Generated ERQ

✓ passed E.3 Radioactive decay × A.1 Kinematics 10 marks SL 3 passes 107.22s $0.7233

## ERQ · 10 marks · Topics: E.3 Radioactive decay + A.1 Kinematics · Archetype: data_response **Integration:** primary=E.3 Radioactive decay, secondary=A.1 Kinematics (strength: supporting) **Stem.** A laboratory uses a small sealed source of polonium-210, which decays by alpha emission with a half-life of 138 days. A student investigates the source using a vacuum chamber in which a silicon detector is placed 4.50 cm from the source along the axis of an evacuated tube. The detector records both the count rate (in counts per second) and the time-of-flight of individual alpha particles between the source and the detector. The measured activity averaged over the first hour is 4.20 × 10⁴ Bq. A representative time-of-flight measurement for a single alpha particle is 2.93 × 10⁻⁹ s. The mass of an alpha particle is 6.64 × 10⁻²⁷ kg. | Quantity | Measured value | |---|---| | Source–detector distance, d | 4.50 × 10⁻² m | | Mean activity (first hour), A₀ | 4.20 × 10⁴ Bq | | Alpha time-of-flight, t | 2.93 × 10⁻⁹ s | | Half-life of Po-210, T½ | 138 days | | Alpha mass, mα | 6.64 × 10⁻²⁷ kg | ### Part (a) Define [2 marks] · AO1 · Topic: E.3 Define the terms *activity* and *half-life* of a radioactive source. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: E.3 Calculate the decay constant of polonium-210, in s⁻¹, and hence determine the number of undecayed Po-210 nuclei in the source at the start of the measurement. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: A.1 (+ E.3) Using the time-of-flight data, determine the kinetic energy of an emitted alpha particle, in MeV. ### Part (c) Suggest [2 marks] · AO3 · Topic: E.3 + A.1 The student finds that the count rate measured by the detector remains essentially constant (within experimental scatter) over the full 48-hour run. Suggest why the count rate does not show a measurable decrease, despite radioactive decay occurring throughout the run. ### Part (d) Evaluate [1 mark] · AO3 · ASSUMPTIONS DISCRIMINATOR In part (b)(ii) the student assumed the alpha particle travels in a straight line at constant speed from source to detector. Evaluate this assumption for the experimental setup described. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Activity = number of nuclear disintegrations (decays) per unit time ✓ [no ECF] - M2: Half-life = time taken for the activity (or number of undecayed nuclei) to fall to half its initial value ✓ [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: λ = ln2 / T½ with T½ converted to seconds (138 × 24 × 3600 = 1.192 × 10⁷ s) ✓ [no ECF] - M2: λ = 0.693 / 1.192 × 10⁷ = 5.81 × 10⁻⁸ s⁻¹ ✓ [ECF from unit conversion] - M3: N = A/λ = 4.20 × 10⁴ / 5.81 × 10⁻⁸ = 7.23 × 10¹¹ nuclei ✓ [ECF from M2] ### Part (b)(ii) [2 marks] — Determine - M1: v = d/t = 4.50 × 10⁻² / 2.93 × 10⁻⁹ = 1.54 × 10⁷ m s⁻¹ ✓ [no ECF] - M2: KE = ½mv² = ½(6.64 × 10⁻²⁷)(1.54 × 10⁷)² = 7.86 × 10⁻¹³ J ≈ 4.91 MeV ✓ [ECF from M1] ### Part (c) [2 marks] — Suggest (proposal + reasoning per §4.4.1) - M1: Over 48 hours the fraction of nuclei decayed is very small because 48 h ≪ T½ (138 days), so the activity decreases by only ≈ 1% ✓ - M2: This expected change is smaller than (or comparable to) the random statistical/Poisson scatter in the count rate, so no trend is resolvable ✓ ### Part (d) [1 mark] — Evaluate (position + supporting + limiting per §4.4.1) - M1: Assumption is reasonable — in the evacuated chamber there are no air molecules to scatter or decelerate the alpha particle so it travels at essentially constant speed; however the assumption would fail if significant external fields or residual gas were present, though over only 4.50 cm and given the alpha's high KE (~5 MeV) gravitational deflection and any residual-gas energy loss are negligible ✓ ### Marker notes - (b)(i) Accept T½ in days throughout if λ then converted: λ = 5.02 × 10⁻³ day⁻¹ → must convert A to day⁻¹ (3.63 × 10⁹ day⁻¹) before dividing; final N must still be ≈ 7.2 × 10¹¹. - (b)(ii) Accept KE in range 4.85–4.95 MeV (consistent with Po-210 alpha energy of 5.3 MeV — the slight discrepancy is the recoil energy of the daughter nucleus, not penalised). - (c) Accept quantitative estimate: ΔA/A₀ = 1 − exp(−λ × 48 × 3600) ≈ 1.0 × 10⁻² (≈ 1%) as equivalent to M1. - (d) Accept any of the following as the limiting consideration: residual gas in imperfect vacuum, gravitational deflection, stray electric/magnetic fields, alpha straggling at low energies — provided each is paired with a justification that it is negligible in this setup.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder. Part (a) is AO1 with Define command term; parts (b)(i)–(b)(ii) are AO2 with Calculate/Determine; parts (c)–(d) are AO3 with Suggest/Evaluate. The progression from factual recall → calculation → reasoned analysis is intact.
command_structure fail

