define and use the terms mass defect and binding energy
Mass Defect and Nuclear Binding Energy
🔬 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 $E = mc^2$.
Why Does Mass Defect Happen?
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.
Calculating Mass Defect
- Find the mass of each proton ($m_p$) and neutron ($m_n$).
- Multiply by the number of each in the nucleus: $Z \times m_p$ and $N \times m_n$.
- Sum them: $M_{\text{separate}} = Z\,m_p + N\,m_n$.
- Subtract the actual nuclear mass ($M_{\text{nucleus}}$):
$$\Delta m = M_{\text{separate}} - M_{\text{nucleus}}$$
From Mass Defect to Binding Energy
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.
Example: Helium‑4 Nucleus
| 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 |
Exam Tip 💡
• 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).
Revision
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