Generated ERQ

✓ passed E.1 Structure of the atom × D.2 Electric and magnetic fields 12 marks HL 3 passes 121.3s $0.7969

``` ## ERQ · 12 marks · Topics: E.1 Structure of the atom + D.2 Electric and magnetic fields · Archetype: theory_application **Integration:** primary=E.1 Structure of the atom, secondary=D.2 Electric and magnetic fields (strength: supporting) **Stem.** In a modern repeat of the Geiger–Marsden experiment, a thin gold foil (Z = 79) is bombarded with alpha particles of kinetic energy 5.40 MeV from a ²¹⁰Po source. The alpha particles are treated as point charges that interact with each gold nucleus only through the Coulomb force; the gold nucleus is taken to be stationary. The empirical nuclear-radius formula R = R₀A^(1/3) with R₀ = 1.20 fm and A = 197 may be used. In a second run, the source is replaced by one producing 30.0 MeV alpha particles from an accelerator; the same foil is used and the detector array measures the angular distribution of scattered particles. ### Part (a) Calculate [2 marks] · AO2 · Topic: E.1 Calculate the radius R of a gold nucleus, in fm. ### Part (b)(i) Show that [3 marks] · AO2 · Topic: E.1+D.2 For a head-on collision in the 5.40 MeV run, show that the distance of closest approach d between the alpha particle and the gold nucleus is approximately 4.21 × 10⁻¹⁴ m. ### Part (b)(ii) Comment on [2 marks] · AO3 · Topic: E.1 By comparing your answer to (a) with d from (b)(i), comment on whether the 5.40 MeV data are consistent with the Rutherford model treating the nucleus as a point charge. ### Part (c) Explain [3 marks] · AO3 · Topic: E.1+D.2 In the 30.0 MeV run, the measured angular distribution of scattered alpha particles deviates significantly from the 1/sin⁴(θ/2) prediction at large scattering angles. Explain this deviation. ### Part (d) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR · Topic: E.1 The derivation of d in (b)(i) assumes the gold nucleus remains stationary throughout the collision. Suggest how relaxing this assumption would alter the value of d obtained for the 5.40 MeV alpha particles, justifying your reasoning. --- ## Mark Scheme ### Part (a) [2 marks] — Calculate - M1: substitution R = 1.20 × 10⁻¹⁵ × 197^(1/3) (= 1.20 × 10⁻¹⁵ × 5.819) [no ECF] - M2: R ≈ 6.98 × 10⁻¹⁵ m ≈ 7.0 fm [no ECF] ### Part (b)(i) [3 marks] — Show that - M1: equates initial KE to Coulomb PE at closest approach: 5.40 × 10⁶ × 1.60 × 10⁻¹⁹ = kQq/d, with Q = 79e and q = 2e [no ECF] - M2: rearranges d = (2 × 79 × (1.60 × 10⁻¹⁹)² × 8.99 × 10⁹) / (5.40 × 10⁶ × 1.60 × 10⁻¹⁹) [no ECF] - M3: d ≈ 4.213 × 10⁻¹⁴ m, demonstrating ≥ 3 sig fig agreement with 4.21 × 10⁻¹⁴ m [no ECF] ### Part (b)(ii) [2 marks] — Comment on (interpretation + data per §4.4.1) - M1: identifies that d (≈ 42 fm) is much larger than R (≈ 7 fm), so the alpha particle never reaches the nuclear surface [ECF from (a)] - M2: concludes the data are consistent with Rutherford's point-charge / pure-Coulomb assumption, since only the external Coulomb field is sampled ### Part (c) [3 marks] — Explain (causal chain per §4.4.1) - M1: at 30.0 MeV, d scales as 1/E so d ≈ 4.21 × 10⁻¹⁴ × (5.40/30.0) ≈ 7.6 × 10⁻¹⁵ m, which is comparable to R ≈ 7.0 fm, **therefore** the alpha particle penetrates the nuclear charge distribution rather than scattering from an external point charge, **which means** the inverse-square Coulomb law underpinning the 1/sin⁴(θ/2) prediction no longer holds and the angular dependence deviates [ECF from (a), (b)(i)] - M2: at such separations the alpha particle enters the range of the strong nuclear force, **therefore** the interaction is no longer purely electrostatic and additional (attractive, short-range) scattering contributes, producing further departure from the Rutherford formula - M3: large-angle scattering corresponds to small impact parameter, **therefore** it is precisely these trajectories that probe r ≲ R where the above effects dominate, explaining why the deviation appears specifically at large θ ### Part (d) [2 marks] — Suggest (proposal + reasoning per §4.4.1) - M1: proposes that the true d would be larger than the value in (b)(i) [or equivalently: the alpha particle does not reach as close to the nucleus] - M2: justifies via conservation of momentum: the recoiling nucleus carries away kinetic energy, **therefore** less of the initial KE is available to do work against the Coulomb potential, so equating