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Radioactivity: Types of Radiation & Half-life

CSEC Physics: Nuclear Processes

Essential Understanding: Radioactivity is the spontaneous disintegration of unstable atomic nuclei, emitting radiation. Understanding the three types of radiation (alpha, beta, gamma) and the concept of half-life is crucial for nuclear physics, medical applications, and radiation safety. Master these concepts to solve decay problems and interpret radioactive graphs.

🔑 Key Skill: Identifying radiation types & properties
📈 Exam Focus: Half-life calculations & graphs
🎯 Problem Solving: Decay equations & safety applications

Types of Radiation: Alpha, Beta, Gamma

α

Alpha Radiation (α)

Composition: Helium nucleus (2 protons + 2 neutrons)

Charge: +2 (positive)

Mass: 4 atomic mass units (heavy)

Penetration: Low (stopped by paper or skin)

Ionizing Power: High (causes intense ionization)

Equation: \( ^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}He \)

β

Beta Radiation (β)

Composition: High-speed electron (β⁻) or positron (β⁺)

Charge: -1 (β⁻) or +1 (β⁺)

Mass: ~1/1836 amu (very light)

Penetration: Medium (stopped by aluminum or plastic)

Ionizing Power: Medium

Equation (β⁻): \( ^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}e + \bar{\nu} \)

γ

Gamma Radiation (γ)

Composition: High-energy electromagnetic wave (photon)

Charge: 0 (neutral)

Mass: 0 (massless)

Penetration: High (requires thick lead or concrete)

Ionizing Power: Low (but dangerous due to penetration)

Equation: \( ^{A}_{Z}X^{*} \rightarrow ^{A}_{Z}X + \gamma \)

½

Half-life (t½)

Definition: Time taken for half of radioactive nuclei to decay

Key Property: Constant for a given radioactive isotope

Equation: \( N = N_0 \times \left(\frac{1}{2}\right)^{t/t_{½}} \)

Graph: Exponential decay curve (always decreasing)

Applications: Carbon dating, medical tracers, nuclear power

Radioactive Decay Formulas

These equations are fundamental to radioactivity calculations:

\[ N = N_0 \times \left(\frac{1}{2}\right)^{n} \quad \text{where } n = \frac{t}{t_{½}} \]
\[ \text{Activity} = \lambda N \quad \text{where } \lambda = \frac{\ln(2)}{t_{½}} \]

Activity (measured in Becquerels, Bq) is the rate of decay: 1 Bq = 1 decay per second.

Interactive Radioactivity Simulator

☢️ Interactive Simulator
Alpha - Heavy, stopped by paper
Beta - Fast, stopped by aluminum
Gamma - Waves, stopped by lead
💡 Learn: Click materials to add shields, then fire different radiation types to see what stops them!
Half-life Speed: 2.0s
0.0
Time (seconds)
50
Atoms Left
100%
Remaining
0.0
Half-lives
💡 Learn: Watch atoms randomly decay over time! After each half-life, exactly half of the remaining radioactive atoms decay.

Radiation Properties Comparison

Analysis: The chart compares key properties of the three radiation types. Note the trade-offs: Alpha has high ionizing power but low penetration, while Gamma has low ionizing power but extremely high penetration.

Property Alpha (α) Beta (β) Gamma (γ)
Nature Helium nucleus (2p⁺ + 2n⁰) High-speed electron/positron Electromagnetic wave (photon)
Charge +2 -1 (β⁻) or +1 (β⁺) 0 (neutral)
Mass 4 amu (heavy) ~1/1836 amu (light) 0 (massless)
Penetration Paper/skin (few cm in air) Aluminum/plastic (few mm) Lead/concrete (many cm)
Ionizing Power Very High Medium Low
Speed ~10% of light speed ~90% of light speed Speed of light (c)
Deflection in Field Small deflection (heavy) Large deflection (light) No deflection (neutral)
Health Risk Dangerous if inhaled/ingested Skin burns, internal damage Whole body penetration

Radiation Penetration Demonstration

Select a radiation type to see what materials can stop it:

α

Alpha Radiation

Stopped by:

  • Sheet of paper
  • Human skin (outer layer)
  • Few cm of air
External: Low Risk
Internal: High Risk
β

Beta Radiation

Stopped by:

  • Aluminum foil (few mm)
  • Plastic shielding
  • Glass
External: Medium Risk
Internal: High Risk
γ

Gamma Radiation

Stopped by:

  • Thick lead (several cm)
  • Dense concrete
  • Water (several meters)
External: High Risk
Internal: High Risk

Safety Rule:

ALARA Principle (As Low As Reasonably Achievable): Minimize exposure time, maximize distance from source, and use appropriate shielding based on radiation type.

Half-life Calculator & Graphs

Half-life Calculator

Calculate the remaining radioactive material after a given time:

After 30 days (3 half-lives), 12.5g of the original 100g remains (12.5%).

