Unit 14 Radioactivity
Key unit competence: Evaluate the properties, uses and hazards of radioisotopes using balanced nuclear equations and half-life calculations.
Key ideas
- Radioactivity is the spontaneous decay of unstable nuclei with emission of radiation. Radioisotopes are isotopes with unstable nuclei. Nuclear reactions change the nucleus (and the element), release huge energy and are unaffected by temperature or chemical state; chemical reactions involve only electrons.
- Emissions: alpha (α, a helium nucleus 42He, charge +2, most ionising, stopped by paper); beta (β^-, a fast electron from n → p + e−, stopped by a few mm of aluminium); gamma (γ, electromagnetic radiation, no charge or mass, reduced by thick lead or concrete); positron (β^+). In electric fields α and β are deflected in opposite directions; γ is not deflected.
- Nuclear equations balance mass numbers and atomic numbers: 23892U → 23490Th + 42He; 146C → 147N + 0−1e; 6027Co → 6028Ni + 0−1e + γ. Decay series (e.g. U-238) end at a stable isotope (Pb-206).
- Stability depends on the neutron : proton ratio (belt of stability: about 1 for light nuclei, about 1.5 for heavy ones). Too many neutrons: β^- decay; too few: β^+ emission or electron capture; Z > 83: α decay.
- Half-life t½: time for half of the radioactive nuclei (or the activity) to decay; decay is first order. N = N0(½)t/t½; k = 0.693 ÷ t½. Carbon-14 (t½ 5730 years) dates organic remains.
- Fission: a heavy nucleus splits after absorbing a neutron (23592U + 10n → 14156Ba + 9236Kr + 310n), giving a chain reaction (nuclear power, atomic bombs). Fusion: light nuclei join (21H + 31H → 42He + 10n) as in the Sun. Energy from the mass defect: E = Δmc2. Uses: C-14 dating, P-32 (plant uptake of fertiliser, leukaemia), Co-60 (radiotherapy, sterilising), I-131 (thyroid). Hazards: radiation damages cells and DNA (burns, cancer, mutations): use shielding, distance, short exposure, film badges.
Common misconceptions
- "Heating a radioactive substance speeds up its decay." No: Radioactive decay is unaffected by temperature, pressure or chemical combination.
- "After two half-lives all of a sample has decayed." No: After two half-lives one quarter remains; decay never reaches exactly zero.
- "Gamma rays change the atomic number of the nucleus." No: Gamma emission changes only the energy of the nucleus, not its mass or atomic number.
Worked examples
Example 1. Compare alpha, beta and gamma radiation (nature, charge, penetration, ionising power, deflection).
Solution
Alpha: helium nucleus, charge +2, mass 4; stopped by paper or a few cm of air; strongly ionising; deflected towards the negative plate.
Beta-minus: electron, charge −1, very small mass; stopped by a few mm of aluminium; moderately ionising; deflected strongly towards the positive plate.
Gamma: electromagnetic wave, no charge or mass; reduced by thick lead/concrete; weakly ionising; not deflected.
Alpha sources are most dangerous inside the body; gamma is most dangerous outside it.
Example 2. A tracer: sodium-24 (t½ = 15 h) is injected to find a leak in an underground water pipe. Explain why it is suitable and how much of a 16 mg dose remains after 60 h.
Solution
Sodium-24 emits β and γ; the γ rays pass through soil and can be detected above ground where the leak is.
Its half-life is long enough to complete the test but short enough not to stay radioactive in the environment.
60 ÷ 15 = 4 half-lives: 16 × (½)4 = 1 mg remains.
Sodium salts are soluble and move with the water.
Practice questions
Define radioactivity.
Show answer
The spontaneous disintegration of unstable nuclei with emission of radiation (α, β or γ).
Common mistake: Saying it is caused by heating.
Give two differences between nuclear and chemical reactions.
Show answer
Nuclear: nucleus changes, new elements, huge energy, unaffected by temperature; chemical: electrons only, same elements, smaller energy, rate depends on temperature (any two).
Common mistake: Saying both change the element.
Write a nuclear equation for the beta decay of 6027Co.
Show answer
6027Co → 6028Ni + 0−1e (+ γ).
Common mistake: Decreasing the atomic number.
What is a decay series?
Show answer
A sequence of decays from a heavy unstable nucleus to a stable one (e.g. U-238 to Pb-206).
Common mistake: Saying it is a series of chemical reactions.
Explain the term chain reaction.
Show answer
Neutrons released by one fission cause further fissions, so the reaction becomes self-sustaining.
Common mistake: Saying it is a series of chemical bonds.
Give two medical uses of radioisotopes.
Show answer
Co-60 radiotherapy; I-131 thyroid treatment; Tc-99m imaging; sterilising instruments (any two).
Common mistake: Listing 'curing malaria'.
State three safety precautions when handling radioactive sources.
Show answer
Use tongs, keep sources in lead boxes, minimise time, keep distance, wear film badges (any three).
Common mistake: Saying gloves alone stop gamma rays.
Why is an alpha source dangerous inside the body but not outside?
Show answer
Outside, skin and air stop α; inside, its strong ionisation damages nearby cells.
Common mistake: Saying alpha is more penetrating.
How does fusion differ from fission?
Show answer
Fusion joins light nuclei; fission splits heavy nuclei.
Common mistake: Swapping the definitions.
What fraction of a radioisotope remains after 5 half-lives?
Show answer
(½)5 = 1/32.
Common mistake: Saying 1/10.
Matching and drag-and-drop
Matching
Match each item in column A with the correct answer in column B. Write the letter next to each number.
Column A Column B 1. Phosphorus-32 can be used to study: a. how plants take up fertiliser 2. The most ionising radiation is: b. alpha 3. The isotope used to date archaeological wood is: c. beta-minus emission 4. Nuclei with too many neutrons usually decay by: d. carbon-14 Show answer
1 → a (how plants take up fertiliser) · 2 → b (alpha) · 3 → d (carbon-14) · 4 → c (beta-minus emission)
- Tracer.
- Large charge and mass.
- t½ 5730 years.
- n → p lowers the n : p ratio.
Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
a helium nucleus · gamma · a fast electron from the nucleus · beta- An alpha particle is .
- A beta-minus particle is .
- The most penetrating radiation is .
Show answer
1: a helium nucleus · 2: a fast electron from the nucleus · 3: gamma
- Two protons and two neutrons.
- From n → p + e−.
- Needs thick lead.
Matching
Match each item in column A with the correct answer in column B. Write the letter next to each number.
Column A Column B 1. The energy released in nuclear reactions comes from: a. increases by 1 2. When an atom emits a beta-minus particle, its atomic number: b. cancer radiotherapy and sterilising equipment 3. Cobalt-60 is used for: c. joining of light nuclei to form a heavier nucleus 4. Nuclear fusion is: d. a small loss of mass (E = Δmc2) Show answer
1 → d (a small loss of mass (E = Δmc2)) · 2 → a (increases by 1) · 3 → b (cancer radiotherapy and sterilising equipment) · 4 → c (joining of light nuclei to form a heavier nucleus)
- Mass defect.
- A neutron becomes a proton.
- Gamma emitter.
- Powers the Sun.
Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
speed up decay · thyroid gland · half the radioactive nuclei to decay · measure the dose of radiation received- A person working with radioactive sources wears a film badge to .
- Half-life is the time for .
- Iodine-131 is used to diagnose and treat problems of the .
Show answer
1: measure the dose of radiation received · 2: half the radioactive nuclei to decay · 3: thyroid gland
- Monitors exposure.
- Constant for each isotope.
- The thyroid absorbs iodine.