24.1. Nuclear Radiation http://www.ck12.org
protons, two neutrons, and two electrons. The combined mass of those six particles is 4.03298 amu. The mass of
a helium atom, to the same number of decimal places, is 4.00260 amu. There has somehow been a loss of 0.03038
amu in going from the separated particles to the intact atom. Themass defectof an atom is the difference between
the mass of an atom and the sum of the masses of its protons, neutrons, and electrons.
Nuclear Binding Energy
If mass is lost as an atom forms from its particles, where does the mass go? Albert Einstein showed that mass and
energy are interconvertible according to his famous equation, E = mc^2. In other words, mass can be converted into
energy and energy can be converted into mass. The mass represented by the mass defect undergoes a conversion
to energy upon the formation of an atom from its particles. We can use Einstein’s equation to solve for the energy
produced when a helium atom is formed. First, the mass defect must be converted into the SI units of kilograms.
0 .03038 amu×1 g
6. 0223 × 1023 amu×
1 kg
1000 g
= 5. 0446 × 10 −^29 kgThe energy is then calculated by multiplying the mass in kilograms by the speed of light in a vacuum (c) squared.
The resulting unit of kg•m^2 /s^2 is equal to the energy unit of a joule (J).
E = mc^2 = (5.0446× 10 −^29 kg)(3.00× 108 m/s)^2 = 4.54× 10 −^12 JThis quantity is called thenuclear binding energy, which isthe energy released when a nucleus is formed from its
nucleons. Anucleonis a nuclear subatomic particle (either a proton or a neutron). The nuclear binding energy can
also be thought of as the energy required to break apart a nucleus into its individual nucleons.
Overall, larger nuclei tend to have larger nuclear binding energies, because the inclusion of each additional nucleon
generally results in an additional release of energy. When comparing the stabilities of different nuclei, a more
relevant value than the absolute nuclear binding energy is the nuclear binding energy per nucleon. For example, the
nuclear binding energy per nucleon for helium is 4.54× 10 −^12 J / 4 nucleons = 1.14× 10 −^12 J/nucleon. Nuclear
binding energies per nucleon are shown as a function of mass number in the figure below (Figure24.2).
FIGURE 24.2
Nuclear binding energy as a function of
the number of nucleons in an atom. A
higher nuclear binding energy per nu-
cleon corresponds to a more stable nu-
cleus.Notice that elements of intermediate mass, such as iron, have the highest nuclear binding energies per nucleon and
are thus the most stable.