Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 252
proton number, Z
A=50
A=100
A=150
neutron number, N
235 U fission yield
probabilities
A=200
Figure 15.14: Fission of 235 U (small red
square, upper right) tends to produce two
neutron-rich fragments. If it split exactly in
two, the result would lie at the midpoint
of the orange line connecting 235U
to the
origin, at the yellow circle. In practice, an
equal split is highly unlikely, as one fragment
tends to be around A ∼ 95 <strong>and</strong> the
other around A ∼ 140, as depicted by the
probability histogram in green. The two
green stars separated along the orange line
represent a more likely outcome for the two
fragments. As long as the green stars are
located so that the yellow circle is exactly
between them, the accounting of proton <strong>and</strong>
neutron number is satisfied. Because the orange
line lies to the right of the stable nuclei,
the fission products tend to be neutron-rich
<strong>and</strong> undergo a series of radioactive β − decays
before reaching stability, which could
take a very long time in some cases.
Example 15.4.1 If one of the two fragments from the fission of a
nucleus (Z 92) after adding a thermal neutron winds up being
(Z 35), what is the other nucleus going to be?
235U
90
The other fragment will preserve total proton count, so Z 92 − 35
57, <strong>and</strong> as such is destined to be the element lanthanum. Which isotope
of lanthanum is produced depends on how many neutrons escape the
split. Table 15.6 summarizes the particle counts of the various players.
If no spare neutrons are left over, the lanthanum must have N
144 − 55 89 neutrons, 27 in which case its mass number will be
27: U
146
A 146, so La. If two neutrons are set free, then the lanthanum
144
will only keep 87 neutrons <strong>and</strong> be La, as depicted in Figure 15.13.
Typically, about 2–3 neutrons are left out of the final fragments, <strong>and</strong>
can go on to promote additional fission events in the chain reaction.
Br
235 had A − Z 235 − 92 143 neutrons,
plus the thermal neutron addition.
235U
90Br
146La
145La
144La
143La
A 235 90 146 145 144 143
Z 92 35 57 57 57 57
N 143 55 89 88 87 86
n 1 0 1 2 3
Table 15.6: Possible outcomes for Example
15.4.1 if we set one of the daughter particles
to be bromine-90, forcing the other daughter
to be lanthanum. Different isotopes of
lanthanum will result for differing numbers
of spare neutrons left after the break-up (last
row).
Being a probabilistic (r<strong>and</strong>om) process, each fission can result in a large
set of possible “daughter” nuclei—only one set of which was explored
in Example 15.4.1. As long as the masses all add up, <strong>and</strong> the two-hump
probability distribution in Figure 15.14 is respected, anything goes. In
other words, we have no control over exactly what pieces come out.
Figure 15.15 provides a graphic illustration of four different possible pairs
of daughter fragments. The counting requirement is satisfied by having
235
the products located diametrically opposite from the U midpoint
(yellow circle). The positions of the stars will distribute along A-values
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.