What is the total binding energy
for a uranium-235 nucleus?
38.12 - Shape of the binding energy curve
The graph of binding energy per nucleon versus mass number has a distinct shape that
proves to be very important. The higher on the graph an element is (indicating more
binding energy per nucleon), the more stable it is.
The most stable elements are at the highest points, with iron-56 in this region, as you
can see in Concept 1.
Very light nuclei (on the left of iron-56 in the binding energy curve) can become more
stable if they combine to form larger nuclei through a process called fusion. By this
process, the binding energy per nucleon is raised, which means that energy is released.
This is the process by which stars, like the Sun, continually transform their mass into
energy. In a multistep process within the Sun, hydrogen nuclei fuse together to become
helium-4 nuclei.
As mentioned, the most stable locations on the curve represent elements such as iron
and nickel. Heavier, radioactive nuclei to their right can increase their binding energy
per nucleon and become more stable by “moving to the left and up” on the curve. For
instance, you can see in Concept 3 that uranium is less stable than iron. A heavy
nucleus could become more stable by emitting particles and becoming slightly smaller
(the process of radioactive decay) or, in extreme cases, by splitting into two medium-
sized nuclei (a process called fission). This is the principle behind radioactivity and
nuclear power.
The shape of the graph also illustrates the relative distances at which the strong and
electrostatic forces effectively operate. The argument that follows is reasonably
complex but provides a good example of how graphical data can be analyzed. The
difference between these two forces can be used to explain why the graph first shows a
rapid increase of binding energy per nucleon, then levels off, and finally declines.Earlier, we discussed the short-range nature of the strong force. It is so short-range that
it acts only between a nucleon and its nearest neighbors. The graph supports this
hypothesis. Why? When there are only a few nucleons, they are all very close and
every nucleon interacts with every other. For instance, when there are two nucleons,
they are next to each other, and exert a strong force on one another. As a third nucleon
is added, it has two neighbors to exert a force on, so the force increases faster than the
number of nucleons. This means the binding energy per nucleon increases, so the line
has a positive slope. (Mathematically, the binding energy of the smaller nuclei increases as the square of the number of nucleons.)
As more nucleons are added, at some point they are too far apart to all be “neighbors”. For instance, when there are 100 nucleons, and
another is added, it can only interact with its close neighbors. A nucleon on one side of the nucleus is too far away to exert a significant strong
force on one on the far side. Adding a nucleon does not increase the binding energy per nucleon. This means with larger nuclei, the additional
binding energy per nucleon becomes constant. The sharp increase in binding energy per nucleon ceases.The strong force needs to be contrasted with the electrostatic force, which acts to push apart the protons, and which acts at a greater distance
than the strong force. When a new proton is added, it is attracted only to its nearest neighbors via the strong force, but is repelled by every
other proton that is already present because the electrostatic force acts at a greater range. This, in turn, makes it easier to disassemble the
nucleus when more of the protons want to be separated.In sum, at first the strong force dominates, causing the increase in binding energy per nucleon. But as the nucleus grows in size, the
electrostatic force plays a larger role, causing an eventual decrease in binding energy per nucleon.Binding energy per nucleon
versus mass number
Highest in the middle
Lighter elements can undergo
fusion and release energy
(^708) Copyright 2007 Kinetic Books Co. Chapter 38