ECZ GRADE 12 PHYSICS (SYLLABUS 5054)

Radioactivity, Nuclear Decay & Half-Life Mastery

Master nuclear physics in Paper 1 and Paper 2: balancing alpha and beta nuclear equations, calculating half-lives from decay curves, nuclear fission, and radiation safety protocols.

14 Min Read Physics Paper 1 & Paper 2 KaTeX Formulas
Physics Candidate Strategy

Radioactivity is tested in the final questions of Paper 1 (Multiple Choice) and Section A / Section B of Paper 2. Balancing nuclear equations and solving half-life problems are rule-based and straightforward. Master mass number and atomic number conservation to score 100% on these questions.

Teaching Guidance

Emphasize to students that radioactive decay is a spontaneous (unaffected by temperature, pressure, or chemical bonding) and random process (impossible to predict which specific nucleus will decay next). Stress the subtraction of background radiation when interpreting GM tube counts.

Table of Contents

1. Atomic Structure & Nuclide Notation

An atom consists of a dense central nucleus containing positively charged protons and neutral neutrons (collectively termed nucleons), surrounded by orbiting negatively charged electrons. In nuclear physics, we represent any nuclide using standard notation:

$$\large ^{A}_{Z}\text{X}$$
  • $A$ (Mass Number / Nucleon Number): Total number of protons plus neutrons in the nucleus ($A = Z + N$).
  • $Z$ (Atomic Number / Proton Number): Total number of protons in the nucleus (defines the chemical element).
  • Isotopes: Atoms of the same chemical element having the same proton number ($Z$) but different mass numbers ($A$) due to different numbers of neutrons (e.g., $^{12}_6\text{C}$ and $^{14}_6\text{C}$).

2. Alpha ($\alpha$), Beta ($\beta$), and Gamma ($\gamma$) Radiation

Unstable radioisotopes achieve nuclear stability by emitting three distinct types of ionizing radiation:

Property Alpha Particle ($\alpha$) Beta Particle ($\beta$) Gamma Ray ($\gamma$)
Nature Helium nucleus ($^4_2\text{He}$): 2 protons, 2 neutrons. Fast-moving high-energy electron ($^0_{-1}\text{e}$ or $^0_{-1}\beta$). High-frequency electromagnetic wave (photon).
Charge $+2e$ (positive) $-1e$ (negative) Neutral ($0$)
Ionizing Power Very Strong (heavy, strips electrons rapidly). Moderate Weak
Penetrating Power Very Weak: Stopped by a sheet of paper or few cm of air. Moderate: Stopped by 3–5 mm of aluminum sheet. Very Strong: Stopped only by several cm of lead or thick concrete.
Electric/Magnetic Deflection Deflected slightly towards the negative plate. Deflected strongly towards the positive plate. Not deflected (neutral waves).

3. Balancing Radioactive Decay Equations

In all nuclear decay equations, two conservation laws must be strictly satisfied:

  1. Conservation of Mass Number: The sum of top numbers ($A$) on the left side must equal the sum on the right side.
  2. Conservation of Atomic Number: The sum of bottom numbers ($Z$) on the left side must equal the sum on the right side.
Alpha Decay Equation

Mass number decreases by 4; atomic number decreases by 2:

$$^{A}_{Z}\text{X} \longrightarrow ^{A-4}_{Z-2}\text{Y} + ^{4}_{2}\text{He}$$

Example: $^{226}_{88}\text{Ra} \longrightarrow ^{222}_{86}\text{Rn} + ^{4}_{2}\text{He}$

Beta Decay Equation

Mass number unchanged; atomic number increases by 1:

$$^{A}_{Z}\text{X} \longrightarrow ^{A}_{Z+1}\text{Y} + ^{0}_{-1}\text{e}$$

Example: $^{14}_{6}\text{C} \longrightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}$

4. Radioactive Half-Life & Decay Curves

Half-Life ($T_{1/2}$): The time required for half the original number of radioactive nuclei in a sample to decay, or the time for its activity (measured in Becquerels or counts per minute) to drop by 50%.

