Binding energy (also called separation energy)
is the minimum energy required to disassemble
a system of particles into separate parts.
This energy is equal to the mass defect - the
amount of energy, or mass, that is released
when a bound system (which typically has a
lower potential energy than the sum of its
constituent parts) is created, and is what
keeps the system together.
If the energy supplied is more than the binding
energy, then the disassembled constituents
possess non-zero kinetic energy.
== General idea ==
In general, binding energy represents the
mechanical work that must be done against
the forces that hold an object together, disassembling
the object into its component parts with enough
distance between them so that further separation
requires negligible additional work.
In bound systems, if the binding energy is
removed from the system, it must be subtracted
from the mass of the unbound system, because
this energy has mass.
Thus, if energy is removed (or emitted) from
the system at the time it is bound, this loss
of energy will also result in the loss of
the system's mass.
The mass of the system is not conserved in
this process because the system is "open"
(i.e., is not an isolated system to mass or
energy input or loss) during the binding process.
There are several types of binding energy,
each operating over a different distance and
energy scale.
The smaller the size of a bound system, the
higher its associated binding energy.
== Types of binding energy ==
== 
Mass-energy relation ==
A bound system is typically at a lower energy
level than its unbound constituents because
its mass must be less than the total mass
of its unbound constituents.
For systems with low binding energies, this
"lost" mass after binding may be fractionally
small, whereas for systems with high binding
energies, the missing mass may be an easily
measurable fraction.
This missing mass may be lost during the process
of binding as energy in the form of heat or
light, with the removed energy corresponding
to the removed mass through Einstein's equation
E = mc2.
In the process of binding, the constituents
of the system might enter higher energy states
of the nucleus/atom/molecule while retaining
their mass, and because of this, it is necessary
that they are removed from the system before
its mass can decrease.
Once the system cools to normal temperatures
and returns to ground states regarding energy
levels, it will contain less mass than when
it first combined and was at high energy.
This loss of heat represents the "mass deficit,"
and the heat itself retains the mass that
was lost (from the point of view of the initial
system).
This mass will appear in any other system
that absorbs the heat and gains thermal energy.For
example, if two objects are attracting each
other in space through their gravitational
field, the attraction force accelerates the
objects, increasing their velocity, which
converts their potential energy (gravity)
into kinetic energy.
When the particles either pass through each
other without interaction or elastically repel
during the collision, the gained kinetic energy
(related to speed) begins to revert into potential
energy, driving the collided particles apart.
The decelerating particles will return to
the initial distance and beyond into infinity,
or stop and repeat the collision (oscillation
takes place).
This shows that the system, which loses no
energy, does not combine (bind) into a solid
object, parts of which oscillate at short
distances.
Therefore, to bind the particles, the kinetic
energy gained due to the attraction must be
dissipated by resistive force.
Complex objects in collision ordinarily undergo
inelastic collision, transforming some kinetic
energy into internal energy (heat content,
which is atomic movement), which is further
radiated in the form of photons - the light
and heat.
Once the energy to escape the gravity is dissipated
in the collision, the parts will oscillate
at a closer, possibly atomic, distance, thus
looking like one solid object.
This lost energy, necessary to overcome the
potential barrier to separate the objects,
is the binding energy.
If this binding energy were retained in the
system as heat, its mass would not decrease,
whereas binding energy lost from the system
as heat radiation would itself have mass.
It directly represents the "mass deficit"
of the cold, bound system.
Closely analogous considerations apply in
chemical and nuclear reactions.
Exothermic chemical reactions in closed systems
do not change mass, but do become less massive
once the heat of reaction is removed, though
this mass change is too small to measure with
standard equipment.
In nuclear reactions, the fraction of mass
that may be removed as light or heat, i.e.,
binding energy, is often a much larger fraction
of the system mass.
It may thus be measured directly as a mass
difference between rest masses of reactants
and (cooled) products.
This is because nuclear forces are comparatively
stronger than the Coulombic forces associated
with the interactions between electrons and
protons that generate heat in chemistry.
=== Mass change ===
Mass change (decrease) in bound systems, particularly
atomic nuclei, has also been termed mass defect,
mass deficit, or mass packing fraction.The
difference between the unbound system calculated
mass and experimentally measured mass of nucleus
(mass change) is denoted as Δm.
It can be calculated as follows:
Mass change = (unbound system calculated mass)
− (measured mass of system)
i.e., (sum of masses of protons and neutrons)
− (measured mass of nucleus)After a nuclear
reaction occurs that results in an excited
nucleus, the energy that must be radiated
or otherwise removed as binding energy in
order to decay to the unexcited state may
be in one of several forms.
This may be electromagnetic waves, such as
gamma radiation; the kinetic energy of an
ejected particle, such as an electron, in
internal conversion decay; or partly as the
rest mass of one or more emitted particles,
such as the particles of beta decay.
No mass deficit can appear, in theory, until
this radiation or this energy has been emitted
and is no longer part of the system.
When nucleons bind together to form a nucleus,
they must lose a small amount of mass, i.e.,
there is a change in mass to stay bound.
This mass change must be released as various
types of photon or other particle energy as
above, according to the relation E = mc2.
Thus, after the binding energy has been removed,
binding energy = mass change × c2.
This energy is a measure of the forces that
hold the nucleons together.
It represents energy that must be resupplied
from the environment for the nucleus to be
broken up into individual nucleons.
The energy given off during either nuclear
fusion or nuclear fission is the difference
of the binding energies of the "fuel," i.e.
the initial nuclide(s), from that of the fission
or fusion products.
In practice, this energy may also be calculated
from the substantial mass differences between
the fuel and products, which uses previous
measurements of the atomic masses of known
nuclides, which always have the same mass
for each species.
This mass difference appears once evolved
heat and radiation have been removed, which
is required for measuring the (rest) masses
of the (non-excited) nuclides involved in
such calculations.
== See also ==
Bond energy and bond-dissociation energy
Gravitational binding energy
Ionization energy (binding energy of one electron)
Nuclear binding energy
Quantum chromodynamics binding energy
Semi-empirical mass formula
Separation energy (binding energy of one nucleon)
Virial mass
Prout's hypothesis, an early model of the
atom that did not account for mass defect
