The mass of any nucleus is not the sum of its constituent protons and neutrons.

Mass defect  : The difference between the mass of the nucleus and the sum of mass of constituent protons and neutrons is called Mass defect of the nucleus.

Binding Energy : If we wanted to separate each proton and neutron in nucleus , we would need to provide the extra missing mass (mass defect) in some form of energy. Since this mass defect keeps the nucleus bound together , and an equivalent of it is to be provided to separate it completely, it is also called binding energy.

For example , to form a deuterium – a proton and neutron is required in the nucleus.

• mass of proton (m_p) = 1.00727u
• mass of neutron (m_n) = 1.008665u
• mass of deuterium nucleus = 2.013553u
• Thus mass defect = 1.00727u + 1.008665u – 2.013553u = 0.002388u

Note : 1 atomic mass unit,u = 1.661 x 10^-27 kg.

To split open a deuterium atom nucleus, this extra mass needs to be provided. On the other hand , when the nucleus forms this mass is released as energy.

• Whenever, the product of nuclear transmutation have a higher binding energy than the original constituents, the mass defect is released as energy.
• Einstein’s equation : The mass defect and binding energy are related by Albert Einstein’s formula, E = mc². In 1905, Einstein developed the special theory of relativity. One of the implications of this theory was that matter and energy are interchangeable with one another.
• Thus if mass defect is denoted as , then the binding energy associated with it is :

Extract from Physics Stage 6 Syllabus © 2017 NSW Education Standards Authority (NESA)