## Mass Defect and Binding Energy

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.