22.0 Radioactivity – Complete Study Sheet

22.0 RADIOACTIVITY

Radioactivity is the spontaneous emission of particles or energy from the nucleus of an unstable atom. This phenomenon, discovered by Henri Becquerel and studied by Marie Curie, reveals the hidden power within atoms. This chapter explores the three main types of radiation, the concept of half-life, nuclear reactions (fission and fusion), and the applications and hazards of radioisotopes in medicine, industry, and energy production.

22.1 ALPHA, BETA, AND GAMMA RADIATIONS

Unstable atomic nuclei undergo radioactive decay by emitting one or more types of radiation. The three main types are alpha (α), beta (β), and gamma (γ) radiation. They differ in nature, penetrating power, ionizing ability, and behavior in electric and magnetic fields.

22.1.1 Alpha (α) Radiation

Nature: A helium nucleus consisting of 2 protons and 2 neutrons (⁴₂He).
Charge: +2 (positive).
Mass: 4 atomic mass units (relatively heavy).
Speed: About 5–7% of the speed of light (slowest of the three).
Penetrating power: Very low – stopped by a sheet of paper or a few centimeters of air. Cannot penetrate human skin (but dangerous if ingested/inhaled).
Ionizing ability: Very high – collides with many atoms along its path, causing ionization. This is why it is highly damaging to living cells.
Effect on nucleus: When an atom emits an alpha particle, its mass number decreases by 4 and its atomic number decreases by 2.
Example: Radium-226 decays to radon-222:
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

22.1.2 Beta (β) Radiation

Nature: A high-energy electron emitted from the nucleus. It is formed when a neutron converts into a proton and an electron (and an antineutrino).
Charge: -1 (negative).
Mass: Very small (same as an electron).
Speed: Up to about 90% of the speed of light.
Penetrating power: Moderate – stopped by a few millimeters of aluminum or a few meters of air. Can penetrate skin but not bone.
Ionizing ability: Moderate – less than alpha but more than gamma.
Effect on nucleus: When an atom emits a beta particle, a neutron becomes a proton. Mass number remains the same, atomic number increases by 1.
Example: Carbon-14 decays to nitrogen-14:
¹⁴₆C → ¹⁴₇N + ⁰₋₁β

22.1.3 Gamma (γ) Radiation

Nature: High-energy electromagnetic radiation (photons) – not particles.
Charge: 0 (neutral).
Mass: No rest mass.
Speed: Speed of light.
Penetrating power: Very high – stopped by thick lead or several centimeters of concrete. Can pass through the human body.
Ionizing ability: Low (but can still damage cells).
Effect on nucleus: No change in mass or atomic number. Gamma emission often accompanies alpha or beta decay as the nucleus loses excess energy.
Example: After beta decay, a nucleus may emit gamma radiation to reach a more stable state:
⁶⁰₂₈Ni* → ⁶⁰₂₈Ni + γ (where * indicates excited state)

22.1.4 Comparison Table

反应反应反应反应反应

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus (⁴₂He)	Electron (⁰₋₁β)	EM radiation (photon)
Charge	+2	-1	0
Mass (relative)	4	1/1836	0
Speed	~5% c	~90% c	c (speed of light)
Penetrating power	Low (paper)	Medium (Al foil)	High (lead/concrete)
Ionizing ability	High	Medium	Low
Deflection in E/B fields	Deflected (opposite to β)	Deflected (opposite to α)	Not deflected

22.2 HALF-LIFE CALCULATIONS

The half-life (t₁/₂) of a radioactive isotope is the time taken for half of the original nuclei in a sample to decay. It is a constant for each isotope, regardless of the sample size or external conditions.

22.2.1 Key Concepts

After one half-life, 50% remains.
After two half-lives, 25% remains.
After n half-lives, fraction remaining = (1/2)ⁿ.
The decay is exponential and random – we cannot predict which atom will decay, but we can predict the behavior of a large sample.

22.2.2 Calculating Half-Life

Method 1: Using fractions

Example: A sample of 32 g of a radioisotope decays to 2 g in 60 days. Find the half-life.

