Chapter 10: Radioactivity

1. Why This Matters

In 1896, a French scientist named Henri Becquerel was studying uranium salts. He placed them in a drawer with some photographic plates, expecting nothing to happen. When he developed the plates, he was astonished to find that they had been exposed — even though they had never seen sunlight. Something invisible was coming from the uranium. Something that could penetrate solid matter. Marie Curie, who later studied this phenomenon with her husband Pierre, called it radioactivity.

Radioactivity is the spontaneous emission of particles or radiation from unstable atomic nuclei. It is a natural process that has been happening since the birth of the universe. It warms the Earth's interior, powers the stars, and has shaped the evolution of our planet. It is also a powerful tool — used in medicine to diagnose and treat cancer, in industry to test materials, and in archaeology to date ancient objects. But it is also dangerous, and understanding it is essential for using it safely. In this chapter, we are going to explore the fascinating and sometimes frightening world of radioactivity. Let us begin.

I once asked a class, "Is radioactivity natural or man-made?" Most students said man-made. They were surprised to learn that radioactivity is completely natural. It has been part of the Earth since before life existed. The potassium in your body, the carbon in the air, and the rocks beneath your feet all contain radioactive atoms. You are slightly radioactive right now. That is not a reason to be afraid — it is a reason to understand.

2. Learning Objectives

By the end of this chapter, you should be able to:

• Describe the structure of the atom and the nucleus.
• Define radioactivity and explain its origin.
• Describe the three main types of radiation: alpha, beta, and gamma.
• Compare the properties of alpha, beta, and gamma radiation.
• Write and balance nuclear decay equations.
• Define half-life and use it to solve problems.
• Describe the detection of radiation.
• Explain the biological effects and safety precautions for radiation.
• Describe nuclear fission and fusion.
• Describe the uses of radioactivity in medicine, industry, and archaeology.
• Appreciate the importance and dangers of radioactivity in modern life.

3. Concept Build-Up

3.1 The Structure of the Atom

Before we can understand radioactivity, we must understand the structure of the atom. An atom consists of a small, dense nucleus surrounded by a cloud of electrons. The nucleus contains protons and neutrons.

Particle	Charge	Mass (u)	Location
Proton	+1	1.007	Nucleus
Neutron	0	1.009	Nucleus
Electron	−1	1/1836	Orbiting nucleus

Atomic number (Z): The number of protons in the nucleus. It determines the element.

Mass number (A): The total number of protons and neutrons in the nucleus.

Think of the nucleus as a tiny, dense ball at the centre of the atom. It contains almost all the mass of the atom but takes up only a tiny fraction of its volume. If the atom were a football stadium, the nucleus would be a pea at the centre. The rest is empty space filled by the electron cloud.

The nucleus is a remarkable thing. It contains positively charged protons packed closely together. According to Coulomb's Law, they should repel each other violently. Why do they not fly apart? Because of the strong nuclear force — an incredibly powerful force that acts over very short distances and holds the nucleus together. Understanding this force is key to understanding radioactivity.

3.2 Isotopes

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. In other words, they have the same atomic number but different mass numbers.

Examples of isotopes:

Isotope	Protons	Neutrons	Mass Number	Stability
Carbon-12	6	6	12	Stable
Carbon-13	6	7	13	Stable
Carbon-14	6	8	14	Radioactive
Uranium-235	92	143	235	Radioactive
Uranium-238	92	146	238	Radioactive

Most elements have several isotopes. Some are stable; others are radioactive. The stability of a nucleus depends on the ratio of protons to neutrons.

Think of isotopes as siblings. They are from the same family (same element) but have different personalities (different stability). Some are calm and stable; others are restless and radioactive.

Carbon-14 is one of the most famous isotopes. It is radioactive and is used to date ancient objects. All living things absorb carbon-14 while they are alive. When they die, the carbon-14 begins to decay. By measuring how much is left, we can determine how long ago the organism died. This is radiocarbon dating, and it has revolutionised archaeology.

3.3 What Is Radioactivity?

Radioactivity is the spontaneous emission of particles or radiation from an unstable atomic nucleus. It occurs when the nucleus has too much energy or an unstable ratio of protons to neutrons.

Key points about radioactivity:

• It is a random process — we cannot predict when a particular nucleus will decay.
• It is a spontaneous process — it does not require any external energy.
• It is unaffected by temperature, pressure, or chemical state.
• It transforms one element into another (transmutation).
• It releases energy in the form of radiation.

Think of an unstable nucleus as a tower of blocks that is just barely balanced. At any moment, it might collapse. You cannot predict exactly when, but you can describe the probability. That is radioactivity — random, spontaneous, and transformative.

