Generated ERQ

✓ passed E.1 Structure of the atom × D.2 Electric and magnetic fields 12 marks HL 3 passes 108.91s $0.5892

## ERQ · 12 marks · Topics: E.1 Structure of the atom + D.2 Electric and magnetic fields **Stem.** A Rutherford-type scattering experiment is repeated using alpha particles directed head-on at a stationary gold-197 nucleus (Z = 79). The alpha particles are produced by a source and accelerated from rest through a potential difference V across parallel plates separated by 4.0 cm, before entering a vacuum chamber where the gold foil is mounted. A detector records the closest approach distance, d, of the alphas to a gold nucleus as 4.55 × 10⁻¹⁴ m. After scattering, some alpha particles enter a region of uniform magnetic field of flux density 0.85 T directed perpendicular to their velocity, and follow a circular arc of radius 0.123 m. Assume the gold nucleus remains stationary and treat all particles non-relativistically. (Mass of alpha = 6.64 × 10⁻²⁷ kg; charge of alpha = +2e.) ### Part (a) Outline [2 marks] · AO1 · Topic: E.1 Outline how the results of the Geiger–Marsden alpha scattering experiment support the nuclear model of the atom. ### Part (b)(i) Show that [3 marks] · AO2/AO3 · Topic: E.1 Show that the kinetic energy of an alpha particle at the moment of closest approach to the gold nucleus is approximately 5.0 MeV. ### Part (b)(ii) Determine [2 marks] · AO2/AO3 · Topic: E.1 Determine the accelerating potential difference V applied across the parallel plates. ### Part (c) Calculate [3 marks] · AO3 · Topic: E.1 + D.2 After scattering, an alpha particle enters the magnetic-field region and moves in a circular arc of radius 0.123 m. Calculate the kinetic energy of this scattered alpha particle, in MeV, and comment on whether the scattering was elastic. ### Part (d) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The kinetic energy obtained in (c) differs slightly from the value in (b)(i). Suggest two reasons, based on the assumptions of the model, why this discrepancy arises. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Most alpha particles passed through with little/no deflection ⇒ atom is mostly empty space [ECF: no] - M2: A very small fraction were deflected through large angles (>90°) ⇒ small, dense, positively charged nucleus containing most of the mass [ECF: no] ### Part (b)(i) [3 marks] - M1: Recognise that at closest approach all KE → electrostatic PE: E_k = kQ₁Q₂/d with Q₁ = 2e, Q₂ = 79e [ECF: no] - M2: Substitution: E_k = (8.99 × 10⁹)(2 × 1.60 × 10⁻¹⁹)(79 × 1.60 × 10⁻¹⁹) / (4.55 × 10⁻¹⁴) [ECF: yes] - M3: E_k = 7.99 × 10⁻¹³ J ≈ 4.99 MeV ≈ 5.0 MeV (2 s.f.) — must show conversion 1 eV = 1.60 × 10⁻¹⁹ J [ECF: yes] ### Part (b)(ii) [2 marks] - M1: Use qV = E_k ⇒ V = E_k / q = (7.99 × 10⁻¹³) / (2 × 1.60 × 10⁻¹⁹) [ECF: yes from b(i)] - M2: V = 2.5 × 10⁶ V (2.50 MV, 2 s.f.) [ECF: yes] ### Part (c) [3 marks] - M1: Equate magnetic force to centripetal: qvB = mv²/r ⇒ v = qBr/m = (2 × 1.60 × 10⁻¹⁹)(0.85)(0.123)/(6.64 × 10⁻²⁷) [ECF: no] - M2: v = 5.04 × 10⁶ m s⁻¹; E_k = ½mv² = ½(6.64 × 10⁻²⁷)(5.04 × 10⁶)² = 8.43 × 10⁻¹⁴ J = 0.527 MeV (accept 0.5 MeV) [ECF: yes] - M3: Comment: this is far less than 5.0 MeV, so scattering was NOT elastic — OR the scattered particle is not the original alpha / energy transferred to nucleus / recoil occurred. Must explicitly compare magnitudes. [ECF: yes] ### Part (d) [2 marks] Award 1 mark each for any two distinct, physically valid critiques: - The gold nucleus was assumed stationary, but in reality it recoils, removing kinetic energy from the alpha - The model treats the nucleus as a point charge; at d ~ 4.5 × 10⁻¹⁴ m the alpha may interact via the strong nuclear force (not purely Coulombic) - Non-relativistic treatment used, but at v ≈ 1.5 × 10⁷ m s⁻¹ for the incident alpha a small relativistic correction exists - Electrons of the gold atom partially screen the nuclear charge, reducing the effective Coulomb potential - The magnetic field may not be perfectly uniform, giving an inaccurate radius measurement ### Marker notes - Alternative for (b)(i): students may quote E_k in J directly and then convert; full marks if all three steps visible. - Alternative for (c): students who use p = qBr then E_k = p²/(2m) earn M1+M2 identically. - (d) discriminator: reject vague answers like "experimental error" or "air resistance" (vacuum chamber). Must reference a stated model assumption. Accept any two from the bulleted list; one mark per distinct, physically valid critique.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ strictly obeys the cognitive ladder. Part (a) is AO1 (Outline); parts (b)(i)–(c) progress through AO2/AO3 with Calculate/Show/Determine; part (d) is AO3 (Suggest) requiring discriminatory reasoning about assumptions. Structure, command terms, and cognitive demand increase appropriately.
cross_theme pass

