The mass of a nucleus is never quite equal to the sums
of the masses of the constituent nucleons (protons and neutrons). It
is a little bit more or a little bit less. The difference between the
mass of a nucleus and the sum of the masses of the nucleons is called
the mass defect. If we assemble a nucleus from scratch it means
bringing together some protons and neutrons from far apart. This
requires work to be done because the positively charged protons repel
one another, while the strong nuclear force which is always
attractive, does not become significant until the protons and
neutrons get very close together. The energy needed to do this work
must come from somewhere. In fact it comes from the masses of the
protons and neutrons that make up the nucleus, from the equation
where
=
the work done to bring the nucleons from far away into close
proximity, measured in Joules
=
the mass defect, measured in kg
the
speed of light in a vacuum.
The binding energy is the amount of work released when
an nucleus is assembled from a few protons and neutrons, or
alternatively, the amount of energy released when a nucleus is
sepated into it's constituent nucleons. The mass defect is thus a
measure of the binding energy, via the relationship
For example, Carbon – 12 is made up of six electrons,
6 protons and six neutrons. The total mass of these isatomic
mass units.
An atom of C – 12 weighsand
1 atomic mass unit is
The mass defect is then
Using the relationshipthis
is equivalent to
The mass defect varies from element to element and atom
to atom. The bigger the mass defect, the more stable the atom.
Systems tend to move in the direction of greater stability. To some
extent, this is what happens during the process of radioactive decay.
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