Property	Description
Random	Cannot predict when a specific nucleus will decay
Spontaneous	Does not need external energy
Unaffected by external conditions	Temperature, pressure, and chemistry do not affect it
Transformative	Changes one element into another
Energy-releasing	Releases radiation

The randomness of radioactive decay is one of the deepest ideas in physics. It is not that we are ignorant of some hidden variable — the universe itself is probabilistic at this level. This is a fundamental feature of quantum mechanics. Einstein famously said, "God does not play dice," but experiments have shown that the universe does indeed play dice.

3.4 Types of Radiation

There are three main types of radiation emitted by radioactive nuclei: alpha (α), beta (β), and gamma (γ).

Type	Nature	Charge	Mass	Symbol
Alpha (α)	Helium nucleus (2 protons + 2 neutrons)	+2	4 u	42He
Beta (β)	Fast-moving electron	−1	1/1836 u	0−1e
Gamma (γ)	High-energy electromagnetic wave	0	0	γ

Alpha decay: The nucleus emits an alpha particle, reducing its mass number by 4 and its atomic number by 2.

Beta decay: The nucleus emits a beta particle (electron), increasing its atomic number by 1. A neutron is converted into a proton and an electron.

Gamma decay: The nucleus releases excess energy as gamma radiation without changing its mass number or atomic number.

Notice how each type of decay changes the nucleus differently. Alpha decay reduces both mass number and atomic number. Beta decay increases atomic number without changing mass number. Gamma decay changes neither. By writing and balancing these equations, you can identify the products of radioactive decay.

3.5 Properties of Alpha, Beta, and Gamma Radiation

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus	Electron	Electromagnetic wave
Charge	+2	−1	0
Mass	4 u	1/1836 u	0
Speed	~5% of c	Up to 99% of c	c (speed of light)
Penetrating power	Low (stopped by paper)	Moderate (stopped by aluminium)	High (stopped by lead)
Ionising power	High	Moderate	Low
Deflected by electric/magnetic fields?	Yes	Yes	No
Range in air	~5 cm	~1 m	Very far

Key relationships:

• Ionising power: Alpha > Beta > Gamma
• Penetrating power: Gamma > Beta > Alpha
• This is an inverse relationship: the more ionising a radiation is, the less penetrating it is.

Think of it this way: alpha particles are big and slow. They collide with many atoms and lose their energy quickly, so they are highly ionising but do not penetrate far. Gamma rays are small and fast. They pass through most materials without interacting, so they are highly penetrating but weakly ionising.

The inverse relationship between ionising power and penetrating power is one of the most important ideas in radioactivity. Alpha radiation is dangerous if inhaled or ingested because it deposits all its energy in a small area of tissue. Gamma radiation is dangerous because it can pass through the body and damage cells deep inside. Each type of radiation has its own dangers and its own uses.

3.6 Nuclear Decay Equations

When a nucleus decays, the total mass number and total atomic number must be conserved. We can write equations to represent these changes.

Example 1: Alpha decay of uranium-238

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Check: Mass number 238 = 234 + 4. Atomic number 92 = 90 + 2.

Example 2: Beta decay of carbon-14

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Check: Mass number 14 = 14 + 0. Atomic number 6 = 7 − 1.

Example 3: Gamma decay of an excited nucleus

⁶⁰₂₇Co* → ⁶⁰₂₇Co + γ

Check: Mass number and atomic number unchanged.

Decay Type	Change in Mass Number	Change in Atomic Number
Alpha	−4	−2
Beta	0	+1
Gamma	0	0

Balancing nuclear equations is a skill that improves with practice. Always check that the total mass number and total atomic number are the same on both sides. This is conservation of nucleons — the total number of protons and neutrons is conserved (except for the beta particle, which is created from a neutron).

3.7 Half-Life

The half-life of a radioactive substance is the time taken for half of the radioactive nuclei in a sample to decay. It is a measure of how quickly a substance decays.

Examples of half-lives:

Isotope	Half-Life	Use
Uranium-238	4.5 billion years	Dating rocks
Carbon-14	5 730 years	Dating organic material
Radon-222	3.8 days	Medical treatment
Iodine-131	8 days	Thyroid treatment
Technetium-99m	6 hours	Medical imaging
Francium-223	22 minutes	Research

Decay curve: The number of remaining nuclei decreases exponentially with time. The graph is a curve that approaches zero but never quite reaches it.

Number of Half-Lives	Fraction Remaining	Percentage Remaining
0	1	100%
1	1/2	50%
2	1/4	25%
3	1/8	12.5%
4	1/16	6.25%
5	1/32	3.125%

Half-life is a beautiful concept because it is constant. It does not matter how much of the substance you have — the half-life is always the same. This is what makes radioactive dating possible. By measuring the ratio of parent to daughter nuclei, we can determine how many half-lives have passed and hence the age of the sample.