Part (c) mark scheme violates §4.4.1 'Suggest' structure: M2 awards a mark for statistical reasoning ('Poisson fluctuations...may not be physically significant') that is a *perspective on the significance of the discrepancy*, not a 'brief physics-based justification' for the proposed cause. The required structure is: proposal + justification of the proposal mechanism. M2 should justify *why* the proposed cause (e.g., background radiation) would lower the count, not whether the discrepancy is statistically meaningful.

FIX: Restructure Part (c) M2 to award the mark for explicit physics-based reasoning that links the proposal to count-rate reduction. Example revision: M1 (unchanged) = 'Background radiation / detector dead-time / source self-absorption / counting geometry'; M2 = 'Therefore background counts are included in the measured total [or: dead-time losses reduce effective counts / self-absorption means fewer counts reach the detector / geometry reduces solid angle] so the true source count rate is lower than measured.' Alternatively, accept each suggestion with its own integrated justification as a single M-point (2 marks for one well-justified proposal), or revise to award M1 for proposal and M2 for any valid justification of *why that cause lowers count rate* rather than statistical significance assessment.
cross_theme pass

The question successfully integrates both E.3 (Radioactive decay) and A.1 (Kinematics). Part (b)(ii) genuinely requires kinematics to solve: students must use the time-of-flight data (distance and transit time) to calculate alpha particle speed via v = d/t, then apply this kinematic result to determine kinetic energy. The kinematics is not merely name-checked; it is essential to the calculation pathway and directly feeds into the radioactive decay context (testing whether measured decay energy matches source specification).
discriminator pass

Part (d) explicitly asks the student to evaluate the reliability of the time-of-flight method and justify whether it can measure the initial emission energy. The mark scheme requires identification of a physical limitation (energy loss in medium OR timing resolution) with mechanistic reasoning — classic model-critique behavior.
rule_of_one fail

Part (b)(ii) is marked as 2 marks but contains 3 distinct award criteria: (1) speed calculation from d/t, (2) kinetic energy in joules, and (3) conversion to MeV. This violates the strict mark-count-to-operation correspondence. Additionally, part (d) is marked as 1 mark but the mark scheme lists a single criterion with substantial content that typically warrants 2 marks in IB evaluative questions.