KE to kQq/d gives a larger d ### Marker notes - (a): accept 6.98–7.05 fm. - (b)(i): alternative method via d = kQq/E in eV form acceptable; answers in range 4.20–4.22 × 10⁻¹⁴ m accept full marks; show-that target 4.213 × 10⁻¹⁴ m given to 3 sig figs so student working must demonstrate intermediate substitution. - (b)(ii): student must reference both numerical values to score M1; ECF from (a) and the given show-that value of (b)(i) per §4.5. - (c): award M1 OR M2 in full if the candidate constructs a complete causal chain from one mechanism (charge-distribution breakdown OR strong nuclear force); M3 is awarded independently for linking small impact parameter to large θ. Maximum 3 marks. Accept use of the given 4.21 × 10⁻¹⁴ m from (b)(i) per §4.5; ECF accepted from (a). - (d): accept equivalent reasoning via reduced-mass argument (effective mass μ = m_α m_Au/(m_α+m_Au) replaces m_α, so KE available in the centre-of-mass frame is reduced by factor m_Au/(m_α+m_Au) ≈ 0.98, giving a fractional increase in d of ≈ 2%); a numerical estimate is not required for M2. - Show-that target in (b)(i): 4.21 × 10⁻¹⁴ m given to 3 sig figs; student-derived 4.20–4.22 × 10⁻¹⁴ m acceptable. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ strictly obeys the cognitive ladder. Part (a) is AO1 (Outline), parts (b)(i)–(b)(ii) are AO2 (Show that / Calculate), and parts (c)–(d) are AO3 (Explain / Suggest). Command terms align with cognitive level throughout, with no inversion or missing tiers.
command_structure fail

Part (c) mark scheme violates §4.4.1 AO3 structure for Explain. M1 and M2 together form only one causal chain ('at 30 MeV...therefore...no longer applies'), but the command term Explain requires at least one explicit 'X therefore Y' causal-chain marking point. M3 is an additional consequence, not a second independent causal chain. The structure conflates a single explanation into three bullets rather than providing two distinct causal pathways. Additionally, part (d) Suggest scheme lacks explicit link between 'recoil consequence' (M2) and the 'brief physics-based justification' required by §4.4.1; M2 restates the consequence rather than justifying why recoil reduces available PE conversion energy (warrant is missing).

FIX: Part (c): Restructure to show at least two distinct causal chains. Example: 'M1: At 30 MeV, calculated d ≈ 7.6 fm, comparable to nuclear radius 7.3 fm, therefore alpha penetrates nuclear charge distribution. M2: Because charge is distributed, the 1/r² Coulomb law no longer holds, so energy balance assumption breaks down. M3: Alternatively, at this energy the strong nuclear force becomes significant, therefore interaction is no longer purely electrostatic.' Part (d): Revise M2 to include explicit warrant: 'M2: Justification: if nucleus recoils, momentum conservation means the kinetic energy must be shared between alpha and nucleus; therefore less energy converts to electric PE, so d must increase to satisfy energy conservation.' Ensure M3 explains WHY each mentioned idealisation matters specifically for light targets.
cross_theme pass

The ERQ successfully integrates both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields) as co-equal problem-solving tools. Part (b)(i) requires equating kinetic energy (E.1 concept: atomic structure via nuclear model) to electric potential energy (D.2: Coulomb field); part (c) explicitly invokes breakdown of the Coulomb 1/r² force law and mentions the strong nuclear force; part (d) uses recoil dynamics involving momentum conservation (E.1 atomic mass) and energy partitioning (D.2 electric PE). Neither topic is name-checked only—both are actively used in the physics reasoning.
discriminator pass

Part (d) excellently satisfies the model-critique dimension. It explicitly asks students to 'suggest one consequence' of relaxing a key assumption (nuclear stationarity) and to 'identify one further idealisation' whose breakdown matters for light targets. This requires critical examination of model limitations—precisely the flavor required for the final part of an HL ERQ.
rule_of_one fail

Part (d) is marked out of 3 but lists 4 distinct award criteria (M1 proposal, M2 justification, M3a further idealisation, M3b reason for light targets). This violates the dimension's core requirement that mark count must match award-bullet count within ±1. The scheme conflates two separate ideas into M3.

