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Module 1 · L20 of 21 40 min ⚡ +50 XP in Learn · +25 to complete Year 11 · Module 1 · IQ2

Nuclear Chemistry

Today's hook, a Geiger counter clicking near a smoke detector, a hospital scan using a radioactive tracer, and the 5,730-year clock buried in an ancient bone, all rely on the same nuclear process. What actually happens inside an unstable nucleus?
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Warm up and recall

Warm up first

Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.

Worksheets

Practise this lesson

Four printable worksheets that build from the foundations up to exam-style questions, start at whatever level suits you.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Exam Exam-style questions
01
Recall, your gut answer first
+5 XP warm-up

You learned in the last lesson that isotopes outside the band of stability are radioactive, their nucleus cannot hold together indefinitely. What do you think an unstable nucleus actually does to become more stable? What might it release, and does the atom stay the same element afterwards?

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What you'll master, and the words for it

03
What you'll master
Know

Key facts

  • Alpha (α), beta (β) and gamma (γ) radiation each have a distinct nature, charge, mass and penetrating power.
  • Natural radioisotopes (e.g. U-238, C-14) and human-made radioisotopes (e.g. Tc-99m, Co-60) have real-world uses, from dating to medicine.
Understand

Concepts

  • Why nuclear equations must conserve both mass number (A) and atomic number (Z) on both sides.
  • Why half-life is a statement about probability, not a fixed countdown for any single nucleus.
Can do

Skills

  • Write and balance nuclear equations for alpha decay, beta decay, and simple fission/fusion reactions.
  • Calculate the mass or fraction of a radioisotope remaining after a given number of half-lives.
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Key terms
Radioisotope
An isotope with an unstable nucleus that spontaneously decays, releasing radiation.
Alpha particle (α)
A helium nucleus (⁴₂He), 2 protons + 2 neutrons, emitted during alpha decay.
Beta particle (β)
A high-speed electron (⁰₋₁e) emitted when a neutron converts to a proton inside the nucleus.
Gamma ray (γ)
A high-energy electromagnetic photon released as the nucleus loses excess energy, no mass or charge.
Transmutation
The change of one element into another as a result of a nuclear reaction (a change in the number of protons).
Half-life
The time taken for half of the radioactive nuclei in a sample to decay.
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Types of Ionising Radiation

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Types of Ionising Radiation
core concept

When an unstable nucleus decays, it releases energy as one (or more) of three types of ionising radiation. Each type differs in what it actually is, its charge, its mass, and, as a direct result, how far it can travel through matter before being stopped.

RadiationNatureNotationChargeRelative massPenetrating power
Alpha (α)A helium nucleus, 2 protons + 2 neutrons bound together⁴₂He or α+24Low, stopped by a sheet of paper or a few cm of air
Beta (β)A high-speed electron, ejected when a neutron converts to a proton⁰₋₁e or β−1≈0 (1/1836)Moderate, stopped by a few mm of aluminium
Gamma (γ)A high-energy electromagnetic photon, no particle at allγ00High, needs several cm of lead or thick concrete to stop
The trade-off: Alpha particles are large and heavily charged, so they interact strongly with matter and lose energy quickly (low penetrating power) but cause intense ionisation over a short distance. Gamma rays have no mass or charge, so they interact weakly and travel much further before losing their energy (high penetrating power) but ionise less per unit distance. Beta particles sit in between on both counts.

Three types of ionising radiation: alpha (α, ⁴₂He, charge +2, mass 4, low penetrating power, stopped by paper); beta (β, ⁰₋₁e, charge −1, mass ≈0, moderate penetrating power, stopped by aluminium); gamma (γ, a photon, no charge, no mass, high penetrating power, needs thick lead/concrete to stop). Penetrating power and ionising power trade off against each other.

Pause, copy the highlighted radiation types table into your book before moving on.

True or false: "Gamma radiation has the lowest penetrating power of the three types of ionising radiation."

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Balanced Nuclear Equations

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Balanced Nuclear Equations
core concept

We just saw the three types of ionising radiation and their properties. That raises a question: when a nucleus emits one of these, what exactly happens to the atom itself, does it stay the same element? This card answers it → nuclear equations, balanced using the same conservation rules for every type of nuclear reaction.

A nuclear equation shows a nuclide changing into new nuclide(s) plus the emitted particle. Just like a chemical equation, it must be balanced, but instead of balancing atoms of each element, you balance two numbers on both sides: the mass number (A), top, and the atomic number (Z), bottom.

