Physics · Ch 8 — Atomic and Nuclear Physics
Binding energy curve
Binding energy curve
Rather than just the total binding energy of a nucleus, it is far more informative to compute the average binding energy per nucleon,
which represents, roughly, the energy needed to pull a single typical nucleon out of that particular nucleus. Plotting against mass number for every known nucleus produces the binding energy curve (Figure 8.24), whose shape carries several important physical consequences:
(1) The curve rises steeply for light nuclei, reaches a maximum of about 8.8 MeV per nucleon at (iron), and then slowly decreases for heavier nuclei.
(2) Nuclei with mass number roughly between and have an average binding energy per nucleon of about 8.5 MeV; these nuclei are comparatively the most stable and are generally not radioactive.
(3) For the very heaviest nuclei the curve continues its slow decline - for example, uranium's binding energy per nucleon is about 7.6 MeV - making these nuclei less tightly bound and typically unstable/radioactive. …
What this figure shows. This figure plots the average binding energy per nucleon in MeV on the vertical axis against the mass number A on the horizontal axis (running from 0 to 250), with several representative nuclei marked directly on the curve: deuterium and helium-3 near the low, steeply rising left end, helium-4 sitting as a small local spike, oxygen-16 further along, iron-56 sitting almost exactly at the peak of the curve around 8.8 MeV, tin-120 on the broad plateau, and uranium-238 on the slowly descending right-hand tail near 7.6 MeV. The overall shape - a sharp rise for light nuclei, a broad flat maximum around iron, and then a slow decline for the heaviest nuclei - is the single graph that explains why fusing light nuclei together and splitting heavy nuclei apart are both energy-releasing processes, s …
Worked out. This worked example simply divides the total binding energy of the helium-4 nucleus found in Example 8.9, namely 28 MeV, by its mass number A = 4, giving a binding energy per nucleon of 28/4 = 7 MeV. This illustrates the routine step of converting a nucleus's total binding energy into the per-nucleon figure that is actually plotted on the binding-energy curve and used to compare the relative stability of …