Generated ERQ

✓ passed E.3 Radioactive decay × B.1 Thermal energy transfers 12 marks SL 2 passes 69.29s $0.4517

``` ## ERQ · 12 marks · Topics: E.3 Radioactive decay + B.1 Thermal energy transfers · Archetype: theory_application **Integration:** primary=E.3 Radioactive decay, secondary=B.1 Thermal energy transfers (strength: supporting) **Stem.** A school physics class investigates the thermal effect of radioactive decay using a sealed cobalt-60 source of initial activity 1.76 × 10¹¹ Bq, embedded in a thermally insulated copper block surrounded by 0.250 kg of water. Each decay of a cobalt-60 nucleus releases a total energy of 2.82 MeV, distributed between a beta particle, an antineutrino, and two gamma photons. The half-life of cobalt-60 is 5.27 years. The students assume that all of the decay energy is absorbed by the water, and that the container is a perfect calorimeter. The specific heat capacity of water is 4180 J kg⁻¹ K⁻¹. The initial water temperature is 20.0 °C. ### Part (a) State [2 marks] · AO1 · Topic: E.3 Radioactive decay State what is meant by the *activity* of a radioactive sample, and state one assumption made when defining the half-life of a radioactive nuclide. ### Part (b) Calculate [3 marks] · AO2 · Topic: E.3 Radioactive decay Calculate the initial power, in watts, released by the cobalt-60 source, assuming all decay energy is converted to thermal energy in the water. ### Part (c) Determine [4 marks] · AO2 · Topic: E.3 Radioactive decay + B.1 Thermal energy transfers The students wish to raise the temperature of the water from 20.0 °C to 21.0 °C. Determine the time, in hours, required to achieve this temperature rise. Assume the activity of the source remains constant over this interval. ### Part (d) Evaluate [3 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR One student claims: *"Because the half-life of cobalt-60 is so long, the assumption of constant activity is justified, and the measured temperature rise should match the predicted value."* Evaluate this claim. --- ## Mark Scheme ### Part (a) [2 marks] — State - M1: activity = number of nuclear decays (disintegrations) per unit time [no ECF] - M2: half-life assumes a large number of nuclei (so that statistical decay constant applies) / OR decay is a random spontaneous process / OR decay constant is independent of external conditions [no ECF] ### Part (b) [3 marks] — Calculate - M1: energy per decay E = 2.82 × 10⁶ × 1.60 × 10⁻¹⁹ = 4.51 × 10⁻¹³ J [no ECF] - M2: substitution P = A × E = 1.76 × 10¹¹ × 4.51 × 10⁻¹³ [ECF from M1] - M3: P = 0.0794 W (accept 0.079–0.080 W) [ECF from M1, M2] ### Part (c) [4 marks] — Determine - M1: Q = mcΔT = 0.250 × 4180 × 1.00 = 1045 J [no ECF] - M2: recognises required time t = Q / P using P from (b) [ECF from (b)] - M3: t = 1045 / 0.0794 = 1.316 × 10⁴ s [ECF from (b), M1] - M4: t = 1.316 × 10⁴ / 3600 = 3.66 h (accept 3.6–3.7 h) [ECF from M3] ### Part (d) [3 marks] — Evaluate (position + supporting + limiting per §4.4.1) - M1: **Position** — the claim is partially correct: the constant-activity assumption is justified, *but* the predicted temperature rise will not be matched in practice [no ECF] - M2: **Supporting consideration** — the elapsed time (~3.7 h) is many orders of magnitude smaller than the half-life of 5.27 years, so the fractional decrease in activity over the experiment is negligible (< 0.01%), validating the constant-activity assumption - M3: **Limiting consideration** — however, antineutrinos escape the apparatus carrying energy that is not deposited as heat (and/or some gamma photons penetrate the calorimeter walls without being absorbed), so the *measured* ΔT will be *less* than the predicted value ### Marker notes - Alternative method accepted for (c): direct one-line calculation t = mcΔT / (A × E) provided all substitutions visible — award M1 for Q, M2 for correct combined expression, M3 for t in seconds, M4 for conversion to hours. - (b) accept use of 2.82 MeV directly with conversion factor 1.60 × 10⁻¹³ J MeV⁻¹ giving 4.51 × 10⁻¹³ J. - (d) M3: accept any ONE valid limiting factor — antineutrino escape, incomplete gamma absorption, heat loss to copper block/surroundings, or non-ideal calorimeter. Do not award M3 for restating that activity decreases (that contradicts M2). - (d) if student argues claim is entirely wrong without acknowledging the validity of the constant-activity part, award maximum [2/3] (M1 forfeited, M3 only if limiting factor identified). - ECF chain: (b) → (c) M2,M3,M4 fully ECF-eligible. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ strictly obeys the cognitive ladder. Part (a) is AO1 (State definition and unit), part (b)–(c) are AO2 (Calculate/Determine numerical values), and part (d) is AO3 (Evaluate claim with supporting and limiting reasoning). The progression from recall through procedural application to critical analysis is correct and complete.
command_structure fail

Part (d) mark scheme violates §4.4.1 structure for Evaluate command term. The scheme lists M1 (supporting), M2 (limiting), M3 (limiting) but does NOT explicitly award a mark for 'position' separate from supporting/limiting considerations. Per §4.4.1, Evaluate requires: position + supporting consideration + limiting consideration as three distinct marking components. Here, M1 conflates position ('constant-activity assumption is justified') with the supporting reasoning, leaving no standalone position mark. Additionally, M3 offers an 'OR' alternative but both M2 and M3 address the same overestimate mechanism (energy absorption), which weakens discrimination between limiting factors.