3.8 Detection of Radiation

Radiation is invisible, but it can be detected using various instruments.

Detector	How It Works
Geiger-Müller (GM) tube	Radiation ionises gas in the tube, causing a pulse of current
Cloud chamber	Radiation leaves a trail of ions in supersaturated vapour, forming a visible track
Spark chamber	Radiation causes sparks between electrodes, showing paths
Photographic film	Radiation darkens the film
Scintillation counter	Radiation causes certain materials to emit light
Dosimeter	Measures cumulative radiation dose

Geiger-Müller tube: This is the most common detector. It consists of a tube filled with a gas at low pressure. When radiation enters the tube, it ionises the gas, creating a pulse of current that is counted by an electronic circuit. The rate of pulses indicates the intensity of the radiation.

Think of a GM tube as a microphone for radiation. It does not tell you what type of radiation it is (unless you use filters), but it tells you how much radiation is present. It is the workhorse of radiation detection.

The cloud chamber is one of the most beautiful detectors. It allows you to actually see the tracks of alpha and beta particles as they pass through. Alpha particles leave thick, straight tracks. Beta particles leave thin, wavy tracks. It is like watching subatomic particles dance. Every physics laboratory should have one.

3.9 Biological Effects and Safety

Radiation can damage living cells by ionising atoms and molecules in the body. This can lead to cell death, mutations, and cancer.

Biological effects of radiation:

• Cell death: High doses can kill cells, leading to radiation sickness.
• DNA damage: Radiation can break DNA strands, causing mutations.
• Cancer: Mutations can lead to uncontrolled cell division.
• Genetic effects: Mutations in reproductive cells can affect future generations.
• Cataracts: Radiation can damage the lens of the eye.
• Burns: High doses can cause skin burns.

Units of radiation:

Unit	Measures	Definition
Becquerel (Bq)	Activity	1 decay per second
Gray (Gy)	Absorbed dose	1 joule per kilogram
Sievert (Sv)	Equivalent dose	Absorbed dose × quality factor

Safety precautions:

• Limit exposure time.
• Increase distance from the source (inverse square law).
• Use lead shielding.
• Never eat, drink, or smoke near radioactive materials.
• Use protective clothing and gloves.
• Monitor exposure with dosimeters.
• Store radioactive materials in lead containers.
• Dispose of radioactive waste safely.

Precaution	Purpose
Time	Reduce total exposure
Distance	Reduce intensity (inverse square law)
Shielding	Absorb radiation
Dosimeter	Monitor exposure

The three principles of radiation safety are time, distance, and shielding. Minimise the time you spend near a source. Maximise your distance from it. Use appropriate shielding. These simple rules have saved countless lives. Respect radiation, but do not fear it — understanding it is the key to using it safely.

3.10 Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, releasing a large amount of energy. It is the process that powers nuclear reactors and nuclear weapons.

How fission works:

1. A neutron is absorbed by a heavy nucleus (e.g., uranium-235).
2. The nucleus becomes unstable and splits into two smaller nuclei.
3. Two or three neutrons are released.
4. A large amount of energy is released.

Chain reaction: The neutrons released in fission can trigger further fission events, leading to a self-sustaining chain reaction. This is the basis of nuclear reactors and nuclear weapons.

Controlled vs uncontrolled chain reactions:

• Controlled: Used in nuclear reactors. Control rods absorb neutrons to regulate the rate of reaction.
• Uncontrolled: Used in nuclear weapons. The reaction grows exponentially in a fraction of a second.

Feature	Controlled Fission	Uncontrolled Fission
Rate	Regulated	Exponential
Use	Nuclear power	Nuclear weapons
Control	Control rods	No control

Nuclear fission is a double-edged sword. It can provide abundant, low-carbon energy, but it also produces radioactive waste and can be used to build devastating weapons. Understanding the physics helps us use it responsibly. The same reaction that powers a city can destroy it — the difference is control.

3.11 Nuclear Fusion

Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, releasing a large amount of energy. It is the process that powers the Sun and other stars.

Conditions for fusion:

• Very high temperature (millions of degrees).
• Very high pressure.
• Sufficient confinement time.

These conditions are needed to overcome the electrostatic repulsion between positively charged nuclei and bring them close enough for the strong nuclear force to take over.

Feature	Fission	Fusion
Process	Splitting heavy nuclei	Joining light nuclei
Fuel	Uranium, plutonium	Hydrogen isotopes
Energy released	Large	Even larger per unit mass
Radioactive waste	Significant	Minimal
Conditions	Moderate	Extreme
Status	Commercial	Experimental

Think of fission as breaking a large log into smaller pieces. Think of fusion as gluing small pieces together to make a larger log. Both release energy, but fusion releases more per unit mass.

