binding energy from the system shows itself as a corresponding reduction of mass in
the assembled nucleus. This is sometimes called the “missing mass”.
38.10 - Interactive checkpoint: calculating the binding energy
For a carbon-12 nucleus with 6
protons and 6 neutrons, and a mass
of 11.9967 u, how much more mass
do the individual nucleons have than
the assembled carbon nucleus? This
is called the mass excess. What is
the binding energy of carbon-12’s
nucleus?
A neutron has a mass of 1.0087 u
and a proton has a mass of 1.0073 u.
1 u = 1.66×10í^27 kg.
Answer:mass excess = u
binding energy = J
38.11 - Binding energy curve
The binding energy is a measure of stability for a nucleus, since the binding energy is
how much energy it takes to completely disassemble a nucleus. Roughly speaking, the
higher the binding energy, the harder it is to pull all the nucleons apart.
However, determining which nuclides are stable is not as simple as calculating the
binding energy. In this section, we discuss how the stability of a nuclide can be
determined.
We will use two nuclides as examples: (iron-56), and (uranium-235).
Using a table of nuclear data, one may find that the binding energy of an iron-56 atom,
which has 26 protons and 30 neutrons, is 492 MeV. The binding energy of a uranium-
235 atom (Z = 92,N = 143) is 1784 MeV.
Does this mean that the uranium nucleus is more stable since it has a greater binding
energy? Not necessarily. To compare the stability of different nuclei, a useful number to
consider is the binding energy per nucleon. To calculate this ratio, divide the binding
energy of the nucleus by the mass number, the total number of protons and neutrons.
This provides a metric to compare the binding energy per nucleon in the iron isotope
with the binding energy per nucleon in uranium.
The binding energy per nucleon in uranium-235 is 7.59 MeV and the binding energy per
nucleon in iron-56 is 8.79 MeV. The binding energy per nucleon is a good measure for
stability; the fact that the binder energy per nucleon is higher for iron than uranium
correctly predicts that iron-56 is more stable than uranium-235. (In fact, the binding
energy per nucleon for iron-56 is among the highest for all nuclides.)
The graph in Concept 2 shows the binding energy per nucleon for naturally occurring
isotopes, plotted against the mass number A. This is called the binding energy curve.
Stability and binding energy
Stability determined by binding energy
per nucleonGraph of binding energy per
nucleon versus mass number
Graph peaks near iron-56