chapters on mechanics are the result of electromagnetic repulsion between the atoms in
the objects that collide with one another. However, neither of these forces explains why
the protons in an atomic nucleus cling together. In fact, the electromagnetic force should
act to make the protons push away from one another, not cling together. Explaining how
things work on the atomic level requires two additional forces that don’t act beyond the
atomic level: the strong and weak nuclear forces. The strong nuclear force binds the
protons and neutrons together in the nucleus. The weak nuclear force governs beta decay.
You don’t need to know any of the math associated with these forces, but you should
know what they are.
Mass Defect
As we have discussed, the mass of a proton is 1.0073 amu and the mass of a neutron is
1.0086 amu. Curiously, though, the mass of an alpha particle, which consists of two
protons and two neutrons, is not 2(1.0073) + 2(1.0086) = 4.0318 amu, as one might
expect, but rather 4.0015 amu. In general, neutrons and protons that are bound in a
nucleus weigh less than the sum of their masses. We call this difference in mass the mass
defect, , which in the case of the alpha particle is 4.0318 – 4.0015 = 0.0202 amu.
Einstein’s Famous Equation
The reason for this mass defect is given by the most famous equation in the world:
As we discussed in the section on relativity, this equation shows us that mass and energy
can be converted into one another.
The strong nuclear force binds the nucleus together with a certain amount of energy. A
small amount of the matter pulled into the nucleus of an atom is converted into a
tremendous amount of energy, the binding energy, which holds the nucleus together.
In order to break the hold of the strong nuclear force, an amount of energy equal to or
greater than the binding energy must be exerted on the nucleus. For instance, the binding
energy of the alpha particle is:
Note that you have to convert the mass from atomic mass units to kilograms in order to
get the value in joules. Often we express binding energy in terms of millions of
electronvolts, MeV, per nucleon. In this case, J = 18.7 MeV. Because there are
four nucleons in the alpha particle, the binding energy per nucleon is 18.7/4 = 4.7
MeV/nucleon.
EXAMPLE
A deuteron, a particle consisting of a proton and a neutron, has a binding energy of 1.12
MeV per nucleon. What is the mass of the deuteron?