Radioactivity & Radioactive Decay
Understand radioactive decay: random and spontaneous, how alpha/beta/gamma change A and Z, and how to subtract background count-rate in exam questions (O Level).
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The core idea
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Learning objectives
- Explain random and spontaneous nuclear decay
- Describe alpha, beta-minus and gamma radiation
- Use nuclide equations for radioactive decay
- Explain background radiation
1. Definition
Radioactivity is the spontaneous emission of ionising radiation from an unstable nucleus.
2. Key Ideas
- Radioactive decay is:
- random (cannot predict which nucleus decays next)
- spontaneous (no external trigger needed)
- not affected by temperature, pressure, or chemical state
- Parent nucleus → daughter nucleus.
- Emissions and how A and Z change:
- alpha ⁴₂He: A-4, Z-2
- beta (β−) ⁰₋₁e: A same, Z + 1
- gamma ⁰₀γ: A and Z unchanged (energy release)
- In measurements, subtract background count-rate to get the net count-rate due to the source.
You should be able to describe radioactive decay as random and spontaneous, track how A and Z change in alpha, beta-minus and gamma emission, and account for background radiation.
3. Detailed Explanations
A. Alpha, beta and gamma changes
For a parent nuclide ^A_ZX:
Alpha decay ^A_ZX → ^(A-4)_(Z-2)Y + ⁴₂He
Beta (β−) decay ^A_ZX → ^A_(Z + 1)Y + ⁰₋₁e
Gamma emission ^A_ZX* → ^A_ZX + ⁰₀γ
Gamma often happens after alpha or beta when the nucleus has excess energy.
In beta-minus decay, a neutron in the nucleus changes into a proton and a beta-minus particle is emitted. This explains why A is unchanged while Z increases by one. At this level, balance the stated nuclear equation using A and Z; additional particles used in more advanced models are outside this calculation method.
Properties (penetrating/ionising/deflection): Alpha/Beta/Gamma Characteristics.
B. Background radiation and net count-rate
Background radiation is present even when the test source is removed. Sources include cosmic rays and radioactive materials in rocks, air and building materials. A GM tube records source contribution + background, so use:
net count-rate = measured count-rate-background count-rate
4. Common Mistakes
- Saying decay is “caused by heating/pressure” (it is not).
- Forgetting gamma does not change A or Z.
- Mixing up alpha vs beta changes (alpha: A-4, Z-2; beta: A same, Z + 1).
- Saying random means the sample has no predictable pattern. Individual decays are unpredictable, but a large population follows a predictable statistical trend.
5. Exam Tips
- Use the keywords: random, spontaneous, not affected by external conditions.
- For decay equations: conserve both A and Z.
- For GM tube questions: subtract background for net count-rate.
6. Worked Examples
Modelled example 1
Net count-rate
Problem
Study the worked solution
Identify the measured total
Method
Recognise that 215 cpm includes source and background.Reason
The detector records environmental background even with the source present.Working
Measured = source contribution + background.Subtract background
Method
Subtract 35 from 215.Reason
This isolates the count-rate attributable to the source.Working
net rate = 215-35 = 180 cpm
Guided practice 2
Identify the decay
Problem
Match both nuclear-number changes
Hints
Hint 1: particle values
Hint 2: identity
View solution step by step
Infer the missing particle
Method
Identify alpha radiation.Reason
An alpha particle carries away two protons and two neutrons.Working
Δ A = -4, Δ Z = -2 ⇒ ⁴₂He
Common misconception 3
Beta (β−) change
Learner response
Balance the emitted electron's Z = -1
View solution step by step
Track nucleon number
Method
Keep A unchanged.Reason
A neutron changes into a proton within the nucleus; the beta particle has A = 0.Working
Δ A = 0Track proton number
Method
Increase daughter Z by 1.Reason
The daughter plus emitted electron must retain the parent’s total Z: (Z + 1) + (-1) = Z.Working
Δ Z = +1
Examiner practice 4
Complete an alpha decay equation
Examination question
Balance both conserved totals
View solution step by step
Find missing values
2 marksMethod
Subtract daughter A and Z from parent values.Reason
The missing emission completes both conserved totals.Working
A = 238-234 = 4, Z = 92-90 = 2Name the emission
1 markMethod
Write an alpha particle.Reason
A = 4, Z = 2 identifies a helium nucleus.Working
? = ⁴₂He
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark A, Z and particle identity.
Challenge 5
Complete a beta (β−) decay equation
Parent–daughter transfer
Find the particle needed to conserve A and Z
Hints
Hint 1: nucleon balance
Hint 2: proton balance
View solution step by step
Balance the missing values
Method
Assign A = 0 and Z = -1 to the emission.Reason
24 = 24 + 0 and 11 = 12 + (-1).Working
A_particle = 0, Z_particle = -1Identify beta-minus
Method
Write ⁰₋₁e.Reason
Those nuclear-equation values represent a beta-minus electron.Working
²⁴₁₁Na → ²⁴₁₂Mg + ⁰₋₁e
7. Mind Stretchers
Mind stretcher 1: Random but predictable?Extension
If decay is random, why can we still predict half-life behaviour for a large sample?
Show Answer
While individual nuclei decay randomly, a large sample contains many nuclei, so the average behaviour becomes predictable (a steady fraction decays per half-life).
Mind stretcher 2: Why external conditions don’t matterExtension
Radioactive decay is not affected by temperature or pressure. Why?
Show Answer
Because radioactive decay is a nuclear process inside the nucleus. Temperature, pressure and chemical reactions mainly affect electrons outside the nucleus, so they do not change the stability of the nucleus.
8. Practice and next step
Compare random trial runs and background-corrected readings in the Radioactivity & Half-Life Explorer, then study the Characteristics of Alpha, Beta and Gamma.