A nucleus weighs less than its sum of nucleons, a quantity known as
the mass defect, caused by release of energy when the nucleus
formed.
LEARNING OBJECTIVES [ edit ]
Calculate the nuclear binding energy of an atom
Calculate the mass defect of an atom
KEY POINTS [ edit ]
Nuclear binding energy is the energy required to split a nucleusof an atom into its components.
Nuclear binding energy is used to determine whether fission orfusion will be a favorable process.
The mass defect of a nucleus represents the mass of the energy binding the nucleus, and is the
difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is
composed.
TERMS [ edit ]
strong force
The nuclear force, a residual force responsible for the interactions between nucleons, deriving
from the color force.
nucleon
One of the subatomic particles of the atomic nucleus, i.e. aproton or a neutron.
mass defect
The difference between the calculated mass of the unbound system and the experimentally
measured mass of the nucleus.
Give us feedback on this content: FULL TEXT [edit ]
Binding Energy
Nuclear binding energy is the energy
required to split a nucleus of an atom into
its component parts: protons and
neutrons, or, collectively, the nucleons.
The binding energy of nuclei is always a
positive number, since all nuclei require
net energy to separate them into
individual protons and neutrons.
Mass Defect
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Nuclear binding energy accounts for a noticeable difference between the actual mass of an
atom's nucleus and its expected mass based on the sum of the masses of its non-bound
components.
Recall that energy (E) and mass (m) are related by the equation:
E = mc
2
Here, c is the speed of light. In the case of nuclei, the binding energy is so great that it
accounts for a significant amount of mass.
The actual mass is always less than the sum of the individual masses of the constituent
protons and neutrons because energy is removed when when the nucleus is formed. This
energy has mass, which is removed from the total mass of the original particles. This mass,
known as the mass defect, is missing in the resulting nucleus and represents the energy
released when the nucleus is formed.
Mass defect (Md) can be calculated as the difference between observed atomic mass (mo) and
that expected from the combined masses of its protons (mp, each proton having a mass of
1.00728 amu) and neutrons (mn, 1.00867 amu):
M d = (m n + m p )
−m
o
Nuclear Binding Energy
Once mass defect is known, nuclear binding energy can be calculated by converting that mass
to energy by using E=mc2. Mass must be in units of kg.
Once this energy, which is a quantity of joules for one nucleus, is known, it can be scaled into
per-nucleon and per-molequantities. To convert to joules/mole, simply multiply by
Avogadro's number. To convert to joules per nucleon, simply divide by the number of
nucleons.
Nuclear binding energy can also apply to situations when the nucleus splits into fragments
composed of more than one nucleon; in these cases, the binding energies for the fragments,
as compared to the whole, may be either positive or negative, depending on where the parent
nucleus and the daughter fragments fall on the nuclear binding energy curve. If new binding
energy is available when light nuclei fuse, or when heavy nuclei split, either of these processes
result in the release of the binding energy. This energy—available as nuclear energy—can be
used to produce nuclear power or build nuclear weapons. When a large nucleus splits into
pieces, excess energy is emitted as photons, or gamma rays, and as kinetic energy, as a
number of different particles are ejected.
Nuclear binding energy is also used to determine whether fission or fusion will be a favorable
process. For elements lighter than iron-56, fusion will release energy because the nuclear
binding energy increases with increasing mass. Elements heavier than iron-56 will generally
release energy upon fission, as the lighter elements produced contain greater nuclear binding
energy. As such, there is a peak at iron-56 on the nuclear binding energy curve.
9
Average binding energy per nucleon (MeV)
O 16
8 C 12
7
6
5
U 235
U 238
Fe 56
He 4
Li 7
Li 6
4
3
H3
He 3
2
2
1 H
1
0 H
0
30
60
90
120
150
180
Number of nucleons in nucleus
210
240
270
Nuclear binding energy curve
This graph shows the nuclear binding energy (in MeV) per nucleon as a function of the number of
nucleons in the nucleus. Notice that iron­56 has the most binding energy per nucleon, making it the most
stable nucleus.
The rationale for this peak in binding energy is the interplay between the
coulombic repulsion of the protons in the nucleus, because like charges repel each other, and
the strong nuclear force, or strong force. The strong force is what holds protons and neutrons
together at short distances. As the size of the nucleus increases, the strong nuclear force is
only felt between nucleons that are close together, while the coulombic repulsion continues to
be felt throughout the nucleus; this leads to instability and hence
the radioactivity and fissile nature of the heavier elements.
Example
Calculate the average binding energy per mole of a U-235isotope. Show your answer in
kJ/mole.
First, you must calculate the mass defect. U-235 has 92 protons, 143 neutrons, and has an
observed mass of 235.04393 amu.
M d = (m n + m p )
−m
o
Md = (92(1.00728 amu)+143(1.00867 amu)) - 235.04393 amu
Md = 1.86564 amu
Calculate the mass in kg:
1.86564 amu x 1 kg
6.02214×10
26
amu
= 3.09797 x 10-27 kg
Now calculate the energy:
E = mc2
E = 3.09797 x 10-27 kg x (2.99792458 x 108
m
s
)2
E =2.7843 x 10-10 J
Now convert to kJ per mole:
2.7843 × 10
−10
J oules
atom
×
6.02×10
23
atoms
mole
×
1 kJ
1000 joules
=
1.6762 x 1011
kJ
mole