Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 249
energy per nucleon in the last column of Table 15.5 starts out small,
but soon settles to the 7–9 range for most of the entries. It is extremely
insightful to plot the binding energy per nucleon as a function of the
nucleon mass number, A, which we do in Figure 15.10.
9
8
12 C
56 Fe
Binding <strong>Energy</strong> Per Nucleon (MeV)
7
6
5
4
3
2
1
0
2 H
1 H
4 He
0 20 40 60 80 100 120 140 160 180 200 220 240 260
Nuclear Mass Number, A
235 U
Figure 15.10: Binding energy per nucleon
as a function of total mass number, A. The
nuclei featured in Table 15.5 are indicated
as red points. Note in particular that 56Fe
sits at the peak of the curve. Fusion operates
from left to right, building larger nuclei, <strong>and</strong>
fission goes from right to left, tearing apart
nuclei. Only actions that climb this curve
are energetically favorable, meaning that
fusion is profitable on the the left-h<strong>and</strong> side,
<strong>and</strong> fission makes sense on the right: each
driving toward the peak binding energy per
nucleon.
The value of Figure 15.10 is hard to over-emphasize. Key take-aways
are:
1. Most nuclei are at around 8 MeV per nucleon, meaning that it
would take an average of about 8 MeV of energy to rip out each
member (proton or neutron) from a nucleus;
2. The peak is at Fe meaning that this is the most tightly bound
nucleus; 22
3. The slope on the left side is much steeper than the slope on the
right side, after the peak, which speaks to why fusion (building
from small to big) is more potent than fission (tearing apart very
massive nuclei);
4. Fusion in stars does not build elements beyond the peak around
iron, since to go beyond the peak is not energetically favorable.
56
, 21 21: Actually, 62Ni
wins by a hair at 8.795
MeV/nuc, but is somewhat overlooked because
it is only 0.006% as abundant as 56 Fe,
whose binding energy per nucleon is essentially
tied for the top at 8.790 MeV/nuc.
22: A peak exists because nucleons initially
find advantage in binding together, but ultimately
the increasing number of mutuallyrepelling
protons makes the environment
less appealing for larger nuclides.
It can be helpful to think of Figure 15.10 upside-down, as in Figure 15.11,
turning the iron “peak” into a trough. A ball will roll toward <strong>and</strong> settle
near the bottom of the trough, which is what both fusion <strong>and</strong> fission do,
but from opposite directions.
15.4 Fission
Having covered some fundamentals, we are ready to tackle aspects of
nuclear energy. Really it is very simple. Enough nuclear material in a
fusion
binding energy
Fe
fission
Figure 15.11: Turning the binding energy
curve upside-down makes it easier to conceptualize
fusion <strong>and</strong> fission driving toward
the most tightly bound point (iron), like a
ball might roll.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.