Nuclear Chemistry

Q1, Sample Band 6 response (8 marks), annotated

Imaging recommendation: I-123 is the most appropriate choice for imaging the thyroid's structure [1]. It is a pure gamma emitter, gamma radiation penetrates tissue and can be detected externally by a gamma camera without depositing much energy inside the body, and its short half-life (13 hours) means the patient's radiation dose decays away quickly after the scan is complete [1].

Treatment recommendation: I-131 is the most appropriate choice for destroying overactive thyroid tissue [1]. Its beta emission has a short range and high ionising power, so it deposits its energy locally within the thyroid tissue that has taken up the iodine, destroying the targeted cells, while its 8-day half-life provides a sustained treatment dose without lasting indefinitely in the body [1].

Why I-123/I-131 are unsuitable for the other role: I-123 is unsuitable for treatment because gamma radiation, being highly penetrating and only weakly ionising per unit distance, would not efficiently destroy the targeted tissue, it would largely pass through without depositing enough localised energy [1]. I-131 is unsuitable for simple imaging because its beta radiation cannot escape the body to be detected externally, and its longer half-life would deliver an unnecessarily larger radiation dose for what should be a low-dose diagnostic procedure [1].

Why Co-60's long half-life is not a safety issue in its use: Co-60 is used as an external-beam source, positioned outside the patient's body and aimed at a tumour rather than being injected or ingested. Its long half-life (5.3 years) means the source itself needs to be replaced infrequently, but the patient is only exposed to the beam for the brief duration of each treatment session, the source's own decay rate does not accumulate inside the patient's body the way an injected tracer's would [1].

Limitation of relying on half-life and radiation type alone: Real clinical selection also depends on factors such as the chemical behaviour of the radioisotope (whether it is taken up selectively by the target organ), production cost and availability, the biological half-life (how quickly the body itself eliminates the substance, separate from radioactive half-life), and patient-specific factors such as allergy or existing thyroid conditions, half-life and radiation type are necessary but not sufficient information on their own [1]. (5 marks for the five dot-point requirements above; award up to 3 additional marks for precision of chemical language, correct comparative reasoning, and depth of evaluation: mark as 8 total.)

Marking criteria (8 marks): 1 = correct imaging recommendation with radiation-type + half-life justification; 1 = correct treatment recommendation with penetrating/ionising power justification; 1 = explains why I-123 unsuitable for treatment; 1 = explains why I-131 unsuitable for imaging; 1 = explains why Co-60's long half-life is safe in external-beam use; 1 = valid limitation of half-life/radiation-type as sole selection criteria; 1 = correct use of specific chemical/physical terminology throughout (ionising power, penetrating power, half-life); 1 = overall evaluative judgement comparing all three radioisotopes coherently.

Q2, Sample Band 6 response (7 marks), annotated

Hypothesis: If each die has an independent 1-in-6 chance of "decaying" (showing a 1) each round, then the number of dice remaining will approximately halve every few rounds, following the same shape as a real radioactive decay curve, rather than decreasing by a fixed number of dice each round [1].

Variables: Independent variable: round number (1, 2, 3, …). Dependent variable: number of dice remaining after each round. Controlled variable: same number of starting dice (100) and the same removal rule (remove any die showing a 1) applied consistently every round [1].

Procedure: (1) Place all 100 dice in the tray and roll them together. (2) Remove every die that lands showing a 1, this round's "decayed" nuclei. (3) Record the number of dice remaining. (4) Repeat the roll-and-remove process with the remaining dice for at least 10 rounds, recording the count after each round. (5) Plot number of dice remaining (y-axis) against round number (x-axis) [1].

Representing probability: Each die "decaying" represents a single unstable nucleus decaying, both events are random and unpredictable for any individual die/nucleus, but happen with a fixed, constant probability (1/6 per round for a die; a fixed decay probability per unit time for a nucleus). With a large starting number, the overall fraction remaining after each round/half-life becomes highly predictable, even though no single die/nucleus's fate can be predicted in advance [1].

Limitation: The dice model only approximates a true half-life because a real half-life corresponds to a die probability of exactly 1/2 per interval, not 1/6, so the shape of the graph is broadly similar (exponential-looking decay) but the numbers do not match a true half-life exactly; also, with a small number of dice remaining late in the experiment, random fluctuation becomes more noticeable than it would be for the astronomically large number of atoms in a real sample [1].

Improvement: Repeat the entire simulation multiple times (e.g. 5 trials) and average the number of dice remaining at each round to smooth out random fluctuation, better approximating the smooth curve expected for a very large real sample [1].

Marking criteria (7 marks): 1 = testable hypothesis correctly predicting a halving-type (not linear) pattern; 1 = correctly identified IV, DV and a controlled variable; 1 = four clear, logically ordered procedure steps; 1 = correct identification of what a decaying die represents (an unstable nucleus) with reference to constant/random probability; 1 = correct explanation of why large numbers make the overall pattern predictable despite individual randomness; 1 = valid limitation of the analogy (probability value or small-number fluctuation); 1 = specific, workable improvement (repeated trials / averaging).