Alpha decay (loses a ⁴₂He nucleus, A decreases by 4, Z decreases by 2):
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Check: mass numbers 238 = 234 + 4 ✓. Atomic numbers 92 = 90 + 2 ✓.
Beta decay (a neutron converts to a proton, ejecting an electron, A stays the same, Z increases by 1):
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Check: mass numbers 14 = 14 + 0 ✓. Atomic numbers 6 = 7 + (−1) ✓.
Beyond the syllabus. Module 1 asks you to write balanced nuclear equations for unstable isotopes. It does not require fission and fusion as separate reaction types, and you will not be assessed here on reactor physics or on how the Sun works. They appear for one reason: they show that the balancing rule you just learned, conserve total A and total Z, holds for every nuclear reaction and not only for alpha and beta decay. Read the next two paragraphs for that point, then put your practice into alpha and beta equations, which is what the exam will ask you to write.

Some heavy nuclei also undergo fission, splitting into two lighter nuclei plus several neutrons and a large release of energy (used in nuclear power stations), while very light nuclei can undergo fusion, combining into a heavier nucleus (the process that powers the Sun). Both are still balanced the same way, by conserving total mass number and total atomic number across the whole equation.

Simple fission example: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n (mass: 235+1 = 141+92+3; atomic number: 92+0 = 56+36+0).

Nuclear equations must conserve total mass number (A, top) and total atomic number (Z, bottom) across both sides. Alpha decay: A −4, Z −2 (emits ⁴₂He). Beta decay: A unchanged, Z +1 (emits ⁰₋₁e, a neutron becomes a proton). Fission splits a heavy nucleus into two lighter nuclei plus neutrons; fusion combines light nuclei into a heavier one. Every case still balances A and Z.

Pause, copy the highlighted alpha and beta decay equations into your book before moving on.

Fill the blanks: drag each value into the balanced alpha decay equation for radium-226.

222 86 4 2

²²⁶₈₈Ra → ___₈₆Rn + ___₂He, where the radon's atomic number is ___ and the alpha particle's atomic number is ___.

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Natural and Human-Made Radioisotopes

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Natural and Human-Made Radioisotopes
core concept

We just saw how to write and balance nuclear equations for alpha and beta decay. That raises a question: which radioisotopes actually occur in the world around us, and which are deliberately manufactured, and what are they used for? This card answers it → natural radioisotopes like U-238 and C-14, and human-made (synthetic) radioisotopes like Tc-99m and Co-60.

RadioisotopeOriginDecay / half-lifeUse
Uranium-238 (U-238)Natural, found in rocks and ores since Earth's formationAlpha decay, part of a long decay chain to stable Pb-206; t½ = 4.5 billion yearsUranium-lead dating of very old rocks (millions to billions of years)
Carbon-14 (C-14)Natural, continuously formed in the upper atmosphere when cosmic-ray neutrons strike N-14; taken up by living things via CO₂Beta decay; t½ = 5730 yearsRadiocarbon dating of once-living material, up to about 50,000 years old
Technetium-99m (Tc-99m)Human-made, produced from a molybdenum-99/technetium-99m generator in hospitalsGamma decay; t½ = 6 hours (short, to minimise patient radiation dose)Medical imaging, injected as a tracer, its gamma emission is detected to image organs and blood flow
Cobalt-60 (Co-60)Human-made, produced by neutron bombardment of cobalt-59 in a nuclear reactorBeta then gamma decay; t½ = 5.3 yearsCancer radiotherapy (gamma rays targeted at tumours) and industrial/medical equipment sterilisation
Why C-14 dating stops working after ~50,000 years: after about 8-9 half-lives, so little C-14 remains that the radioactivity is too faint to measure reliably above background radiation, this sets a practical limit on the technique, not a limit of the underlying half-life concept.

Natural radioisotopes: U-238 (uranium-lead dating of rocks, t½ = 4.5 billion years), C-14 (radiocarbon dating of once-living material, t½ = 5730 years). Human-made radioisotopes: Tc-99m (medical imaging, short t½ = 6 hours to limit patient dose), Co-60 (cancer radiotherapy and sterilisation, t½ = 5.3 years). A radioisotope's half-life is chosen or exploited to match its intended use.

Add the highlighted radioisotope table to your notes before the check below.

Match each radioisotope to its primary real-world use.

  • U-238
  • C-14
  • Tc-99m
  • Co-60
  • Radiocarbon dating of once-living material
  • Dating very old rocks (uranium-lead dating)
  • Cancer radiotherapy and sterilisation
  • Medical imaging tracer
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Half-Life

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Half-Life
core concept

We just saw that different radioisotopes have wildly different half-lives, from hours to billions of years. That raises a question: what does "half-life" actually mean, and how do you calculate how much of a sample is left after a given time? This card answers it → half-life is a probability statement about a huge number of nuclei, and it gives a simple doubling-based calculation.

The half-life (t½) of a radioisotope is the time taken for half of the radioactive nuclei in a sample to decay. Crucially, this is a statement about probability, not a countdown timer for any single nucleus. Each individual unstable nucleus has a constant probability of decaying in any given time interval, you cannot predict exactly when one particular nucleus will decay. But with the enormous number of atoms in a real sample (billions upon billions), the overall fraction remaining after each half-life is highly predictable.

