Binding Energy
The total energy required to break up a nucleus into its
constituent protons and neutrons can be calculated from
,
called nuclear binding energy. It we divide the binding energy of a nucleus
by the number of protons and neutrons (number of nucleons), we get the
binding energy per nucleon. This is the common term used to describe
nuclear reactions because atomic numbers vary and total binding energy
would be a relative term dependent upon that. The following figure (adapted
from Beiser), called the binding
energy curve, shows a plot of nuclear binding energy as a function of mass
number.
The peak is at iron (Fe) with mass number equal to 56.
The eventual dropping of the binding energy curve at high mass numbers tells us that nucleons are more tightly bound when they are assembled into two middle-mass nuclides rather than into a single high-mass nuclide. In other words, energy can be released by the nuclear fission, or splitting, of a single massive nucleus into two smaller fragments.
The rising of the binding energy curve at low mass numbers, on the other hand, tells us that energy will be released if two nuclides of small mass number combine to form a single middle-mass nuclide. This process is called nuclear fusion.
Nuclear Masses
Nuclear masses can change due to reactions because this "lost" mass is converted into energy. For example, combining a proton (p) and a neutron (n) will produce a deuteron (d). If we add up the masses of the proton and the neutron, we get
mp + mn = 1.00728u + 1.00867u = 2.01595u
The mass of the deuteron is md = 2.01355u
Therefore change in mass = (mp + mn) - md = (1.00728u + 1.00867u) - (2.01355u) = 0.00240u
An atomic mass unit (u) is equal to one-twelfth of the mass of a C-12 atom which is about 1.66 X 10-27 kg. So, using E=mc2 gives us energy/u = (1.66 X 10-27 kg)(3.00 X 108 m/s)2(1eV/1.6 X 10-19 J) which is about 931 MeV/u. So, our final energy is
The quantity 2.24MeV is the binding energy of the deuteron.