Module E.3 IBDP SL/HL Track

Radioactive Decay

Model exponential decay rules, half-life probabilities, and alpha, beta, and gamma radiation tracking.

01. Observe 02. Think 03. Apply 04. Achieve Excellence

Radioactive Decay

Introduction

Radioactive decay links nuclear stability, binding energy, random decay, and practical measurement. The guide covers alpha, beta, and gamma changes at SL/HL, then adds exponential decay law and nuclear stability detail at HL.

Guide Focus

  • Use isotopes, binding energy, mass defect, and E = mc^2.
  • Describe alpha, beta minus, beta plus, and gamma decay equations.
  • Apply half-life, activity, background correction, and HL exponential decay.

Key Concepts

1. Isotopes and binding energy

Isotopes have the same proton number but different neutron numbers. Binding energy is the energy required to separate a nucleus into nucleons, and mass defect is linked to binding energy by E = mc^2.

2. Types of radiation

Alpha particles are strongly ionizing and weakly penetrating. Beta particles are moderately penetrating and ionizing. Gamma radiation is weakly ionizing but highly penetrating.

3. Decay equations

Alpha decay reduces A by 4 and Z by 2. Beta minus increases Z by 1 and emits an antineutrino. Beta plus decreases Z by 1 and emits a neutrino. Gamma emission changes energy state without changing A or Z.

4. Half-life and activity

Decay is random and spontaneous, but large samples follow predictable statistics. Activity is rate of decay. HL adds N = N0 e^(-lambda t), A = lambda N, and T1/2 = ln2 / lambda.

Common Mistakes

  • Not subtracting background count rate from measured count rate.
  • Confusing activity with count rate.
  • Treating half-life as the time for all nuclei to decay.

Exam Tips

  • Balance A and Z separately in every nuclear equation.
  • Choose isotopes for applications by matching both penetration type and half-life.
  • Binding energy per nucleon indicates relative nuclear stability.

Practice Questions

Question 1 (Multiple Choice)

After two half-lives, the fraction of undecayed nuclei remaining is:

A. 1/4 B. 1/2 C. 1/8 D. 0

Correct Answer: A

Solution Architecture

Each half-life halves the remaining sample: 1 -> 1/2 -> 1/4.

Question 2 (Structured Paper 2 Style)

A radioactive sample has initial activity 800 Bq and half-life 6.0 hours.

(a) Calculate the activity after 18 hours. [2 marks]

(b) Explain why individual decay events cannot be predicted. [1 mark]

Paper 2 Structured Problem

Markscheme Breakdown

Part (a) Solution:

18 hours is three half-lives, so A = 800 / 2^3 = 100 Bq.

Part (b) Solution:

Radioactive decay is random and spontaneous at the level of individual nuclei.