Beyond the syllabus. What Module 1 assesses about half-life is the idea itself, and why a radioisotope's half-life is chosen to match its use: Tc-99m's six hours to limit a patient's dose, C-14's 5730 years for dating. The (1/2)ⁿ arithmetic below goes further than Module 1 requires. Work through it, it is quick and it makes the idea concrete, but do not treat it as a mastery gate for this module. The definition, and the reasoning about why one isotope suits a job better than another, are what you need for the exam.
Calculation: after n half-lives, the fraction of the original sample remaining = (1/2)ⁿ, where n = total elapsed time ÷ half-life. Each half-life always halves whatever amount remains, it never removes a fixed absolute amount, so the decay curve keeps approaching zero without a sample ever mathematically reaching exactly zero.
Exponential radioactive-decay curve and matched remaining-amount bars: 100 percent initially, 50 percent after one half-life, 25 percent after two and 12.5 percent after three. Equal time intervals remove half of what remains, not a fixed amount, and the curve approaches zero without reaching it.

Trace it: compare the vertical drops over equal time intervals. The fraction lost stays at one-half, but the absolute amount lost becomes smaller each time.

Half-life (t½) = time for half of the radioactive nuclei in a sample to decay. It is a probability statement (constant decay probability per nucleus per unit time), not a fixed countdown for any single atom. Fraction remaining after n half-lives = (1/2)ⁿ, where n = elapsed time ÷ t½. Each half-life halves whatever amount is left at that point.

Pause, write the highlighted half-life definition and formula into your book.

Quick check: a radioisotope has a half-life of 6 hours. What fraction of the original sample remains after 24 hours?

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Short Answer Questions

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Short Answer Questions
core concept

6. Write a balanced nuclear equation for the alpha decay of uranium-238 (²³⁸₉₂U), and identify the daughter nuclide produced. 4 MARKS

✏️ Answer in your book

7. A radioisotope used in medical imaging has a half-life of 8 hours. A hospital starts with a 160 mg sample. (a) Calculate the mass remaining after 32 hours. (b) Explain what "half-life" means as a statement about probability, using this sample as your example. 4 MARKS

✏️ Answer in your book

We just saw what half-life means and how to calculate remaining mass. That raises a question: how do you structure full-mark exam answers on nuclear equations and half-life calculations? This card answers it → always check conservation of A and Z explicitly, and always show the number of half-lives elapsed before calculating the remaining amount.

For nuclear equation answers: identify the decay type, apply the A/Z change, write the full balanced equation, then explicitly check that A and Z balance on both sides. For half-life calculations: find n = elapsed time ÷ t½ first, then apply fraction remaining = (1/2)ⁿ, then multiply by the original mass. Always explain half-life as a probability statement, not a fixed countdown.

Pause, copy the highlighted nuclear-equation and half-life exam strategies into your book before moving on.

Lock-in task: Cobalt-60 (Co-60) undergoes beta decay. In one or two sentences, predict what happens to its mass number and atomic number, and name the element formed.

Worked examples

Worked examples · reveal as you go

Worked example +5 XP on full reveal

Thorium-234 (²³⁴₉₀Th) undergoes beta decay. Write the balanced nuclear equation, identify the daughter nuclide, and check that the equation is balanced.

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Identify the change: beta decay emits ⁰₋₁e; A stays the same, Z increases by 1
A neutron in the nucleus converts to a proton, ejecting an electron (the beta particle). No nucleon is lost, so the mass number is unchanged, but the atom now has one more proton.
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New atomic number: Z = 90 + 1 = 91. Mass number unchanged: A = 234
Z = 91 corresponds to protactinium (Pa).
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Balanced equation: ²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e
The daughter nuclide is protactinium-234.
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Check: mass numbers 234 = 234 + 0 ✓. Atomic numbers 90 = 91 + (−1) ✓
Always check both totals explicitly, this is what an exam marker is looking for.
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Worked example +5 XP on full reveal

A sample of a radioisotope with a half-life of 5 days starts at a mass of 400 mg. Calculate the mass remaining after 20 days.

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Number of half-lives elapsed: n = total time ÷ t½ = 20 ÷ 5 = 4
Always convert elapsed time into a number of half-lives first, this is the key step most students skip.
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Fraction remaining = (1/2)⁴ = 1/16
Each half-life multiplies the remaining amount by 1/2, four half-lives means four successive halvings.
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Mass remaining = 400 × (1/16) = 25 mg
Multiply the original mass by the fraction remaining.
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Check by halving successively: 400 → 200 (5 days) → 100 (10 days) → 50 (15 days) → 25 mg (20 days) ✓
Halving step-by-step is a good way to check your answer if you are unsure about the exponent.
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Misconception to fix

Common errors · the 3 traps that cost marks

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Misconception to fix

Wrong: Alpha radiation is the most dangerous type because it has the highest penetrating power.