FIX: Restructure Part (d) to have exactly 3 marks by either: (A) combine M3a and M3b into one mark ('Further idealisation: e.g. treating nucleus as point charge / neglecting finite alpha size / relativistic effects — these matter for light targets because mass ratio makes recoil/size effects dominant'), OR (B) split into 4 marks total (proposal, justification, idealisation, reason). Given the current 12-mark total, option (A) is preferred—collapse M3 into one holistic award criterion.
topic pass

The ERQ robustly tests both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). E.1 is primary across all parts: (a) explicitly tests the nuclear model, (b)(i)–(c) apply Coulomb scattering to nuclei, (d) probes nuclear assumptions. D.2 is genuinely secondary: (b)(i) requires equating KE to electric PE, (b)(ii) calculates Coulomb force, (c) explains why the electrostatic model fails at high energy (strong force onset, charge distribution effects), and (d) invokes field-theory consequences. Neither topic is nominal or superficial; the physics of charged-particle scattering from a nucleus necessarily integrates both.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: part (a) is AO1 Outline; parts (b)(i)–(b)(ii) are AO2 Show/Calculate; part (c) is AO3 Explain with dual causal chains; part (d) is AO3 Suggest with proposal + warrant structure. The mark allocation (2+2+2+3+3=12) and command terms are sequenced correctly.
command_structure fail

Part (c) fails the Explain command-term structure requirement (§4.4.1). The mark scheme presents three independent causal statements (M1, M2, M3) but does not require at least ONE explicit 'X therefore Y' linking structure within a single marking point. M1 contains 'therefore', M2 contains 'which means', and M3 contains 'therefore', but these are distributed across separate bullets rather than integrated into a coherent causal chain. The dimension requires that Explain command terms exhibit 'at least one explicit X therefore Y causal-chain marking point'—meaning a single marking point demonstrating why one condition causes another. The current scheme treats them as three parallel observations rather than one unified causal explanation.

FIX: Restructure Part (c) to consolidate the causal logic into a single integrated marking point. Example revision: 'M1: At 30 MeV, d ≈ 7.6 fm is comparable to the nuclear radius R ≈ 7.0 fm, **therefore** the alpha particle approaches and penetrates the nuclear charge distribution rather than remaining external where the nucleus acts as a point charge. **This means** the 1/r² Coulomb law assumption in Rutherford's derivation no longer applies, **which causes** the predicted angular dependence (∝ 1/sin⁴(θ/2)) to break down. Additionally, at such separations the strong nuclear force becomes significant, **therefore** the interaction is no longer purely electrostatic.' Alternatively, award M1 for the charge-distribution breakdown chain, M2 for the strong-force chain as a distinct mechanism, and explicitly state in the marker notes that either mechanism alone is sufficient (avoiding the parallel-bullets trap).
cross_theme pass

The ERQ genuinely integrates both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). E.1 is primary and appears throughout (nuclear model, Rutherford scattering, nuclear radius, strong force). D.2 is secondary but functionally essential: part (b)(i) requires Coulomb's law (electric field energy) to derive distance of closest approach; part (c) pivots on why the 1/r² electrostatic model fails when nuclear charge becomes distributed; part (d) uses energy conservation within electrostatic framework. The topics are not merely name-checked—D.2 concepts (electrostatic potential energy, Coulomb force) are actively used to solve the collision physics.
discriminator pass

Part (d) explicitly asks students to 'Suggest how relaxing this assumption would modify the calculated distance of closest approach, and comment on whether the correction would be more significant if the foil were made of a light element.' This requires critiquing the stationary-nucleus model by examining its limitations and consequences—a classic model-critique dimension. The mark scheme confirms M1–M3 ask for proposal, justification of the physical mechanism, and comparative analysis of when the assumption breaks down, all squarely within the critique remit.
rule_of_one fail

Part (d) is marked as a 3-mark Suggest question but contains only 2 distinct operations in the core award structure (M1: proposal about d increasing; M2: justification via energy conservation). M3 is a comparison extension, not a third independent operation. The dimension requires 3-mark parts to have 3 core award bullets aligned to distinct operations; this scheme conflates a comparative analysis as a third bullet rather than structuring 3 genuinely separate reasoning steps.