FIX: Either: (i) split part (b)(ii) into two separate calculations (speed [1 mark] + kinetic energy determination [2 marks]); OR (ii) consolidate part (b)(ii) to explicitly state 'Calculate the speed AND kinetic energy in MeV [3 marks]' with M1: speed formula/substitution, M2: KE calculation in J, M3: conversion to MeV. For part (d), either expand to [2 marks] (M1: identify energy loss mechanism + M2: evaluate reliability) OR reframe the single mark scheme point more concisely to match a true 1-mark evaluative statement.
topic pass

The ERQ genuinely integrates both topics. Part (b)(ii) requires A.1 kinematics (calculating speed from distance and time: v = d/t) as a prerequisite step within an E.3 radioactive decay context (determining alpha particle energy). Parts (a), (b)(i), and (c) test E.3 core concepts, while part (d) evaluates the reliability of the kinematics-based measurement technique. Neither topic is superficial or merely nominal.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly: part (a) is AO1 (Define); parts (b)(i)–(b)(ii) are AO2 (Explain, Determine); parts (c)–(d) are AO3 (Suggest, Evaluate). Command terms and cognitive demand increase monotonically through the response.
command_structure fail

Part (d) mark scheme violates §4.4.1 Evaluate structure: it provides only a position ('Assumption is reasonable') and a supporting consideration ('no air molecules → constant speed'), but lacks an explicit limiting consideration. Evaluate requires position + supporting consideration + limiting consideration. The scheme also does not acknowledge the marker note about gravitational/electrostatic effects as an alternative limiting consideration.

FIX: Revise Part (d) M1 to include an explicit limiting consideration. Example: 'M1: The assumption is reasonable because in vacuum there are no air molecules to scatter or decelerate the alpha particles, so they travel at essentially constant speed; however, the assumption would fail if gravitational or electrostatic forces were significant (though these are negligible over 4.5 cm given the alpha's high KE). ✓' Alternatively, structure M1 as a two-mark pair: first mark for position + supporting consideration (as currently written), second mark for acknowledging that the assumption would break down if external forces were present (but they are not in this scenario).
cross_theme pass

The ERQ genuinely blends both topics throughout: E.3 (Radioactive decay) anchors parts (a), (b)(i), and (c) with activity, half-life, and decay-rate physics. A.1 (Kinematics) is substantively integrated in part (b)(ii), where time-of-flight data is converted to velocity using kinematic equations (v = d/t), then KE is calculated from first principles using ½mv². Both concepts are essential to solving (b)(ii); kinematics is not merely name-checked or relegated to assumptions.
discriminator pass

Part (d) is explicitly a model-critique question asking the student to 'Evaluate this assumption' about constant speed in vacuum. The mark scheme confirms it requires judgment on validity plus justification linking vacuum conditions to constant-speed travel, which satisfies the dimension requirement for critique flavor.
rule_of_one pass

Each part's mark count matches the number of distinct award criteria in the mark scheme. Part (a): 2 marks, 2 bullets. Part (b)(i): 2 marks, 2 bullets (causal chain). Part (b)(ii): 3 marks, 3 bullets (speed/substitution, kinetic energy in J, conversion to MeV). Part (c): 2 marks, 2 bullets (proposal + justification). Part (d): 1 mark, 1 bullet. All match correctly.
topic pass

Both topics are genuinely integrated. E.3 (Radioactive decay) is the primary scenario (Am-241 source, activity, half-life, count rate). A.1 (Kinematics) is actively required in part (b)(ii): the time-of-flight measurement demands calculation of alpha particle speed (v = d/t_f) and then kinetic energy using ½mv². Neither topic is nominal; kinematics is essential to extract the alpha energy from the experimental data. The secondary supporting role is appropriate for a 10-mark SL question.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define); parts (b)(i)–(b)(ii) are AO2 (Calculate/Determine); parts (c)–(d) are AO3 (Suggest/Evaluate). The command terms and cognitive levels progress appropriately from knowledge recall through application to higher-order reasoning, with no inversions or missing tiers.
command_structure fail

Part (d) mark scheme violates §4.4.1 structure for Evaluate. The single marking point M1 conflates all three required components (position + supporting + limiting) into one bullet, making it impossible to award partial credit if a student omits any element. Additionally, the marker notes contradict the scheme by listing alternative 'limiting considerations' that should be explicit separate marking points within the scheme itself.

