What is Mass defect and binding energy? — Physics

Definition 33.5 High School Physics · Chapter 33 — Nuclear Energy: Fission, Fusion, E=mc2

Weigh a nucleus ${}^{A}_{Z}\mathrm{X}$ (mass $m$ ), then weigh its $Z$ protons and $A - Z$ neutrons separately: the parts are heavier than the whole. The difference

\Delta m = Z\,m_p + (A - Z)\,m_n - m > 0, \qquad m_p = 1.007\,28\,\mathrm{u},\; m_n = 1.008\,66\,\mathrm{u},

is the mass defect; the binding energy $E_b = \Delta m\,c^2$ is the energy needed to pull the nucleus apart into free nucleons — equally, the energy released when it is assembled. A bound nucleus sits below its parts.

An energy ladder: the bound nucleus lies E_b below its separated nucleons — assembling it releases E_b, dismantling costs it. — An energy ladder: the bound nucleus lies $E_b$ below its separated nucleons — assembling it releases $E_b$ , dismantling costs it.

Examples

Example 33.6 (Helium-4)

The ${}^{4}_{2}\mathrm{He}$ nucleus has $m = 4.001\,51\,\mathrm{u}$ ; its parts: $2 \times 1.00728 + 2 \times 1.00866 = 4.031\,88\,\mathrm{u}$ . So $\Delta m = 0.030\,37\,\mathrm{u}$ and $E_b = 0.03037 \times 931.5 \approx 28.3\,\mathrm{MeV}$ : the nucleus weighs $0.75\%$ less than its parts — the “one part in a thousand” of Example 33.4.

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Examples

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