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## Nuclear binding energy and mass defect

The binding energy between the nucleons can be calculated if one uses the Einstein relation of the equivalence of mass and energy as a basis:

- $$\text{E.}=\text{m}\cdot {\text{c}}^{2}\phantom{\rule{2em}{0ex}}\begin{array}{l}\text{E = energy}\\ \text{m = mass}\\ \text{c = speed of light}\end{array}$$

The mass for example one ${}^{4}\text{Hey}$Core would have to be composed of the sum of the masses of two protons and two neutrons:

- $$\begin{array}{l}2{\text{m}}_{\text{p}}=2\cdot \mathrm{1,67265}\cdot {10}^{-24}\text{G}=\mathrm{3,34530}\cdot {10}^{-24}\text{G}\\ 2{\text{m}}_{\text{n}}=2\cdot \mathrm{1,67265}\cdot {10}^{-24}\text{G}=\mathrm{3,34530}\cdot {10}^{-24}\text{G}\\ \\ \phantom{\rule{0.7999999999999999ex}{0ex}}\Rightarrow {\text{m}}_{\text{2p}+\text{2n}}=\mathrm{6,69520}\cdot {10}^{-24}\text{G}\\ \end{array}$$

However, very precise measurements of the mass have shown that the mass of the helium nucleus

- $$\text{m}\left({\phantom{\rule{0.1ex}{0ex}}}^{\text{4}}\text{Hey}\right)=\mathrm{6,6448}\cdot {10}^{-24}\text{G}$$

amounts to. The bulk of the ^{4}So helium core is around 0.0504⋅10^{-24}$\text{G}$ less than the sum of the masses of its core building blocks. This mass difference (mass defect) arises from the fact that when protons and neutrons merge to form a nucleus, a small part of their mass is converted into energy. This energy is released in the form of high-energy radiation (γ-quanta) and also occurs in the form of kinetic energy of the relevant nucleus.

If you want to break such a core down into its core building blocks, exactly this energy has to be used again. The energy is therefore called the nuclear binding energy. The mass defect therefore corresponds exactly to the binding energy of the nucleus via the Einstein relationship.

The larger the mass defect in nucleation, the greater its binding energy.