Heavy elements like uranium have a large number of protons, which all repel one another. As the number of protons increases, the repulsive

force keeps growing and growing, making the nucleus more and more unstable.

Neutrons counteract this growing instability by increasing the distance between protons, which decreases the electrostatic forces, and by

attracting each other and the protons with the strong nuclear force.

However, there comes a point when the nucleus gets too large, and will be unstable no matter how many neutrons are present. This can be

understood by considering the relative ranges of the strong and electrostatic forces. The strong force only acts between very close neighbors,

while the repulsive electrostatic force acts between all protons regardless of their position within a nucleus. When there are lots of protons

already present, and one more proton is added, it will be subject to repulsive electrostatic forces from every proton that is already there, while

the attractive strong force will only be exerted by a few very close neutrons or protons. Eventually, it becomes impossible for the nucleus to

“hold in” an additional proton because the strong force cannot overcome the electrostatic force.

38.9 - Nuclear binding energy

Binding energy: The energy that must be added

to disassemble, or unbind, a nucleus into the

protons and neutrons that make it up.

You may have heard of radioactivity, and know that uranium atoms will spontaneously

decay into other elements, while other elements such as common iron (iron-56) are

stable. Stable nuclei such as iron all have one thing in common: Their nucleons are

tightly bound. Unstable atoms are not as tightly bound. What does it mean to be “tightly

bound”?

Note that the term “stability” in nuclear physics is not making a statement about the

tendency of an atom to enter into chemical reactions. For example, we say that iron is

“stable” in the nuclear sense, even though it rusts. When iron combines with oxygen to

form iron oxide, it is a chemical reaction, not a nuclear reaction. The iron remains iron

when it becomes iron oxide; it shares electrons with oxygen but the element’s nucleus

remains unchanged.

What makes the protons and neutrons in a radioactive uranium atom less tightly bound

than the nucleons in an extremely stable iron atom? Can we quantify and compare the

stability of nuclei?

As it turns out, we can. One way to measure the stability of a nucleus is to try and rip

the nucleons apart, overcoming the strong force. When physicists conduct such

experiments, they find it takes energy to break the nuclear bonds (which the strong

force is responsible for), that is, to take apart a nucleus into separate protons and

neutrons. (This makes sense, because if no energy was required to separate them, they

would fall apart on their own.)

The particles that emerge when the nucleus is forced apart can be analyzed. Careful

measurements show that the sum of the masses of the separate nucleons is always

greater than the mass of the nucleus when it is whole.

Concept 1 shows this, using an isotope of hydrogen, deuterium, as an example.

Why should the mass of the nucleus increase when it is broken up? To a classical

physicist, unacquainted with Einstein’s theory of special relativity, this would be a

surprise since mass is assumed to be conserved.

However, we know that another conservation principle applies here: the total of mass

and energy (or mass-energy) must remain the same, though the individual terms may

vary. Einstein’s principle of mass-energy equivalence, summed up by the equation

E = mc^2 , applies. This is shown in Concept 2. It takes energy to separate the particles,

and the energy added to the nucleus to fragment it into nucleons shows up as the

“extra” mass. (We will assume for the sake of simplicity that the kinetic energies of the

particles and of the nucleus are negligible.)

The energy that must be added to completely disassemble the nucleus is known as the

binding energy. This works in both directions. The binding energy is released when the

protons and neutrons come together to form a bound nucleus. This is illustrated in

Concept 3.

The terminology could be a little confusing. You can think of it like gravity: You must

“add” energy to pull apart two particles, or lift a rock farther from the surface of the

Earth. That is analogous to the binding energy.

Because of the equivalence of energy and mass, the binding energy may also be

related to mass. When energy is added to a nucleus to disassemble it, the mass of the

parts increases. On the other hand, when a nucleus is assembled, the release of

Binding energy

Energy that must be added to

disassemble nucleus completely

Increased energy of separate particles

reflected in increased mass

Binding energy becomes mass

Separate particles have more mass than

assembled nucleus

Assembling the nucleus

Binding energy released when nucleus

is assembled

Decreased energy of nucleus reflected

in decreased mass

Mass becomes binding energy

(^706) Copyright 2007 Kinetic Books Co. Chapter 38