Preview
IB DP Physics — Unit E: Nuclear and Quantum Physics | SL & HL | E.3 Radioactive Decay
📋 What You Will Learn
- Observe why nuclei hold together despite the electrostatic repulsion between protons, and identify the role of the strong nuclear force
- Define mass defect and binding energy, and explain their physical meaning using Einstein's mass–energy equivalence
- Calculate binding energy and binding energy per nucleon from nuclear masses and atomic mass units
- Interpret the binding energy per nucleon curve and use it to explain why both fission and fusion release energy
- Apply the concept of nuclear stability to predict which nuclei are most stable and why
- Evaluate common misconceptions about binding energy and connect nuclear stability to radioactive decay and nuclear reactions
🌍 Real-World Context The Sun has been burning for approximately 4.6 billion years, releasing an almost incomprehensible amount of energy every second — roughly \( 3.8 \times 10^{26} \) joules per second. This energy does not come from chemical reactions like burning fuel; it comes from something far more fundamental: the conversion of mass into energy deep inside the Sun's core, where hydrogen nuclei are fused together to form helium. The fact that a tiny change in nuclear mass — far less than the mass of a grain of sand — can release energy equivalent to thousands of tonnes of TNT tells us that the forces holding atomic nuclei together are unlike anything we encounter in everyday life.
🔍 Guiding Question What holds the nucleus together, and why does the assembly of nucleons release energy — and how does this explain both the power of the Sun and the destructive force of nuclear weapons?
Physical Setup: Inside the Nucleus
To understand nuclear stability, we must first appreciate the extraordinary challenge the nucleus faces. Packed into a region roughly \( 10^{-15} \) m across — about 100,000 times smaller than the atom itself — are protons and neutrons. Protons carry positive electric charge, and like charges repel. So why does the nucleus not simply fly apart?
The answer lies in a force that is not part of our everyday experience: the strong nuclear force. This force acts between all nucleons (protons and neutrons alike), is attractive at short range, and is far more powerful than the electrostatic repulsion between protons — but only over distances of about \( 10^{-15} \) m. Beyond that range, it drops to essentially zero.
Notice from the diagram that the strong nuclear force dominates at very short separations — the distances between neighbouring nucleons inside the nucleus. The electrostatic repulsion, while always present between protons, is overcome by the strong force at these tiny scales. This balance between attraction and repulsion determines whether a nucleus is stable or unstable.
The Strong Nuclear Force
Before we can discuss binding energy, we need to understand the properties of the strong nuclear force in detail. Unlike gravity or electrostatic force, the strong force does not follow a simple inverse-square law, and it behaves in ways that are initially surprising.
📖 Key Definition — The Strong Nuclear Force The strong nuclear force is a short-range attractive force that acts between all nucleons (protons and neutrons). It is charge-independent (acts equally between p–p, p–n, and n–n pairs), has a range of approximately \( 3 \times 10^{-15} \) m (3 fm), and is approximately 100 times stronger than the electrostatic force at nuclear distances. At separations below about 0.5 fm, it becomes repulsive, preventing nucleons from merging.
The short range of the strong force has a