Pool (Billiard) balls all have exactly *same* mass. Listen to how this fellow uses energy in his patter about how to arrange his shot...

    So, you'd like box with *what kind* of nuclei in it to slow fast neutrons down with very few collisions??

    Moderators

    Best moderators for neutrons:

    • Regular water (contains mostly ${}^1H=$ 1 proton) is pretty good at slowing neutrons, but unfortunately it also has a pretty high likelihood of $$n+{}^1H\to{}^2H$$ (neutron absorption, resulting in deuterium).
    • "Heavy water" containing deuterium (${}^2H$) nuclei is the best, but is very expensive and takes a while to acquire in large quantities.
    • Solid carbon, ${}^{12}C$, (graphite) is not quite as good, but much cheaper.

    First human-made chain reaction

    1942 - Enrico Fermi's team created the first controlled chain reaction in the "Chicago-Pile-1" at the University of Chicago...located close to downtown Chicago!

    • Bricks of Uranium oxide mixed with a graphite moderator (to slow neutrons).
    • Uranium was natural *not enriched*: 0.7% U-235. (A much larger mass was required of Uranium than than the critical mass of enriched Uranium for a bomb.
    • Cadmium (good neutron absorber) rods were slowly removed and re-inserted into the pile of uranium oxide bricks to control the chain reaction.
    • 18 months to completion.

    [There was probably a naturally-occurring one in Gabon in pre-historic times.]

    Modern nuclear reactors

    • fuel rods containing unenriched Uranium,
    • in a tank, which is then filled up with water, when you're ready to get the reaction going.
    • There are also "control rods" made of neutron-absorbing material that can be moved in or out of the core.

    Why do the control rods come down from above rather than getting pushed up from below???

    This means you can work with unenriched uranium, and so it's much harder to get a runaway chain reaction to happen.

    PWRs

    Most U.S. reactors are pressurised water reactors (PWRs) where water is both a coolant and a moderator.

    Water slows neutrons $\Rightarrow$ increasing the probability of fission.

    What happens if the water boils off or leaks out? Do we get negative or positive feedback?

    -> No moderation
    -> Neutrons are now fast instead of slow
    -> lower probability of fission.

    This is negative feedback.

    Chernobyl disaster

    The Chernobyl plant was a graphite-moderated reactor of a design unique to the USSR.

    The first accident reports faulted human operators for not following operating procedures, but later reports pointed out 2 design flaws resulting in positive feedback loops:

    • Core contained graphite and water. Here the purpose of the water is to absorb the heat.
    • Moderation was mostly due to graphite. Under these conditions neutron absorption by water becomes more important than water moderation. Water plays the role of a weak "control rod" in such a reactor.
    • If the cooling water turns to steam, fewer neutrons are absorbed, and so more fissions happened.
    • As the control rods were inserted, displacing water(?), moderation temporarily increased, speeding fission.

    Fuel "lava" in the basement of the reactor:

    Radioactivity released was:

    • 400 times more than the amount released at Hiroshima, but
    • 500-1000 times less than nuclear testing of 1950s and 60s.

    3 kinds of nuclear energy plants

    Breeder reactor

    PFBRWhen U-238 is bathed in neutrons we get Pu-239 which will also fission.

    A breeder is designed to create as much new fissionable material as possible, and then burns the re-processed new stuff.

    Breeders are much more efficient, and can actually consume plutonium -> reducing long-term nuclear waste.

    Disadvantage is that there's more plutonium produced, which could be used in a weapon.

    Fusion reactors

    ${}_1^2H + {}_1^3H \rightarrow {}_2^4He + {}_0^1n$

    Deuterium can be extracted from seawater. Not renewable, but time to peak is ~10s of millions of years.

    Fusion products (waste) is non-radioactive Helium.

    Requires sun-like temperatures. Has stayed 30-40 years away for the last 30 or 40 years.

    Image credits

    World Nuclear Association, Abraham Marrero, Spaceman.ca, Wikipedia