Mass defect

Mass defect is the difference in the combined masses of an atom’s components and the measured mass of the atom.

An atom is composed of electrons and nucleons (protons and neutrons). The constituents of its nucleus, the neutrons and positively charged protons, are held together by an energy called the nuclear binding energy, E_binding. In other words, the nuclear binding energy is the minimum energy that is required to split the nucleus into its components and is always a positive number, i.e.

$E_{atom}+E_{binding}=E_{protons}+E_{neutrons}+E_{electrons}\; \; \; \; \; \; \; \; 8$

As energy and mass are related by Einstein’s formula of E = mc², we can rewrite eq8 as:

$m_{atom}c^2+m_{binding}c^2=m_{protons}c^2+m_{neutrons}c^2+m_{electrons}c^2$

$m_{atom}+m_{binding}=m_{protons}+m_{neutrons}+m_{electrons}\; \; \; \; \; \; \; \; 9$

Eq9 shows that the mass of an atom is always less than the sum of its masses of protons, neutrons and electrons, with the exception of ¹H where m_neutrons = 0 and thus m_binding = 0. As this defect in mass (for atoms other than ¹H) is due to the atom’s nuclear binding energy, we refer the mass equivalent of the nuclear binding energy as the mass defect of the atom.

$m_{binding}=m_{defect}$

Hence, mass defect is the difference in the combined masses of an atom’s components and the measured mass of the atom.

$m_{defect}=m_{protons}+m_{neutrons}+m_{electrons}-m_{atom}\; \; \; \; \; \; \; \; 10$

The heavier the atom, that is the more protons and neutrons it has, the greater the mass defect, since a larger amount of binding energy is needed to hold a greater number of positively charged protons and the neutrons together.

As an illustration, if we simply add the subatomic particles of a deuterium atom, we have:

$m_{D,calculated}=m_{protons}+m_{neutrons}+m_{electrons}$

Substituting the values of subatomic masses from the previous article in the above equation, we have: m_{D, calculated} = 2.01648996 u. The value of the relative mass of deuterium that is experimentally determined via mass spectrometry is 2.014104 u. The difference of about 0.00238596 u is due to the mass defect of deuterium.

NExt article: Nuclear binding energy per nucleon

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