Radioactivity Maths & Applications

OCR Applied Science • Interactive Teaching Resource • Board Friendly Edition

1. Fundamentals of Radioactivity

Key Ideas

  • Radioactive decay is spontaneous and random.
  • We cannot predict when ONE nucleus will decay.
  • We CAN predict behaviour of LARGE numbers of nuclei.
  • Unstable nuclei release radiation to become more stable.

Activity = number of decays per second.

1 Bq = 1 decay per second

Radiation Comparison

Type
Ionising Power
Penetrating Power
Alpha
Very High
Low
Beta
Medium
Medium
Gamma
Low
Very High

2. Nuclear Equations Builder

Click the buttons to see how alpha, beta and gamma decay affect nuclei.

Choose a decay type

The example equation and explanation will appear here.

Exam Reminders

  • Mass number MUST balance.
  • Atomic number MUST balance.
  • Alpha = helium nucleus.
  • Beta minus = electron.
  • Gamma changes energy only.
Quick Challenge 1:

Complete this equation:

¹⁴₆C → ¹⁴₇N + ?

Answer: ⁰₋₁e or β⁻. Atomic number increases by 1, mass number stays the same.

Quick Challenge 2:

Complete this alpha decay equation:

²¹⁰₈₄Po → ? + ⁴₂He

Answer: ²⁰⁶₈₂Pb. Subtract 4 from mass number and 2 from atomic number.

3. Half-Life Simulator

Watch how radioactive nuclei decay over time. The graph shows the overall pattern: random individual decays, but a predictable curve.

Live Readout

Undecayed nuclei: 100

Decayed nuclei: 0

Approximate activity: 0 Bq

Time: 0 s

Graph Skill

To find a half-life graphically, pick a value, halve it, then read the time difference.

Example: from 80 undecayed nuclei to 40 undecayed nuclei.

4. Radioactivity Maths

Core Equations

Click each equation for term explanations, a worked example and practice questions.

5. Effective Half-Life Interactive

Definitions

  • Physical half-life: decay of nuclei.
  • Biological half-life: removal from body.
  • Effective half-life: both processes combined.

Important: effective half-life is ALWAYS shorter.

Interactive Example

Physical half-life = 6 h

Biological half-life = 3 h

Effective = 2.0 h

6. Radiation Hazards

Irradiation vs Contamination

Irradiation
Contamination
Key Difference
Exposed to radiation
Radioactive material transferred
Only contamination makes object radioactive

Examples

  • X-ray → irradiation
  • Inhaling radioactive dust → contamination

Biological Effects

  • Radiation ionises atoms.
  • DNA can be damaged.
  • Mutations may occur.
  • Large doses can kill cells.

Direct vs Indirect Ionisation

Direct: radiation hits DNA directly.

Indirect: radiation ionises water to create free radicals.

7. Uses of Radionuclides

Radiopharmaceuticals and Medical Tracers

A radiopharmaceutical is a radioactive substance used in medicine.

A medical tracer is introduced into the body so doctors can follow where it goes. It can show how organs are working, whether blood is flowing properly, or whether a particular tissue is taking up a substance.

The tracer must give useful information while keeping the radiation dose as low as possible.

Medical Tracers Need

  • Usually gamma emitters
  • Short half-life
  • Low ionisation
  • Can escape the body for detection

Choosing the Correct Source

Use
Radiation Needed
Reason
Medical tracer
Gamma
Escapes body
Cancer treatment
Beta/Gamma
Kills cells
Sterilisation
Gamma
Penetrating

8. Exam Practice Quiz

Question 1

Which type of radiation has the greatest ionising power?

Alpha
Beta
Gamma

Question 2

Why is gamma radiation useful for medical tracers?

It is strongly ionising
It escapes the body and can be detected externally
It has mass

Question 3

What happens to activity over time?

It increases exponentially
It decreases exponentially
It stays constant