Fraction remaining = 2/32 = 1/16 = (1/2)⁴.
So 4 half-lives have passed in 60 days.
Half-life = 60 / 4 = 15 days.

Method 2: Using the decay formula (for more complex calculations)

N = N₀ × (1/2)ᵗ/ᵀ where N = final amount, N₀ = initial amount, t = time, T = half-life.

Or using logarithms: t/T = log₂(N₀/N).

Worked example: If a radioactive isotope has a half-life of 8 days, how long will it take for a sample to decay to 1/8 of its original mass?

1/8 = (1/2)³ → 3 half-lives.
Time = 3 × 8 = 24 days.

Worked example (using count rate): A Geiger counter records 800 counts per minute for a sample. After 30 minutes, the count rate is 100 counts per minute. What is the half-life?

Fraction remaining = 100/800 = 1/8 = (1/2)³.
3 half-lives = 30 minutes.
Half-life = 10 minutes.

22.3 NUCLEAR EQUATIONS: FISSION VS. FUSION

Nuclear reactions involve changes in the nucleus, releasing enormous amounts of energy compared to chemical reactions.

22.3.1 Nuclear Fission

Fission is the splitting of a heavy nucleus (like uranium-235 or plutonium-239) into two smaller nuclei, accompanied by the release of neutrons and a large amount of energy.

Induced fission: When a neutron is absorbed by U-235, it becomes unstable and splits.
Chain reaction: The neutrons released can trigger further fissions, leading to a self-sustaining chain reaction.
Example:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + energy
(The products vary; many different fission products are possible.)
Applications: Nuclear power plants (controlled fission), nuclear weapons (uncontrolled chain reaction).

22.3.2 Nuclear Fusion

Fusion is the joining of two light nuclei to form a heavier nucleus, releasing even more energy than fission (per unit mass).

Example (proton-proton chain in stars):
²₁H + ³₁H → ⁴₂He + ¹₀n + energy
Conditions required: Extremely high temperatures (millions of degrees) and high pressures to overcome electrostatic repulsion between positively charged nuclei.
Applications: Energy production in stars (including the Sun). Controlled fusion for power generation is a major research goal (ITER project).

22.3.3 Comparison: Fission vs. Fusion

bon

Feature	Fission	Fusion
Process	Heavy nucleus splits	Light nuclei combine
Fuel	Uranium-235, Plutonium-239	Hydrogen isotopes (deuterium, tritium)
Energy released per unit mass	~8 × 10¹³ J/kg	~3 × 10¹⁴ J/kg (higher)
Waste products	Long-lived radioactive waste	Helium (non-radioactive)
Conditions	Room temperature (with critical mass)	Extremely high temperature and pressure
Applications	Nuclear power, weapons	Stars, hydrogen bombs, research

22.4 USES AND DANGERS OF RADIOISOTOPES

22.4.1 Uses of Radioisotopes

Medical applications:
- Cancer treatment (radiotherapy): Gamma rays from cobalt-60 or cesium-137 are used to kill cancer cells.
- Sterilization: Gamma radiation sterilizes medical equipment (syringes, bandages) without heat.
- Tracers: Technetium-99m is used in medical imaging to diagnose organ function (thyroid, bone scans). Iodine-131 is used to study and treat thyroid disorders.
Industrial applications:
- Thickness gauging: Beta radiation monitors thickness of paper, plastic, or metal sheets.
- Non-destructive testing: Gamma radiography inspects welds and pipelines for flaws.
- Smoke detectors: Americium-241 emits alpha particles to ionize air; smoke disrupts the current, triggering the alarm.
Archaeology and geology:
- Carbon-14 dating: Used to determine the age of organic materials (up to ~50,000 years) by measuring remaining ¹⁴C.
- Uranium-lead dating: Used for dating rocks and geological formations.
Power generation:
- Nuclear reactors: Use controlled fission of uranium-235 to produce electricity.

