Radioactivity & Radioactive Decay

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.

3. Detailed Explanations

A. Alpha, beta and gamma changes

For a parent nuclide AZX:

Alpha decay AZX → A⁻⁴Z₋₂Y + ⁴₂He

Beta (β−) decay AZX → AZ₊₁Y + ⁰₋₁e

Gamma emission AZX* → AZX + 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.

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

1. Use the keywords: random, spontaneous, not affected by external conditions.
2. For decay equations: conserve both A and Z.
3. For GM tube questions: subtract background for net count-rate.

6. Worked Examples

Example 1: Net count-rateCore

Background is 35 cpm. With a source, the meter reads 215 cpm. Find the net count-rate.

Show Answer

Net count-rate = 215 - 35 = 180 cpm.

Example 2: Identify the decayCore

After decay, A decreases by 4 and Z decreases by 2. What type of radiation was emitted?

Show Answer

Alpha radiation.

Example 3: Beta (β−) changeCore

A nuclide undergoes β− decay. What happens to its proton number and nucleon number?

Show Answer

Z increases by 1. A stays the same.

Example 4: Complete an alpha decay equationCore

Complete:

²³⁸₉₂U → ²³⁴₉₀Th + ?

Show Answer

The missing particle has A = 4 and Z = 2, so it is an alpha particle:

⁴₂He

Example 5: Complete a beta (β−) decay equationCore

Complete:

²⁴₁₁Na → ²⁴₁₂Mg + ?

Show Answer

A stays the same and Z increases by 1, so it is β− emission:

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.