PHY094 · Quantum & Nuclear Physics · Class 12 + College
Binding energy
Objective: To calculate the binding energy of a nucleus from its mass defect and compare stability using binding energy per nucleon.
🧰 Apparatus
- (Calculation) data table of nuclear masses
- Calculator
- Graph paper for the E_b/A curve
📐 Formulas and SI units
Δm = Zm_p + Nm_n − M
E_b = Δm c² = Δm (u) × 931.5 MeV
💡 Theory
A nucleus weighs less than its separate protons and neutrons. This mass defect Δm, times c², is the binding energy: the energy needed to pull the nucleus apart (1 u = 931.5 MeV). Binding energy per nucleon peaks near iron-56, so fusing light nuclei or splitting heavy ones releases energy.
🪜 Procedure
- Choose a nucleus and add up the masses of its protons and neutrons.
- Subtract the measured nuclear mass to find Δm.
- Convert to MeV: E_b = Δm × 931.5.
- Divide by the number of nucleons.
- Mark the point on the E_b/A curve and find the most stable nucleus.
📋 Observations Simulated values
✅ Result and conclusion
Helium-4 has Δm = 0.0304 u, so E_b = 28.3 MeV, about 7.08 MeV per nucleon; iron-56 has the highest value (8.79 MeV).
🔬 In a real lab
Measured masses come from mass spectrometers to many decimal places; small rounding changes E_b in the last digit.
⚠️ Safety
A calculation-only activity; no nuclear materials are used.
❓ Quick check
1. The most tightly bound nucleus is near…
2. 1 u of mass defect is about…
3. Fission releases energy because the products have…
🏋️ Practice
EasyΔm = 0.1 u. E_b?
Answer: 93.15 MeV
MediumE_b = 92 MeV for ¹²C. Per nucleon?
Answer: ≈ 7.68 MeV
ChallengeWhich releases energy: fusing ²H or splitting ²H?
Answer: Fusing