22.4.2 Dangers and Safety Precautions

Health effects: Radiation can ionize atoms in living cells, causing:
- Acute effects: High dose causes radiation sickness (nausea, burns, death).
- Long-term effects: Increased risk of cancer (mutations), genetic damage (inherited defects).
Safety precautions:
- Time: Minimize exposure time.
- Distance: Maximize distance from source (intensity decreases with 1/r²).
- Shielding: Use appropriate shielding (paper for α, Al for β, lead/concrete for γ).
- Containment: Handle radioactive materials in sealed containers; use fume hoods for volatile substances.
- Monitoring: Use dosimeters and Geiger counters to measure exposure.
Nuclear waste: Long-lived radioactive waste from reactors must be stored safely for thousands of years. Disposal methods include deep geological repositories.

✍️ COMPREHENSIVE PRACTICE QUESTIONS

Section A: Short Answer & Definitions

Name the three types of radioactive emissions. Which one has the greatest penetrating power?
Describe the nature, charge, and mass of an alpha particle.
What is the effect of beta decay on the atomic number and mass number of a nucleus?
Why are gamma rays not deflected by electric or magnetic fields?
Define half-life.
A radioactive sample has a half-life of 10 days. What fraction remains after 30 days?
Distinguish between nuclear fission and nuclear fusion.
Write a nuclear equation for the alpha decay of uranium-238 (²³⁸₉₂U).
Write a nuclear equation for the beta decay of carbon-14.
Give two medical uses of radioisotopes and two industrial uses.
List three safety precautions when handling radioactive materials.

Section B: Application & Explanation

Explain why alpha particles are highly ionizing but have low penetrating power.
Why is gamma radiation used to sterilize medical equipment rather than alpha or beta radiation?
A patient receives a dose of iodine-131 to treat thyroid cancer. Explain why iodine-131 is suitable for this purpose and what precautions are taken.
Explain how carbon-14 dating works. What assumptions are made?
Why is it important to store radioactive waste in deep geological repositories?
Explain why nuclear fusion is not yet a practical source of energy on Earth, despite being the power source of the Sun.
Describe how a smoke detector uses alpha radiation to detect smoke.
Why does a Geiger counter record a decreasing count rate over time for a radioactive sample?
Explain why radioactive decay is described as a random process.

Section C: Fill in the Blanks

An alpha particle consists of __________ protons and __________ neutrons.
Beta decay increases the atomic number by __________.
Gamma radiation has no __________ and no __________.
The half-life of a radioisotope is the time for half of the __________ to decay.
After three half-lives, the fraction remaining is __________.
In nuclear fission, a __________ nucleus splits into two smaller nuclei.
Nuclear fusion requires extremely high __________ to overcome electrostatic repulsion.
The isotope used in smoke detectors is __________-241.

Section D: Half-Life Calculations

A radioactive isotope has a half-life of 8 hours. What fraction of the original sample remains after 24 hours?
If a sample starts with 80 mg of a radioisotope and after 20 years only 5 mg remains, what is the half-life?
A Geiger counter measures 1600 counts per minute from a source. After 30 minutes, the count rate is 200 counts per minute. Calculate the half-life.
The half-life of polonium-210 is 138 days. How long will it take for a 100 g sample to decay to 6.25 g?
A sample of radioactive material has an activity of 800 Bq. After 12 days, the activity is 100 Bq. What is the half-life?
Iodine-131 has a half-life of 8 days. If a patient receives a dose containing 40 mg, what mass remains after 24 days?
Calculate the half-life of a radioisotope if 75% of the sample decays in 12 hours. (Hint: 75% decay means 25% remains.)

Section E: Nuclear Equations and Challenge Questions

Complete and balance the following nuclear equations:
- a) ²³⁸₉₂U → ²³⁴₉₀Th + _____
- b) ¹⁴₆C → ¹⁴₇N + _____
- c) ⁶⁰₂₇Co → ⁶⁰₂₈Ni + _____ + γ
- d) ²³⁵₉₂U + ¹₀n → ⁹⁰₃₈Sr + _____ + 3¹₀n
- e) ²H + ³H → ⁴He + _____
A sample of wood found in an ancient tomb has a ¹⁴C activity that is 12.5% of that found in living wood. Given that the half-life of ¹⁴C is 5730 years, how old is the wood?
Explain the concept of critical mass in nuclear fission. Why is it important in nuclear reactors and weapons?
Compare and contrast the advantages and disadvantages of nuclear power (fission) compared to fossil fuels.
Discuss the ethical and environmental considerations surrounding the disposal of high-level nuclear waste.