Part (c) genuinely integrates both E.1 and D.2. The velocity selector calculation requires understanding alpha-particle kinematics (E.1: kinetic energy from nuclear scattering context) AND applying the D.2 force-balance condition (qE = qvB) in crossed fields. Neither topic is name-checked only; both are actively used in solving the problem. Part (d) remains discriminator-focused on E.1 assumptions, which is acceptable design.
discriminator pass

Part (d) explicitly asks students to 'Suggest one reason why the distance of closest approach calculated in (b)(i) overestimates the true radius of the gold nucleus.' This is a model-critique question requiring identification and explanation of assumptions/limitations (point-charge approximation, nuclear recoil, strong force effects, finite particle size). It directly discriminates between students who mechanically apply formulas and those who understand model validity.
rule_of_one fail

Part (d) is marked as 2 marks but contains only 1 award criterion (identify an idealisation). The second mark asks for explanation of how this makes d an overestimate, but this is a consequence/justification of the first point, not a distinct operation. A 2-mark Suggest part should have 2 independent award bullets; this scheme conflates identification + explanation into a single logical unit.

FIX: Restructure Part (d) mark scheme to have exactly 2 distinct operations: (Mark 1) Identify a specific idealisation/assumption in the model [e.g. point-charge alpha, ignored nuclear recoil, ignored strong force, finite alpha size]. (Mark 2) State a second distinct idealisation OR explain the consequence in sufficient detail to warrant a separate mark. Alternatively, reduce Part (d) to 1 mark if only identification is required, or reframe as a 3-mark Explain to accommodate both identification and mechanistic explanation.
topic pass

The ERQ genuinely integrates both topics: E.1 (Structure of the atom) is tested throughout parts (a), (b), and (d) via nuclear model evidence and closest-approach calculations; D.2 (Electric and magnetic fields) is tested in part (c), where students must apply the velocity-selector equilibrium condition (qE = qvB) using the electric field strength and calculated velocity. Both topics are conceptually essential—part (c) cannot be solved without understanding field balance, and parts (a)–(b) require nuclear physics. Neither topic is superficial or nominally invoked.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: part (a) is AO1 (Outline), parts (b)(i)–(b)(ii) and (c) progress through AO2 (Show that, Calculate) and AO3 (Determine), and part (d) is AO3 (Suggest) requiring discussion of physical assumptions. Command terms align with cognitive demand at each tier.
cross_theme warning

critic parse error: Expecting ',' delimiter: line 5 column 148 (char 190); raw: ```json { "passed": true, "severity": "pass", "reasoning": "The ERQ genuinely integrates both E.1 (Structure of th
discriminator pass

Part (d) explicitly asks students to 'Suggest reasons, with reference to the physical assumptions of the model, why these two values differ.' This is a clear model-critique question that requires identification and discussion of idealisations (e.g. point-charge approximation, stationary nucleus, neglect of strong force, finite size effects). The mark scheme confirms this is AO3 and discriminates among students by the depth and distinctness of assumptions identified.
rule_of_one pass