FIX: Restructure Part (d) marking to explicitly separate three components: (M1) Position statement — 'The claim is partially correct / justified but incomplete' [1 mark]. (M2) Supporting consideration — 'Time interval ~3.7 h ≪ half-life of 5.27 years means fractional activity loss is negligible (< 0.01%), so constant-activity assumption is valid' [1 mark]. (M3) Limiting consideration — 'However, antineutrinos escape without depositing energy in the calorimeter (and/or gamma photons may not be fully absorbed / heat loss to surroundings), so observed ΔT will be lower than predicted' [1 mark]. This gives clear three-part AO3 structure required by §4.4.1 and avoids the 'OR' ambiguity that leaves graders uncertain whether one or two limiting factors are required.
cross_theme pass

Both E.3 (radioactive decay) and B.1 (thermal energy transfers) are genuinely integrated throughout the question. Part (c) requires students to use the decay constant and activity (E.3) to calculate power output, which is then combined with calorimetry (heat capacity, mass, temperature change—B.1) to find time. Part (d) evaluates the validity of both assumptions through the lens of energy loss mechanisms, requiring understanding of both decay physics and heat transfer.
discriminator pass

Part (d) explicitly requires evaluation of the student's claim about the constant-activity assumption and the overestimate mechanism. The mark scheme requires supporting evidence (M1: fractional decay is negligible) and limiting factors (M2/M3: antineutrino escape, heat loss, gamma escape, etc.). This is a genuine model-critique question that asks students to identify and justify assumptions and their limitations.
rule_of_one fail

Part (c) is marked as 4 marks but contains 5 distinct award criteria (M1–M4 listed, plus M4 itself requires two sub-operations: calculation of t in seconds AND conversion to hours). This exceeds the acceptable tolerance. A 4-mark Calculate part should have exactly 4 award bullets; the current scheme conflates multiple operations into M4 without clear delineation.

FIX: Restructure Part (c) mark scheme to have exactly 4 M-bullets: (M1) Q = mcΔT = 1045 J; (M2) E_decay in joules = 4.51 × 10⁻¹³ J; (M3) P = A × E_decay = 0.0794 W; (M4) t = Q/P and conversion to hours = 3.66 h. Alternatively, reduce to 3 marks if you wish to combine M3 and M4 into 'calculate time in hours' as a single operation.
topic pass

The ERQ effectively integrates both topics. E.3 (Radioactive decay) is the primary focus: parts (a)–(c) require activity, decay constant, and the number of decays. B.1 (Thermal energy transfers) is genuinely invoked in part (c), where the energy released per decay must be converted to power and then related to temperature change via Q = mcΔT. Part (d) further tests understanding of how neutrino escape (a decay physics concept) impacts the energy balance (a thermal transfers concept), ensuring both topics are substantively coupled rather than merely named.

Iteration 1 — passed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (State), part (b) is AO2 (Calculate), part (c) is AO2 (Determine), and part (d) is AO3 (Evaluate). The progression from knowledge through application to critical evaluation is sound and follows IB requirements.
command_structure pass

The mark scheme correctly implements the AO3 'Evaluate' command-term structure per §4.4.1: M1 provides an explicit position (claim is partially correct, with a clear but/however pivot); M2 supplies a supporting consideration (elapsed time << half-life validates constant-activity assumption with quantification); M3 delivers a limiting consideration (antineutrinos and gamma escape reduce measured ΔT). All AO2 parts properly avoid formula-statement marking and correctly apply ECF annotations to method steps in (c) and dependent marks in (b). The mark scheme is rigorous and internally consistent.
cross_theme pass

Both E.3 (radioactive decay) and B.1 (thermal energy transfers) are genuinely integrated throughout the question. E.3 drives parts (a)–(b) and (d)'s activity analysis, while B.1 is essential in part (c): the thermal energy equation Q = mcΔT is directly combined with the decay power P = AE to determine heating time. Neither topic is name-checked only; both concepts are actively used to solve the scenario.
discriminator pass

Part (d) explicitly requires evaluation of a claim about assumptions, distinguishing between the validity of the constant-activity assumption and the discrepancy between predicted and measured values. The mark scheme requires a position statement plus supporting and limiting considerations—a genuine critique of the model's applicability and limitations (e.g., antineutrino escape, incomplete photon absorption). This is a clear model-critique dimension.
rule_of_one pass

All parts have mark counts matching their award-bullet counts within acceptable tolerance. Part (a) [2 marks, 2 bullets], (b) [3 marks, 3 bullets], (c) [4 marks, 4 bullets], (d) [3 marks, 3 bullets] are all correctly aligned. The scheme is internally consistent and well-structured.
topic pass

The ERQ successfully integrates both topics. E.3 Radioactive decay is tested throughout (parts a, b, c defining activity, calculating power from decay rate and energy). B.1 Thermal energy transfers is genuinely required in part (c) where the thermal energy equation Q = mcΔT is applied to determine the time needed to raise water temperature, and in part (d) where energy loss mechanisms (antineutrino escape, incomplete absorption) are evaluated as limiting factors to heat deposition. Neither topic is superficial; both are operationally essential to solving the problem.

Planner output (stage 1)

Archetype: real-world device
Scenario: A radioactive sample of cobalt-60 is sealed in a thermally insulated container of water. The decay of Co-60 emits beta particles and gamma radiation, which are absorbed by the water, raising its temperature over time. Students measure the mass of water, its temperature change, and the activity of the sample to determine the relationship between radioactive decay rate and thermal energy released to the surroundings.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State
b	3	AO2	Calculate
c	4	AO2\|AO3	Determine
d	3	AO3	Evaluate

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