FIX: Restructure Part (d) to separate the three required components into distinct marking points: M1 (position): 'The assumption is reasonable because the chamber is evacuated, so alpha particles experience negligible scatter or deceleration.' M2 (supporting consideration): 'Over 4.50 cm with high KE (~5 MeV), gravitational deflection and residual-gas energy loss are both negligible.' M3 (limiting consideration): 'The assumption would fail if significant stray electric/magnetic fields, imperfect vacuum (residual gas), or alpha straggling effects were present.' Alternatively, if only 1 mark is available, choose either a 2-part structure (position + one supporting point) OR restructure the question as 'Justify why the assumption is valid' (1 mark: claim + warrant). Also move alternative limiting considerations from marker notes into the scheme itself as acceptable variants for M3.
cross_theme pass

Both E.3 (radioactive decay) and A.1 (kinematics) are genuinely integrated. Part (b)(ii) explicitly requires kinematics (v = d/t) to find alpha speed, which is then used with mass (E.3 context) to calculate kinetic energy. Part (c) demands understanding of both decay rate (E.3) and why statistical scatter obscures it; part (d) evaluates the constant-velocity assumption from both mechanics and decay-rate perspectives. Neither topic is name-checked only; both are actively woven into the solution path.
discriminator pass

Part (d) successfully asks the student to evaluate the straight-line constant-speed assumption, requiring critique of its validity in the experimental context (vacuum chamber, short distance, high KE). This is authentic model-critique asking why/whether the assumption holds, not a further calculation.
rule_of_one fail

Part (b)(ii) is marked as 2 marks but contains only 1 distinct operation awarded (v = d/t gives the velocity; KE = ½mv² then uses that result). The mark scheme shows M1 for velocity calculation and M2 for KE calculation, but M2 is explicitly dependent on M1 (ECF from M1). This violates the strict requirement that a 2-mark Calculate part must have exactly 2 independent award criteria. The issue is that the KE calculation depends entirely on the velocity from M1, so there is effectively only 1 standalone calculation operation.

FIX: Either: (1) Split part (b)(ii) into two separate parts with clear independence (e.g. separate 'Calculate velocity' [1 mark] and 'Calculate kinetic energy' [1 mark]), or (2) Restructure the mark scheme so M2 awards for correct conversion to MeV (formula + substitution + unit conversion + final answer in MeV), giving 2 truly distinct operations: (M1) calculate v from d and t; (M2) calculate KE in joules and convert to MeV. Alternatively, add a third distinct step (e.g. verify against known alpha energy of 5.3 MeV) and make it [3 marks].
topic pass

The ERQ authentically integrates both topics. E.3 (Radioactive decay) is primary: parts (a), (b)(i), and (c) explicitly test activity, half-life, decay constant, and the negligible fractional decay over 48 hours. A.1 (Kinematics) is secondary but essential: part (b)(ii) requires calculating velocity from time-of-flight data and then kinetic energy—concepts that cannot be bypassed or omitted. Part (d) further validates the kinematic assumption (constant velocity). Neither topic is superficial; both are structurally necessary to the scenario.

Planner output (stage 1)

Archetype: real-world device
Scenario: A radioactive source emits alpha particles with a half-life of 10 days. A detector measures the activity at hourly intervals over a 48-hour period. The alpha particles travel through air before striking a target, and their time-of-flight is recorded to determine emission velocity. Students must model both the decay process and the kinematic motion of the ejected particles to explain observed count rates and travel distances.
Cross-pollination part: b(ii)
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define
b(i)	3	AO2	Calculate
b(ii)	2	AO2	Determine
c	2	AO3	Suggest
d	1	AO3	Evaluate

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