🔬 Mass defect is the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons.
💡 Binding energy is the energy equivalent of that mass difference, calculated using Einstein’s famous equation \$E = mc^2\$.
Think of a team of friends (protons + neutrons) who decide to join together to form a stronger bond. When they bond, the team becomes a bit lighter because some of the “extra weight” (energy) is released into the world as light or radiation. That lost weight is the mass defect.
\$\Delta m = M{\text{separate}} - M{\text{nucleus}}\$
Use Einstein’s equation to convert the mass defect into energy:
\$E_b = \Delta m \, c^2\$
Here, \$E_b\$ is the binding energy of the nucleus. It tells us how much energy would be required to break the nucleus apart.
| Item | Value (u) |
|---|---|
| Proton mass (\$m_p\$) | 1.007276 |
| Neutron mass (\$m_n\$) | 1.008665 |
| Number of protons (\$Z\$) | 2 |
| Number of neutrons (\$N\$) | 2 |
| Separate mass (\$M_{\text{separate}}\$) | \$2\times1.007276 + 2\times1.008665 = 4.031882\$ |
| Actual nuclear mass (\$M_{\text{nucleus}}\$) | 4.001506 |
| Mass defect (\$\Delta m\$) | \$0.030376\$ u |
| Binding energy (\$E_b\$) | \$28.3\$ MeV |
• Remember the order of operations: first calculate the separate mass, then subtract the actual nuclear mass to get the mass defect.
• Convert the mass defect to binding energy using \$E = \Delta m\,c^2\$.
• Check units: 1 atomic mass unit (u) ≈ 931.5 MeV/\$c^2\$.
• Practice with different nuclei (e.g., \$^{12}\$C, \$^{56}\$Fe) to see how binding energy per nucleon changes.
• In multiple‑choice questions, look for the answer that matches the magnitude of the binding energy (tens of MeV for light nuclei, hundreds for heavy nuclei).