23.2 Radioactive Decay

2026 📋 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand that fluctuations in count rate provide evidence for the random nature of radioactive decay
  2. Understand that radioactive decay is both spontaneous and random
  3. Define activity and decay constant, and recall and use A = λN
  4. Define half-life
  5. Use λ = 0.693 / t₁/₂
  6. Understand the exponential nature of radioactive decay, and sketch and use x = x₀e^(–λt), where x can be activity, number of undecayed nuclei, or received count rate

📖 Main Content

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1. What is Radioactive Decay?

Radioactive decay is when an unstable nucleus breaks apart (disintegrates) on its own to become more stable. When this happens, it releases energy and particles — either an alpha particle (α), a beta particle (β), or gamma radiation (γ).

The key word here is unstable. Some nuclei just do not have a stable arrangement of protons and neutrons. To become more stable, they decay.

2. The Random Nature of Radioactive Decay

What does "random" mean?

Radioactive decay is described as a random process. This means:

  • It is impossible to predict which nucleus in a sample will decay next
  • It is impossible to predict exactly when any given nucleus will decay
  • Every nucleus has a fixed probability (a fixed chance) of decaying in any given time period — this probability never changes

Think of it like rolling a dice. You know you have a 1-in-6 chance of rolling a six, but you cannot tell exactly when you will roll a six.

How do we know decay is random? — Fluctuations in Count Rate

A Geiger-Müller (GM) tube is a device used to detect and count radioactive particles. When you place a GM tube near a radioactive source, it records a count rate — the number of particles detected per second.

If decay were a perfectly ordered, predictable process, the count rate would fall smoothly and evenly. But this is not what we observe.

Instead, the count rate fluctuates — it jumps up and down irregularly, even though it generally trends downwards over time. These random fluctuations in the count rate are direct evidence that radioactive decay is random. You cannot predict exactly how many nuclei will decay in any one second.

Key Point: The irregular, unpredictable jumps in the count rate measured by a GM tube are evidence that radioactive decay is a random process.

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