HSC Exam Practice

Sample response. Half-life is the time taken for half of the radioactive nuclei in a sample to decay (1 mark). It is a statement of probability because each individual nucleus 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; only with a very large number of nuclei does the overall fraction remaining become predictable (1 mark).

Marking notes. 1 mark for a correct definition. 1 mark for explaining the probability basis (constant per-nucleus decay probability; unpredictable for a single atom, predictable for a large sample).

Sample response. Alpha decay emits a ⁴₂He particle: mass number decreases by 4, atomic number decreases by 2 (1 mark). New atomic number = 84 − 2 = 82 (lead); new mass number = 210 − 4 = 206 (1 mark). Balanced equation: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He; the daughter nuclide is lead-206 (1 mark).

Marking notes. 1 mark for correctly applying the alpha-decay A/Z change. 1 mark for the correct new mass number and atomic number. 1 mark for the fully balanced equation with the daughter nuclide correctly named.

Sample response. Alpha particles are large (a whole helium nucleus) and heavily charged (+2), so they interact strongly and frequently with the atoms they pass, losing their energy over a very short distance, this gives high ionising power but low penetrating power (1 mark). Gamma rays have no mass and no charge, so they interact only weakly with matter and can travel much further before losing their energy, giving low ionising power per unit distance but high penetrating power (1 mark). There is a direct trade-off: the same properties (mass and charge) that make a particle interact strongly with matter (high ionising power) also cause it to be absorbed quickly (low penetrating power), and vice versa (1 mark).

Marking notes. 1 mark for the alpha explanation (mass/charge → strong interaction → short range/high ionising power). 1 mark for the gamma explanation (no mass/charge → weak interaction → long range/low ionising power). 1 mark for explicitly stating the trade-off between penetrating power and ionising power.

Sample response. Alpha decay emits a helium nucleus (⁴₂He): the mass number decreases by 4 and the atomic number decreases by 2 (2 marks: 1 for particle, 1 for both A/Z changes). Beta decay emits a high-speed electron (⁰₋₁e), created when a neutron converts to a proton: the mass number is unchanged (no nucleon lost) and the atomic number increases by 1 (2 marks: 1 for particle, 1 for both A/Z changes).

Marking notes. 1 mark for correctly identifying the alpha particle with both its A and Z changes. 1 mark for stating the alpha particle notation or composition. 1 mark for correctly identifying the beta particle with both its A and Z changes. 1 mark for stating the beta particle notation or origin (neutron → proton + electron).

Sample response. The student is incorrect: carbon-14 dating only works for material that was once living (which absorbed carbon, including C-14, from the atmosphere while alive), not for inorganic rock, and its 5730-year half-life makes it unreliable much beyond about 50 000 years because too little C-14 remains to measure reliably (1 mark). Uranium-238 (U-238) is a more suitable radioisotope for dating very old rocks (1 mark). U-238 has a much longer half-life (4.5 billion years), so measurable quantities of U-238 (and its stable end-product, Pb-206) remain even in rocks that are millions to billions of years old, unlike C-14, which would have completely decayed away long before reaching geological timescales (1 mark).

Marking notes. 1 mark for identifying the error (C-14 dates once-living material / has too short a half-life for geological timescales). 1 mark for naming U-238 (or another suitably long-half-life radioisotope). 1 mark for justifying the choice using half-life matching the timescale being dated.

Sample response (a). 1/16 = (1/2)⁴, so 4 half-lives have elapsed (1 mark). Age = 4 × 5730 = 22 920 years (2 marks: 1 for correctly finding n = 4, 1 for the correct final age).

Sample response (b). After about 8–9 half-lives (roughly 50 000 years), so little C-14 remains in the sample that its radioactivity becomes too faint to reliably distinguish from background radiation (1 mark). This is a practical measurement limit, not a change in the decay process itself, C-14 continues to decay at the same constant half-life indefinitely, there is just not enough of it left to detect accurately (2 marks: 1 for identifying the measurement/background-radiation limit; 1 for distinguishing this from an actual change in the decay process).

