Preview
IB DP Physics — Unit E: Nuclear and Quantum Physics | SL & HL | E.3 Radioactive Decay
📋 What You Will Learn
- Observe and describe the random, spontaneous nature of radioactive decay using real-world examples
- Define activity, decay constant, and half-life, and understand the relationships between them
- Derive the exponential decay law and the half-life equation from first principles
- Apply the decay equations to solve graph-based and calculation problems involving activity and number of nuclei
- Analyse activity–time and number–time graphs, extracting half-life and decay constant from graphical data
- Evaluate the nature and sources of background radiation and explain how it affects experimental measurements
🌍 Real-World Context In hospitals around the world, doctors inject patients with radioactive tracers — substances that emit radiation detectable from outside the body. The tracer must be active enough to produce a clear image, yet it must also decay away quickly so the patient is not exposed to prolonged radiation. The medical team relies on a precise understanding of how quickly the radioactive substance loses its activity over time. This rate of decay is not something that can be controlled, sped up, or slowed down — it is a fundamental property of the nucleus itself, and it follows a beautifully predictable mathematical pattern even though each individual decay event is entirely random.
🔍 Guiding Question How does the activity of a radioactive sample change over time, and what does this tell us about the fundamental nature of nuclear decay?
Physical Setup: What Does Radioactive Decay Look Like?
Imagine a sample of radioactive material sitting on a laboratory bench. Inside the sample, unstable nuclei are spontaneously emitting radiation — alpha particles, beta particles, or gamma rays — as they transform into more stable daughter nuclei. You cannot predict which nucleus will decay next, or exactly when any individual nucleus will decay. Yet if you count the number of decays occurring per second using a Geiger–Müller tube and counter, you observe a clear trend: the count rate starts high and gradually decreases over time, following a smooth, curved pattern.
This decreasing count rate reflects the fact that as nuclei decay, there are fewer unstable nuclei remaining to decay in the future. The more nuclei present, the more decays happen per second; as the number of undecayed nuclei falls, so does the rate of decay. This self-reinforcing relationship between the number of nuclei and the rate of decay is the key physical insight that drives everything in this topic.
Notice in the diagram that the count rate curve never actually reaches zero — even when all the original radioactive nuclei have decayed, the detector still registers some counts. This is due to background radiation, which we will address shortly. The smooth exponential shape of the curve is a direct consequence of the probabilistic nature of nuclear decay, and understanding this shape is central to the entire topic.
Background Radiation
Before we can measure the activity of a radioactive source accurately, we must account for the radiation that is always present in the environment, regardless of whether our source is there or not. This ever-present radiation is called background radiation, and it comes from a variety of natural and artificial sources.
📖 Key Definition — Background Radiation Background radiation is the low-level ionising radiation that is always present in the environment, originating from natural sources (such as cosmic rays, radon gas, and radioactive materials in rocks and soil) and artificial sources (such as