2

Misconception to fix

Right: Alpha radiation actually has the lowest penetrating power (stopped by paper or skin) but the highest ionising power at short range, it is most dangerous if the source is inhaled or ingested, where it can directly damage internal tissue. Gamma radiation has the highest penetrating power but lower ionising power per unit distance.

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Forgetting to balance the atomic number, not just the mass number

Students often correctly balance the top (mass) numbers in a nuclear equation but forget to check the bottom (atomic) numbers, or vice versa, missing that beta decay changes the element identity even though the mass number is unchanged.

Fix: Always check both totals separately after writing a nuclear equation: sum of mass numbers on the left must equal the sum on the right, and the same for atomic numbers. If either doesn't balance, an equation term is wrong.

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Drill, then revisit

Quick-fire practice · 5 reps +2 XP per reveal

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What is an alpha particle, and what is its charge?

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Write the balanced equation for the alpha decay of polonium-210 (²¹⁰₈₄Po).

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Name one natural and one human-made radioisotope, and give one use for each.

4

A radioisotope has a half-life of 10 years. What fraction of a sample remains after 30 years?

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Why is half-life described as a "probability statement" rather than a fixed countdown?

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Revisit your thinking

Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?

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Interactive Tool, Atomic Structure Builder Open fullscreen ↗
The Atomic Structure tool shows that the atomic number of an element equals…
✓

Multiple choice

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Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next.

Spot the error+5 XP

A student balances the beta decay of iodine-131 (¹³¹₅₃I). One line contains an error, click it.

  • Beta decay ejects a ⁰₋₁e particle; a neutron converts to a proton inside the nucleus.
  • Mass number decreases by 1: A = 131 − 1 = 130. Atomic number increases by 1: Z = 53 + 1 = 54.
  • The daughter nuclide is xenon-131 (¹³¹₅₄Xe).
  • Balanced equation: ¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e.
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Short answer
ApplyApply4 MARKS

Q1. 6. Write a balanced nuclear equation for the alpha decay of uranium-238 (²³⁸₉₂U), and identify the daughter nuclide produced.

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ApplyApply4 MARKS

Q2. 7. A radioisotope used in medical imaging has a half-life of 8 hours. A hospital starts with a 160 mg sample. (a) Calculate the mass remaining after 32 hours. (b) Explain what "half-life" means as a statement about probability, using this sample as your example.

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📖 Comprehensive answers (click to reveal)

Activity 1

Co-60 (Z=27) undergoes beta decay: a neutron converts to a proton, ejecting an electron. Mass number stays at 60 (no nucleon lost). Atomic number increases by 1, from 27 to 28. The product is nickel-60 (⁶⁰₂₈Ni): ⁶⁰₂₇Co → ⁶⁰₂₈Ni + ⁰₋₁e.

❓ Multiple Choice

1. Alpha particles are helium nuclei (⁴₂He), charge +2, mass 4, with low penetrating power (stopped by paper) but high ionising power at short range.

2. Nuclear equations must conserve both the total mass number (A) and total atomic number (Z) across both sides, this is the same balancing principle for alpha decay, beta decay, fission and fusion.

3. C-14 dating works because living organisms continuously exchange carbon with the atmosphere (maintaining a constant C-14 ratio), but once an organism dies, C-14 decays with no further replacement, so the remaining fraction of C-14 indicates elapsed time since death.

4. Tc-99m is chosen for medical imaging partly because its short half-life (6 hours) means it decays away quickly after the scan, minimising the patient's total radiation dose while still providing enough activity to produce a clear image.

5. After 4 half-lives, the fraction of a sample remaining is (1/2)⁴ = 1/16.

Short Answer Model Answers

Q6 (4 marks): Alpha decay emits a ⁴₂He particle: mass number decreases by 4, atomic number decreases by 2 (1 mark). New atomic number = 92 − 2 = 90 (thorium); new mass number = 238 − 4 = 234 (1 mark). Balanced equation: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He (1 mark). Check: 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓; the daughter nuclide is thorium-234 (1 mark).

Q7 (4 marks): (a) n = 32 ÷ 8 = 4 half-lives (1 mark). Mass remaining = 160 × (1/2)⁴ = 160 × 1/16 = 10 mg (1 mark). (b) Half-life is a probability statement: each individual radioactive nucleus in the sample has a constant, fixed probability of decaying in any given time interval, it is impossible to predict exactly when any one particular nucleus will decay (1 mark). However, because the original 160 mg sample contains an enormous number of nuclei, the overall fraction remaining after each 8-hour half-life is highly predictable and reproducible, even though individual decay events are random (1 mark).