Sample response (c). Uranium-238 (U-238) is more suitable (1 mark). Its half-life is 4.5 billion years, far longer than C-14's 5730 years, so it is only useful for dating extremely old, non-living (mineral/rock) material where the timescale is millions to billions of years; using C-14 on such an old sample would show essentially zero remaining activity and give no useful information (2 marks: 1 for correct radioisotope named; 1 for justification matching half-life to the very long timescale).

Marking notes. Part (a): 1 mark for correctly identifying n = 4 half-lives from the fraction 1/16; 2 marks for the correct final numerical age with working shown. Part (b): 1 mark for identifying the background-radiation/measurement-sensitivity limit; 2 marks for distinguishing this practical limit from the (unchanged) underlying decay process. Part (c): 1 mark for naming U-238 (or equivalent very-long-half-life radioisotope); 2 marks for justification based on matching half-life timescale to the age of the sample.

Sample response. Half-life is an important factor in choosing a radioisotope for a given purpose, but it is not the only relevant property, radiation type and its resulting penetrating and ionising power are equally essential, and the claim that half-life alone determines usefulness is an oversimplification. For medical imaging, technetium-99m is chosen because it is a gamma emitter (gamma penetrates tissue and can be detected externally without extensive absorption) with a short half-life of about 6 hours, long enough to complete a scan but short enough to minimise the patient's cumulative radiation dose. A gamma emitter with the same short half-life but was instead an alpha or beta emitter would be useless for imaging, because those radiation types cannot escape the body to reach an external detector, radiation type, not just half-life, is decisive here. For cancer therapy, iodine-131 (beta and gamma emitter, half-life 8 days) is effective because its beta radiation has a short range and high ionising power, depositing its energy locally within targeted tissue that has absorbed the iodine, destroying cancerous cells; a purely gamma-emitting isotope with the same half-life would be far less effective at directly damaging localised tissue because gamma radiation deposits its energy over a much larger volume with lower ionising power per unit distance. Cobalt-60, with a far longer half-life (5.3 years), is also used in radiotherapy, but only as an external beam source, its long half-life here is not a safety problem because the patient is only briefly exposed to the beam during treatment sessions, rather than having the isotope inside their body continuously decaying. For dating natural materials, carbon-14 (half-life 5730 years) is matched to timescales of thousands to tens of thousands of years for once-living material, while uranium-238 (half-life 4.5 billion years) is matched to the vastly longer timescales of geological rock formation; using the wrong half-life for the sample's true age would give either no detectable remaining activity (half-life far too short) or an imprecise, barely-changed reading (half-life far too long relative to the sample's age). One key limitation of judging suitability by half-life alone is that it ignores radiation type entirely, a purely half-life-based comparison could not distinguish which of the three radioisotopes above would actually be safe or effective for imaging versus therapy versus dating, since two radioisotopes with identical half-lives but different radiation types (e.g. one alpha, one gamma) would have completely different practical applications and safety profiles. In conclusion, half-life determines the appropriate timescale over which a radioisotope remains useful or hazardous, but radiation type and its associated penetrating and ionising power determine what the radioisotope can actually do, both properties must be considered together, so the claim that half-life alone determines usefulness is not supported.

Marking criteria (7 marks). 1 = correctly explains medical imaging suitability using both radiation type (gamma, penetrates/escapes body) and half-life (short, limits dose), naming Tc-99m or equivalent. 1 = correctly explains cancer therapy suitability using both radiation type (beta, short range/high ionising power for local damage) and half-life, naming I-131 or equivalent. 1 = correctly explains dating suitability by matching half-life to sample timescale, naming both C-14 and U-238 (or equivalent) with contrasting half-lives. 1 = correctly explains why Co-60's long half-life is not a safety issue in external-beam use specifically (contrasted with an injected/ingested isotope). 1 = identifies a specific, well-reasoned limitation of half-life alone as a sufficient criterion (i.e. it ignores radiation type). 1 = uses precise chemical/physical terminology throughout (penetrating power, ionising power, half-life, radiation type) with correctly named radioisotopes. 1 = reaches an explicit evaluative conclusion that both half-life and radiation type must be considered together, not treating the claim as either fully true or fully false without justification.