📝 ANSWERS TO SELECTED QUESTIONS

1. Alpha (α), beta (β), gamma (γ). Gamma has greatest penetrating power.
2. Alpha: helium nucleus, 2 protons + 2 neutrons, charge +2, mass 4.
3. Atomic number increases by 1, mass number unchanged.
4. Gamma rays are EM radiation with no charge; no deflection.
5. Half-life: time for half the nuclei to decay.
6. 30 days = 3 half-lives, fraction = (1/2)³ = 1/8.
7. Fission: splitting heavy nucleus; Fusion: joining light nuclei.
8. ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.
9. ¹⁴₆C → ¹⁴₇N + ⁰₋₁β.
10. Medical: cancer therapy (Co-60), tracers (Tc-99m). Industrial: thickness gauging, smoke detectors (Am-241).
11. Time, distance, shielding.
12. Large mass, charge → many collisions (ionizing) → quickly stopped.
13. Gamma penetrates deeply, kills bacteria without heat; alpha/beta don't penetrate equipment well.
14. Iodine accumulates in thyroid; beta radiation kills thyroid cells; patient isolated to protect others.
15. ¹⁴C/¹²C ratio decreases predictably; assumes constant ¹⁴C production in atmosphere and no contamination.
16. Waste remains hazardous for thousands of years; geological repositories isolate it.
17. Requires extremely high temperatures (millions of degrees) to overcome repulsion.
18. Alpha ionizes air, creating current; smoke particles reduce ionization, current drops, alarm triggers.
19. Random decay; count rate decreases exponentially.
20. Cannot predict which nucleus decays at which moment; only probabilities.
21. 2, 2
22. 1
23. charge, mass
24. nuclei / atoms
25. 1/8
26. heavy
27. temperature
28. americium
29. 24/8 = 3 half-lives → fraction = 1/8.
30. 80 → 40 (1) → 20 (2) → 10 (3) → 5 (4). 4 half-lives = 20 years → half-life = 5 years.
31. 1600 → 800 (1) → 400 (2) → 200 (3). 3 half-lives = 30 min → half-life = 10 min.
32. 100 → 50 (1) → 25 (2) → 12.5 (3) → 6.25 (4). 4 half-lives = 4 × 138 = 552 days.
33. 800 → 400 (1) → 200 (2) → 100 (3). 3 half-lives = 12 days → half-life = 4 days.
34. 24/8 = 3 half-lives. Mass = 40 × (1/2)³ = 40 × 1/8 = 5 mg.
35. 75% decay → 25% remains = 1/4 = (1/2)². 2 half-lives = 12 hours → half-life = 6 hours.
36. a) ⁴₂He; b) ⁰₋₁β; c) ⁰₋₁β; d) ¹⁴³₅₄Xe (or ¹⁴³₅₄Xe); e) ¹₀n.
37. 12.5% = 1/8 = (1/2)³ → 3 half-lives. Age = 3 × 5730 = 17,190 years.
38. Critical mass: minimum mass for self-sustaining chain reaction; crucial for reactor control and weapon design.
39. Nuclear: no CO₂, high energy density, but waste disposal, meltdown risk. Fossil fuels: cheaper infrastructure, but CO₂, pollution, finite.
40. Waste remains hazardous for millennia; need secure storage; ethical responsibility to future generations; accidents could release radioactivity.

These notes are your complete guide to radioactivity. Master the properties of alpha, beta, and gamma radiation, become proficient in half-life calculations, understand the difference between fission and fusion, and appreciate the powerful applications and serious dangers of radioisotopes. This knowledge connects nuclear physics to medicine, energy, and environmental responsibility. Keep learning.

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