All parts have mark counts that align well with the number of distinct award criteria. Part (a): 2 marks, 2 bullets ✓. Part (b)(i): 3 marks, 3 bullets (formula/substitution/answer) ✓. Part (b)(ii): 2 marks, 2 bullets (method/answer-with-units) ✓. Part (c): 2 marks, 2 bullets (substitution/conversion-with-units) ✓. Part (d): 3 marks, 3 bullets (reasoning + 2 distinct idealisations) ✓. The scheme is internally consistent and matches the IB rigorous structure.
topic pass

Both topics are genuinely and substantively required. Part (b)(i) explicitly combines E.1 (nuclear structure/closest approach concept) with D.2 (Coulomb's law and electric potential energy). Parts (b)(ii) and (c) apply D.2 (electrostatic force, Coulomb interaction) to the nuclear radius from E.1. Part (d) synthesizes both by requiring discussion of nuclear model assumptions alongside electric field limitations. Neither topic is superficial or merely nominal.

Iteration 2 — failed

ao_ladder fail

The cognitive ladder is broken. Part (c) is marked as AO3 (Calculate) but should be AO2/AO3 (Calculate/Determine); more critically, part (d) is marked as AO3 (Suggest) when it should be the final AO3 tier, yet part (c)'s 'comment on elasticity' already requires AO3 evaluative reasoning. The progression does not cleanly ascend: (a) AO1 → (b)(i)–(ii) AO2/AO3 → (c) AO3 with embedded evaluation → (d) AO3 evaluation feels redundant rather than culminating. Part (c) conflates calculation (AO2) with elasticity evaluation (AO3) in a single part; ideally calculation and evaluation should be separated vertically.

FIX: Restructure to enforce strict cognitive ascent: (a) Outline [2, AO1]; (b)(i)–(ii) Show/Determine [5, AO2]; (c) Calculate KE only [2, AO2]; (d) Discuss elasticity and suggest reasons for discrepancy [3, AO3]. Alternatively, keep current structure but relabel (c) as AO2 (Calculate only, defer comment to separate mark) and make (d) explicitly AO3 (Evaluate the model assumptions). The 'comment on elasticity' must not appear in (c) if (d) is the final AO3 tier.
cross_theme pass

The question genuinely integrates both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). Part (b)(i)–(b)(ii) use electrostatic potential energy from the nuclear model to find incident kinetic energy and accelerating voltage. Part (c) then uses the magnetic force and circular motion (D.2) to independently calculate the scattered alpha's kinetic energy from the measured radius, enabling direct comparison and elasticity assessment. Both topics are essential to solving the core problem; D.2 is not name-checked or relegated to assumptions only.
discriminator pass

Part (d) explicitly asks students to 'Suggest two reasons, based on the assumptions of the model, why this discrepancy arises.' This directly critiques the model assumptions (stationary nucleus, point-charge nucleus, non-relativistic treatment, screening, field uniformity), requiring students to identify and explain limitations of the theoretical framework used in parts (a)–(c). The mark scheme confirms this is a model-critique dimension with no calculation component.
rule_of_one pass

All parts have mark allocations that align well with award criteria. Part (a) 2 marks / 2 bullets; (b)(i) 3 marks / 3 bullets (formula, substitution, answer with conversion); (b)(ii) 2 marks / 2 bullets (formula application, numerical answer); (c) 3 marks / 3 bullets (force balance, velocity calculation + KE answer, elasticity comment); (d) 2 marks / variable up-to-2 bullets (two distinct critiques). The divergence rule is satisfied throughout.
topic pass

The ERQ rigorously tests both E.1 (Structure of the atom) and D.2 (Electric and magnetic fields). Parts (a), (b)(i), (b)(ii), and (d) require authentic application of nuclear structure concepts (Coulomb barrier, electrostatic PE, closest approach). Part (c) fundamentally requires D.2 magnetic field theory (Lorentz force, circular motion in B-field) to extract the alpha particle's velocity and kinetic energy after scattering. The scenario is physically integrated: the magnetic deflection is essential to characterizing the scattered particle, making both topics genuinely interdependent rather than sequential or nominal.

Generate another →