With the exception of only Hydrogen, the atom of every chemical element contains at least two protons. Since protons all carry a positive charge, they repel each other. For a nucleus to remain stable, energy is needed to overcome the forces of repulsion. This energy is known as the Nuclear Binding Energy.
A more basic summary of the components of the atom is available in the article A Simple Explanation of Atomic Structure.
Where Does Nuclear Binding Energy Come From?
The short answer to this question is that the energy to hold the nucleus together comes from some of the mass of the protons and neutrons in the nucleus. The total mass of the nucleus does not equal the sum of the mass of the protons and neutrons in it, but is slightly less. This "lost" mass is used to provide the energy needed to hold the nucleus together.
How is Nuclear Mass Calculated?
The mass of the proton and neutron are known very accurately. They are:
Neutron: 1.6749286 x 10^(-24) g, and
Proton: 1.6726231 x 10^(-24) g
For every chemical element, the number of protons in the nucleus equals the atomic number. The number of neutrons equals the atomic mass minus the number of protons in it. For example, the element molybdenum has atomic number 42. One of the isotopes of Molybdenum, Mo96, has 54 neutrons.
The expected mass of 1 mole of this nucleus is:
54 x 1.6749286 x 10^(-24) x 6.02214179 x 10^(23) +
42 x 1.6726231 x 10^(-24) x 6.02214179 x 10^(23)
= 96.77360 g
The actual mass of 1 mole of this nucleus, as measured experimentally, is 95.9046785 g.
The mass that is "missing", or used to hold the nucleus together, is the difference between the two numbers, which is 0.86892 g. This represents about 1% of the expected mass.
How is Nuclear Binding Energy Calculated?
Einstein's famous equation from the Theory of Relativity, E = mc^2, is used to convert the mass into energy, where:
E = Energy (Joules),
m = Mass (Kilogrammes), and
c = Speed of light (Metres /sec)
So for 1 mole of this Molybdenum atom, the energy needed is:
0.86892 x 10^(-3) x 299792458^2
= 78 billion kilojoules.
This explains why atomic bombs are so powerful, as the energy stored in the nucleus is extremely high. Releasing even a small proportion of the energy stored within will still yield massive amounts of energy in the form of heat and radiation.
Summary of Nuclear Binding Energy
The protons in the atomic nucleus repel each other as they all carry the same, positive charge. The energy needed to overcome the repulsive forces is large, and it needs of the order of 1% of the nuclear mass to be sacrificed to maintain the nucleus in a stable form. Other nuclei use different percentages.
References for Nuclear Binding Energy
G. Freidlander, J.W. Kennedy, E. S. Macias, J. M. Miller, Nuclear and Radiochemistry. 3rd ed, 1981.
 |