Fusion is the holy grail of energy. It promises abundant, clean energy with minimal radioactive waste. But achieving it on Earth is incredibly difficult. We need to create conditions similar to the core of the Sun. Scientists have been working on this for decades, and progress is being made. It may be the energy source of the future.

3.12 Uses of Radioactivity

Field	Application	How It Works
Medicine	Cancer treatment (radiotherapy)	Gamma rays destroy cancer cells
Medicine	Medical imaging	Radioactive tracers emit gamma rays detected by cameras
Medicine	Sterilisation	Gamma rays kill bacteria on equipment
Industry	Thickness measurement	Radiation absorption depends on material thickness
Industry	Leak detection	Radioactive tracers detect leaks in pipes
Archaeology	Carbon dating	Measures carbon-14 decay to date organic materials
Geology	Rock dating	Measures uranium decay to date rocks
Agriculture	Food preservation	Gamma rays kill bacteria and pests
Smoke detectors	Detect smoke	Americium-241 ionises air; smoke interrupts current

Radioactivity is a powerful tool. It can diagnose and treat cancer, date ancient artefacts, and detect leaks in pipelines. It can also be dangerous if misused. Like fire, it is a good servant but a bad master. Understanding it is the key to using it wisely.

4. Formula Box

5. Worked Examples

Example 1: Alpha Decay Equation

Question: Radium-226 undergoes alpha decay. Write the balanced nuclear equation.

Answer:

Alpha decay: mass number decreases by 4, atomic number decreases by 2.

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

Answer: Radium-226 decays into radon-222 and an alpha particle.

Units check: mass numbers balance (226 = 222 + 4) and atomic numbers balance (88 = 86 + 2). Always check both.

Example 2: Beta Decay Equation

Question: A nucleus of lead-214 undergoes beta decay. Write the balanced nuclear equation.

Answer:

Beta decay: mass number unchanged, atomic number increases by 1.

²¹⁴₈₂Pb → ²¹⁴₈₃Bi + ⁰₋₁e

Answer: Lead-214 decays into bismuth-214 and a beta particle.

Units check: mass numbers balance (214 = 214 + 0) and atomic numbers balance (82 = 83 − 1). The beta particle has atomic number −1 because it is an electron.

Example 3: Half-Life Calculation

Question: A radioactive sample has a half-life of 8 days. What fraction of the original sample remains after 32 days?

Answer:

Number of half-lives: n = t / T_1/2 = 32 / 8 = 4

Fraction remaining: (1/2)⁴ = 1/16

Answer: 1/16 of the original sample remains.

Units check: the answer is a fraction. After 4 half-lives, 1/16 remains. This is the same as 6.25%. Half-life calculations are straightforward once you know the number of half-lives.

Example 4: Carbon Dating

Question: A sample of wood from an ancient tool has 25% of its original carbon-14 content. The half-life of carbon-14 is 5 730 years. Calculate the age of the tool.

Answer:

25% = 1/4 = (1/2)², so n = 2 half-lives.

Age = n × T_1/2 = 2 × 5 730 = 11 460 years

Answer: The tool is approximately 11 460 years old.

Units check: the answer is in years. This is a classic carbon dating problem. By measuring the remaining carbon-14, we can determine how many half-lives have passed, and hence the age of the sample.

Example 5: Completing a Decay Chain

Question: Uranium-238 decays by alpha emission to thorium-234. Thorium-234 then decays by beta emission. Write the equation for the second decay.

Answer:

Thorium-234 (Z = 90) undergoes beta decay, so atomic number increases by 1 to 91 (protactinium), mass number stays 234.

²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e

Answer: Thorium-234 decays into protactinium-234 and a beta particle.

Units check: mass numbers balance (234 = 234 + 0) and atomic numbers balance (90 = 91 − 1). This is part of the uranium decay series, which eventually ends in stable lead-206.

6. Graph Work

7. Practical / Experiment

8. Common Mistakes

• Confusing alpha, beta, and gamma radiation. Remember: alpha is a helium nucleus, beta is an electron, gamma is a wave.
• Forgetting that alpha decay reduces mass number by 4 and atomic number by 2.
• Forgetting that beta decay increases atomic number by 1.
• Thinking that gamma decay changes the element. It does not — it only releases energy.
• Confusing half-life with total lifetime. Half-life is the time for half the sample to decay.
• Forgetting to subtract background radiation in experiments.
• Thinking that radioactivity can be turned on and off. It is spontaneous and random.
• Underestimating the dangers of radiation. Always follow safety precautions.

9. Checkpoint Questions

10. Structured Exam-Style Questions

11. Challenge Questions

12. Real-World Applications

13. Closing Thought

Radioactivity is the invisible energy released by unstable atoms — a force of nature that can heal or harm, power our cities or destroy them, and in understanding it, we learn to use it wisely for the benefit of all.