Half-life Graph Patterns

Radioactive decay follows predictable graphical patterns:

Exponential Decay

The number of remaining atoms decreases exponentially with time: \( N = N_0 e^{-\lambda t} \)

Constant Half-life

Half-life is constant regardless of how much material remains or how long it has been decaying.

Activity Decay

Activity (decays per second) also follows the same exponential decay pattern as the number of atoms.

Worked Examples & Past Paper Questions

📝

Example 1: Basic Half-life Calculation (CSEC 2019)

Question: A radioactive sample has a half-life of 8 days. If you start with 160g of the material, how much remains after 24 days?

1
Determine number of half-lives: 24 days ÷ 8 days/half-life = 3 half-lives
2
Apply half-life formula: Remaining = Initial × (½)n where n = number of half-lives
3
Calculate: Remaining = 160g × (½)3 = 160g × ⅛ = 20g
4
Alternative step-by-step:
After 8 days (1st half-life): 160g → 80g
After 16 days (2nd half-life): 80g → 40g
After 24 days (3rd half-life): 40g → 20g
5
Answer: 20g remains after 24 days.
📝

Example 2: Identifying Radiation Type (CSEC 2021)

Question: A radiation type is deflected toward the positive plate in an electric field, has medium penetration, and is stopped by aluminum. Identify the radiation type and explain your answer.

1
Analyze deflection: Deflected toward positive plate means it has negative charge (opposites attract).
2
Analyze penetration: Medium penetration rules out alpha (low) and gamma (high).
3
Analyze stopping material: Stopped by aluminum confirms beta radiation.
4
Answer: Beta radiation (β⁻). It's negatively charged (deflected toward positive plate), has medium penetration, and is stopped by aluminum.
📝

Example 3: Decay Equation (CSEC 2018)

Question: Uranium-238 decays by alpha emission to form Thorium-234. Write the nuclear equation for this decay.

1
Identify original nucleus: Uranium-238: \( ^{238}_{92}U \)
2
Identify decay product: Thorium-234: \( ^{234}_{90}Th \)
3
Identify emitted particle: Alpha particle: \( ^{4}_{2}He \)
4
Check conservation:
Mass numbers: 238 = 234 + 4 ✓
Atomic numbers: 92 = 90 + 2 ✓
5
Write equation: \( ^{238}_{92}U \rightarrow ^{234}_{90}Th + ^{4}_{2}He \)

Key Examination Insights

Common Mistakes

  • Confusing half-life with the time for all material to decay (it never reaches zero!).
  • Mixing up properties of alpha, beta, and gamma radiation.
  • Forgetting that gamma rays accompany alpha/beta decay (they're emitted from excited nuclei).
  • Not conserving mass and atomic numbers in decay equations.

Success Strategies

  • For half-life problems: Count the number of half-lives first, then use (½)n.
  • Use the mnemonic "A Bit Grumpy" to remember penetration: Alpha (paper), Beta (aluminum), Gamma (lead).
  • Always check conservation laws in decay equations: Mass number and atomic number must balance.
  • Remember: Half-life is constant for a given isotope, regardless of amount or time.

CSEC Practice Arena

Test Your Understanding

1
Which type of radiation has the greatest penetrating power?
Alpha (α)
Beta (β)
Gamma (γ)
All have equal penetration
Explanation: Gamma rays are high-energy electromagnetic waves with no charge and negligible mass, allowing them to penetrate several centimeters of lead or meters of concrete.
2
A radioactive isotope has a half-life of 6 hours. If you start with 800g, how much remains after 18 hours?
400g
200g
100g
50g
Solution: Number of half-lives = 18 ÷ 6 = 3. Remaining = 800g × (½)3 = 800g × ⅛ = 100g.
3
Which radiation type would be deflected the most in a magnetic field?
Alpha (heavy, +2 charge)
Beta (light, -1 charge)
Gamma (no charge)
All deflect equally
Explanation: Beta particles are much lighter than alpha particles (1/1836 the mass) and carry charge, so they experience greater acceleration in magnetic fields and deflect more.
4
What is the main reason gamma rays are dangerous to humans?
They have high ionizing power
They can penetrate deeply into the body
They are positively charged
They have significant mass
Explanation: Gamma rays have low ionizing power but are dangerous because they can penetrate deeply into the body, damaging internal organs and DNA. External alpha radiation is less dangerous because it can't penetrate skin.

Radioactive Decay Chain Explorer

Explore how radioactive elements decay into other elements:

Uranium-238 → Thorium-234 (α decay, 4.5×10⁹ years) → Protactinium-234 (β decay, 24 days) → Uranium-234 (β decay, 2.5×10⁵ years)
🎯

CSEC Examination Mastery Tip

Half-life Graph Interpretation: When given a decay graph in exams:

  • Find half-life: Look for the time it takes for the quantity to drop to half its initial value.
  • Check units: Ensure time units are consistent (don't mix hours with days!).
  • Extrapolate: You can extend the curve to find values beyond the graph.
  • Remember: The curve never reaches zero (asymptotic approach).

For radiation questions, use the "Charge-Mass-Penetration" checklist to identify radiation types systematically.

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