Mass Defect: UNIZOR.COM - Physics4Teens - Atoms - Fission

Notes to a video lecture on http://www.unizor.com

Mass Defect

We will discuss a concept and measurement of mass, as related to elementary particles and atoms.

The mass of elementary particles is often measured in atomic mass units (abbreviated as amu or simply u, or Da after John Dalton).
The definition of this unit is related to a notion of having a mass of a proton or a neutron to be close to 1 unit.
Physicists measured a mass of an atom of carbon ¹²C₆ that has 6 protons and six neutrons and decided that 1/12 of this mass is a good unit of mass, so protons and neutrons will have their mass close to 1 unit.

After many experiments the mass of three main elementary particles (proton, neutron and electron) was calculated.
In terms of the atomic mass units (amu) they are:
Proton - 1.0072766 amu
Neutron - 1.0086649 amu
Electron - 0.0005486 amu

Consider now an atom of Deuterium that has 1 proton, 1 neutron and 1 electron ²H¹.
Experiments show that its mass is 2.014102 amu.
The sum of masses of its components is
1.0072766 + 1.0086649 +
+ 0.0005486 = 2.0164901

It appears that the mass of an atom of Deuterium is less than the sum of masses of its components.
Where did the matter go?

Just to be sure, let's do a similar calculation for an atom of Uranium ²³⁸U⁹² that has 92 protons, 146 neutrons and 92 electrons.
Experiments show that its mass is 238.02891 amu.
The sum of masses of its components is
92·1.0072766+146·1.0086649+
+ 92·0.0005486 = 239.9849938

As in the case of Deuterium, the mass of an atom of Uranium is less than the sum of masses of its components.

The answer to this discrepancy is in the most famous formula of the Theory of Relativity
E = m·c²

This formula (that we are using without a proof) connects mass m, energy E stored in it and speed of light in vacuum c.
It states that any object has inner energy needed to keep this object in its state, to preserve it.
Atom contains elementary particles that must stay together to assure the atom's integrity. It requires . Therefore, the energy must be taken from the mass of components to put the atom together.

The difference between the mass of an atom and a sum of masses of its components, so called mass defect, is the source of the energy that maintains the atom's integrity.

In case of Deuterium ²H¹ the mass defect is
2.0164901 − 2.014102 =
= 0.002388 amu

In case of Uranium ²³⁸U⁹² the mass defect is
239.9849938 − 238.02891 =
= 1.95608 amu