Lesson 5.3
Nuclear Energy
Nuclear binding energy and the mass defect
A neutron has a slightly larger mass than the proton. These are often given in terms of an atomic
mass unit, where one atomic mass unit (u) is defined as 1/12th of the mass of a carbon12 atom.
Is there something odd here? The carbon12 atom has a mass of 12.000 u, and yet it contains 12
objects (6 protons and 6 neutrons) that each has a mass greater than 1.000 u. The fact is that
these six protons and six neutrons have a larger mass when they're separated than when they're
bound together into a carbon12 nucleus.
This is true for all nuclei, that the mass of the nucleus is a little less than the mass of the
individual neutrons and protons. This missing mass is known as the
mass defect
, and is
essentially the equivalent to the energy that binds the nuclear particles together called the
binding energy.
This is a measure of the energy that is needed to take the nucleus particles
apart. Einstein's famous equation
E = mc
2
establishes the equivalency of mass and energy.
If you convert some mass to energy, Einstein's equation tells you how much energy you get. In
any nucleus there is some binding energy, the energy you would need to put in to split the
nucleus into individual protons and neutrons. To find the binding energy, then, all you need to do
is to add up the mass of the individual protons and neutrons and subtract the mass of the nucleus.
If
∆
m is the mass defect, then
∆
m = total mass of individual nucleon – the mass of the nuclesu
The binding energy is then:
Binding energy =
∆
m c
2
In a typical nucleus the binding energy is measured in MeV (million electron volts), considerably
larger than the few eV associated with the binding energy of electrons in the atom. Nuclear
reactions involve changes in the nuclear binding energy, which is why nuclear reactions give you
much more energy than chemical reactions; those involve changes in electron binding energies.
To judge the relative stability of nuclei, binding energy per nucleon is a better measure than
absolute energy since large nuclei always have more binding energy than smaller ones. The
following figure illustrates how binding energy per nucleon depends on the mass of a nucleus.
The binding energy per nucleon varies widely from element to element. For hydrogen and
helium it is very low, for iron it is at a maximum, and for elements beyond iron it decreases.
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View Full DocumentThe graph of binding energy per nucleon suggests that nuclides with a mass number larger than
about 230 amu should spontaneously split apart to form
lighter, more stable, nuclides. Such a
process is called
nuclear fission
. Experimentally, we find that spontaneous fission reactions
occur for only the very heaviest nuclides
those with mass numbers of 230 or more. Even
when they do occur, these reactions are often very slow. The halflife for the spontaneous fission
of
238
U, for example, is 10
16
years, or about two million times longer than the age of our planet!
We don't have to wait, however, for slow spontaneous fission reactions to occur. By irradiating
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 Spring '11
 George
 Physics, Energy, Mass, Nuclear Fission, Nuclear Fusion, Neutron, Light, Binding energy, fission

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