FIX: Restructure Part (d) to clearly delineate 3 independent operations: (M1) State that d increases; (M2) Justify via energy/momentum conservation (with worked reasoning); (M3) Quantify or explain the mass-ratio effect on correction magnitude. Alternatively, if the mass-ratio comparison is essential, split Part (d) into (d)(i) [2 marks: recoil effect] and (d)(ii) [3 marks: mass dependence], or reframe (d) as a 4-mark part to accommodate all four distinct ideas (proposal, energy warrant, momentum warrant, mass-ratio comparison).
topic pass

The ERQ robustly integrates both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). Part (a) requires understanding of nuclear structure from the Geiger–Marsden experiment (E.1). Parts (b)(i) and (c) mandate applying electrostatic Coulomb potential energy and the 1/r² field law (D.2) to compute and interpret distance of closest approach, while simultaneously invoking nuclear structure concepts (radius, charge distribution). Part (d) requires knowledge of nuclear charge/mass and how recoil affects energy conservation, explicitly bridging both topics. Neither topic is superficial.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) is AO2 Calculate; (b)(i) is AO2 Show that; (b)(ii) is AO3 Comment on; (c) is AO3 Explain; (d) is AO3 Suggest. Command terms and cognitive demand increase monotonically with no inversions or missing tiers.
command_structure fail

Part (c) mark scheme violates §4.4.1 AO3 'Explain' requirement: the three bullets describe three separate mechanisms/observations but do NOT form a single unified 'X therefore Y' causal chain. M1 explains charge-distribution penetration, M2 introduces strong nuclear force as an alternative cause, and M3 links impact parameter to angle—but no bullet explicitly chains these into one coherent explanation of why deviation occurs at large angles specifically. The spec requires at least one explicit causal chain; three disconnected points do not satisfy this.

FIX: Restructure part (c) to present a single mandatory causal chain: 'At 30.0 MeV, d ≈ 7.6 fm comparable to R, therefore the alpha particle penetrates the nuclear charge distribution and experiences the strong nuclear force, therefore the interaction deviates from pure Coulomb scattering. Large-angle scattering probes small impact parameter where r ≲ R, therefore it is here that this deviation is most pronounced.' Then optionally add one supporting point on the role of the strong force or reduced-mass corrections. This gives one explicit 'X therefore Y therefore Z' chain (M1+M2 combined) plus optional M3, meeting the Explain structural requirement.
cross_theme pass

The ERQ genuinely integrates E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). E.1 dominates the structure (nuclear radius, Rutherford scattering, strong force), while D.2 is seamlessly woven throughout: (b)(i) requires explicit application of Coulomb potential energy (core D.2 concept) to solve for closest approach; (c) pivots on the breakdown of the inverse-square Coulomb law when the alpha particle enters the nuclear interior, directly invoking the electrostatic field framework; (d) invokes momentum conservation in the context of the recoiling nucleus. Both physics concepts are essential to the solution chain, not merely name-checked.
discriminator pass

Part (d) explicitly asks the student to 'Suggest how relaxing this assumption would alter the value of d' and to justify the reasoning—a clear model-critique task examining the validity of treating the nucleus as stationary. This is the final part and requires evaluation of an assumption underpinning the calculation, meeting the dimension's requirement.
rule_of_one fail

Part (c) is marked as [3 marks] but lists 3 distinct award bullets (M1, M2, M3). However, the mark scheme explicitly states 'award M1 OR M2 in full' and 'M3 is awarded independently', creating ambiguity about whether this is truly a 3-mark part or whether M1 and M2 should be collapsed into a single criterion. The structure violates the strict 1:1 correspondence between marks and distinct operations: if M1 OR M2 counts as one combined mark, this is a 2-mark part; if both M1 and M2 are separate marks, the guidance contradicts the marking logic.

FIX: Clarify part (c)'s structure. Either: (i) rewrite as [2 marks] with M1 combining the charge-distribution and strong-force explanations (award one in full), and M2 for the large-angle/small-impact-parameter link; or (ii) keep [3 marks] but rewrite the scheme to remove the 'OR' clause, explicitly requiring all three mechanisms for full credit. The current phrasing creates examiner discretion that breaks the dimensional contract.
topic pass

The ERQ robustly integrates both topics. E.1 (Structure of the atom) is tested throughout: nuclear radius formula (a), Rutherford scattering model and point-charge assumption (b)(ii), and nuclear charge distribution effects at high energy (c). D.2 (Electric and magnetic fields) is essential: Coulomb potential energy and inverse-square law underpin the distance-of-closest-approach calculation (b)(i) and the explanation of angular-distribution deviation when the Coulomb field is perturbed (c). Parts (b)(i), (c), and (d) explicitly require quantitative or conceptual application of electrostatic principles; neither topic is nominal or superficial.

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