18.2.2 Mass Defect

Let’s use the helium-4 nucleus as an example.

\displaystyle {}_{2}^{4}He

Since He-4 consists of 2 protons and 2 neutrons, its mass is roughly 4u. But look carefully at the data:

Mass of 2 protons and 2 neutrons

\displaystyle \begin{aligned}&=2{{m}_{p}}+2{{m}_{n}}\\&=2(1.008665u+1.007276u)\\&=4.03188u\end{aligned}

Mass of 1 helium-4 nucleus \displaystyle =4.00151u

Did you notice that the mass of a He-4 is smaller than the mass of the 2 protons and 2 neutrons that formed it?

The difference between the mass of a nucleus and the mass of its constituent nucleons is called the mass defect, Dm. In other words, for a \displaystyle {}_{Z}^{A}X nuclide,

\displaystyle \Delta m=(Z{{m}_{p}}+N{{m}_{n}})-{{m}_{X}}

For the He-4,

\displaystyle \displaystyle \begin{aligned}\Delta m&=(2{{m}_{p}}+2{{m}_{n}})-{{m}_{{He}}}\\&=2(1.008665u+1.007276u)-4.00151u\\&=0.03037u\end{aligned}

How do we interpret the mass defect? Consider the system consisting of the 2 protons and neutrons. The system is at a higher energy level when the protons and neutrons are at infinite distances apart, compared to when they are bound together as a helium nucleus[1]. From the mass-energy equivalence principle, the mass defect is merely a reflection of the loss of energy by the system. The mass defects of nuclides have been measured to incredibly high precision and have provided evidence for the mass-energy equivalence principle.

Concept Test 3610

[1] This is similar to the situation of the electron and proton bound in a hydrogen atom, or the Moon and Earth bound to each other; Just like EPE and GPE are negative due to the attractive electrical and gravitational forces, nuclear potential energy is negative due to the attractive nuclear forces.

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