Binding energy

Nuclear & Particle Physics - OCR A-Level Physics

Worked Example
Calculate the binding energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energyThe capacity to do work. Measured in joules (J).. multiplied by c². of helium-4 (⁴₂He). Given: mass of proton = 1.00728 u, mass of neutron = 1.00867 u, mass of He-4 nucleus = 4.00151 u. 1 u = 931.5 MeV/c².
Show Solution
1

He-4 has 2 protons and 2 neutrons.

2

Total mass of individual $nucleons = 2(1.00728) + 2(1.00867) = 2.01456 + 2.01734 = 4.03190 u$.

3

Mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. $\Delta m = 4.03190 - 4.00151 = 0.03039 u$.

4
Convert to energy

$E = 0.03039 \times 931.5 = 28.3 MeV.$

5

Binding energyThe energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c². per $nucleon = 28.3 / 4 = 7.07 MeV per nucleon$.

Answer
Binding $energy = 28.3 MeV. Binding energy per nucleonThe binding energyThe energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defect multiplied by c². of a nucleus divided by its nucleon number (mass number). Higher values indicate greater nuclear stability. = 7.07 MeV$.
Nuclear & Particle Physics Overview
In every nuclear reaction 9 of 10 Radioactive decay