The Background Radiation Rule:

Whenever an exam question states: "A Geiger-Muller tube records a count rate of 140 counts/min with a background radiation of 20 counts/min," you must subtract background radiation first before calculating half-life:

$$\text{Corrected Count Rate} = 140 - 20 = 120\text{ counts/min}$$

5. Worked Past Paper Half-Life Examination Problems

ECZ Physics Paper 2

Problem: A radioactive isotope has a mass of $80\text{ g}$ and a half-life of 6 hours. Calculate:

  1. The mass remaining after 24 hours. [2 Marks]
  2. The fraction of the original sample that has decayed after 18 hours. [2 Marks]
Step-by-Step Solution:

Part (a): Mass remaining after 24 hours

Number of half-lives elapsed: $$n = \frac{\text{Total Time}}{\text{Half-life}} = \frac{24\text{ hours}}{6\text{ hours}} = 4\text{ half-lives}$$ Step-by-step decay: $$80\text{ g} \xrightarrow{1} 40\text{ g} \xrightarrow{2} 20\text{ g} \xrightarrow{3} 10\text{ g} \xrightarrow{4} 5\text{ g}$$ Or mathematically: $$\text{Remaining Mass} = 80 \times \left(\frac{1}{2}\right)^4 = 80 \times \frac{1}{16} = 5\text{ g}$$ Final Answer: $5\text{ g}$ [2 Marks]

Part (b): Fraction decayed after 18 hours

$$n = \frac{18\text{ h}}{6\text{ h}} = 3\text{ half-lives}$$ Fraction remaining: $$\left(\frac{1}{2}\right)^3 = \frac{1}{8}$$ Fraction that has decayed: $$1 - \frac{1}{8} = \frac{7}{8}$$ Final Answer: $\frac{7}{8}$ (or $87.5\%$) [2 Marks]

6. Nuclear Fission vs Nuclear Fusion

Examiners frequently ask candidates to contrast nuclear fission and fusion:

Feature Nuclear Fission Nuclear Fusion
Process Splitting of a heavy unstable nucleus (e.g., $^{235}\text{U}$) into two lighter nuclei upon absorbing a slow thermal neutron. Joining together of two light nuclei (e.g., Deuterium and Tritium) to form a heavier helium nucleus.
Conditions Required Critical mass and thermal neutron bombardment in a controlled nuclear reactor. Extremely high temperatures (millions of °C) and high pressures to overcome electrostatic repulsion.
Natural Occurrence Does not occur naturally; engineered in nuclear reactors and atomic bombs. Powers the Sun and stars; thermonuclear hydrogen bombs.
Energy Yield Releases immense energy per reaction. Releases significantly more energy per unit mass than fission with minimal long-lived radioactive waste.

7. Applications of Radioisotopes & Safety Precautions

Medical & Industrial Uses
  • Cancer Radiotherapy: Cobalt-60 ($\gamma$-rays) targets and destroys malignant tumor cells.
  • Medical Tracers: Technetium-99m with a short 6-hour half-life tracks blood flow and organ function.
  • Carbon Dating: Measuring $^{14}\text{C}$ to $^{12}\text{C}$ ratios to determine the age of ancient organic archaeological fossils.
  • Industrial Thickness Control: Beta sources monitor the thickness of paper or aluminum sheets in manufacturing mills.
Radiation Safety Rules
  • Store radioactive sources inside thick lead-lined containers.
  • Always handle sources with long metal tongs; never touch with bare hands.
  • Wear protective lead-lined aprons and safety goggles.
  • Wear radiation film badges (dosimeters) to monitor cumulative occupational exposure over time.

8. Frequently Asked Questions

Can chemical reactions alter the half-life of a radioactive sample?

No. Radioactive decay is an intra-nuclear property completely independent of chemical combination, heating, freezing, pressure, or magnetic fields.

What is the difference between nuclear radiation and nuclear contamination?

Radiation is exposure to ionizing rays (like standing in the sun). Contamination occurs when radioactive material physically touches or enters the body or environment (like having radioactive dust on your clothes).

Why are alpha emitters dangerous inside the human body despite low penetrating power?

If inhaled or ingested, alpha particles cannot penetrate out through dead skin cells and instead cause intense localized ionization of internal living tissue, destroying DNA and inducing cancerous mutations.

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