Generated ERQ

✓ passed C.2 Wave model × D.2 Electric and magnetic fields 12 marks HL 3 passes 112.22s $0.6983

## ERQ · 12 marks · Topics: C.2 Wave model + D.2 Electric and magnetic fields · Archetype: theory_application **Integration:** primary=C.2 Wave model, secondary=D.2 Electric and magnetic fields (strength: supporting) **Stem.** A student sets up a Young's double-slit experiment in a sealed chamber. Coherent monochromatic light of wavelength 550 nm illuminates two narrow slits separated by 0.25 mm, and the interference pattern is observed on a screen 1.5 m beyond the slits. The chamber is initially evacuated and a sharp pattern of bright and dark fringes is recorded. The chamber is then filled with low-pressure air, and a uniform horizontal electric field of magnitude E is applied across the region between the slits and the screen, perpendicular to the direction of light propagation. Stray ionization (from background radiation) produces a low density of singly-charged positive ions (mass m = 4.8 × 10⁻²⁶ kg, charge +e) within the light path. As the field strength is increased above ~1.0 × 10⁵ V m⁻¹, the student observes that the fringes progressively lose contrast and eventually disappear. ### Part (a) State [2 marks] · AO1 · Topic: C.2 State two conditions that the light sources at the two slits must satisfy in order for a stable interference pattern to be observed on the screen. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: C.2 Calculate the fringe spacing on the screen when the chamber is evacuated. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: C.2 Determine the path difference, in nm, between waves arriving at the centre of the first dark fringe from the two slits. ### Part (c) Explain [3 marks] · AO3 · Topic: C.2 + D.2 The applied electric field accelerates the positive ions along the field direction. Using F = qE, the ions reach a typical kinetic energy of order 10⁻¹⁸ J before recombining or colliding. Explain how the work done on these charged particles by the field, together with their interaction with the light passing through the medium, leads to a loss of fringe visibility. ### Part (d) Evaluate [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR Evaluate the assumption, used in part (b), that the air in the chamber can be treated as an undisturbed optical medium when the field is applied. --- ## Mark Scheme ### Part (a) [2 marks] — State - M1: the two sources must be coherent / maintain a constant phase difference [no ECF] - M2: the two sources must have the same frequency/wavelength (OR comparable amplitude / same polarization) [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: identifies s = λD/d and substitutes: s = (550 × 10⁻⁹)(1.5)/(0.25 × 10⁻³) [no ECF] - M2: correct evaluation of numerator/denominator, e.g. 8.25 × 10⁻⁷ / 2.5 × 10⁻⁴ [ECF from M1] - M3: s = 3.3 × 10⁻³ m (3.3 mm) [ECF from M1, M2] ### Part (b)(ii) [2 marks] — Determine - M1: identifies that first minimum corresponds to path difference = λ/2 [no ECF] - M2: path difference = 275 nm (accept 2.75 × 10⁻⁷ m) [ECF from M1] ### Part (c) [3 marks] — Explain (causal chain per §4.4.1) - M1: the electric force F = qE does work on the ions, giving them kinetic energy and accelerating them along randomly-distributed trajectories (since ions originate at random positions/times) [fact] - M2: the moving ions (and the field-induced dipoles in neutral molecules along the field direction) locally and time-dependently alter the refractive index of the air along each light path, therefore the optical path length traversed by light reaching the screen from each slit fluctuates randomly in time [linking — therefore] - M3: therefore the phase difference between waves from the two slits at any screen point fluctuates randomly, so on time-averaging the bright and dark fringes wash out and fringe visibility is reduced [linking — therefore + consequence] ### Part (d) [2 marks] — Evaluate (position + supporting + limiting per §4.4.1) - M1: position + supporting: the assumption is justified for the evacuated/field-free case — the wave model with a uniform medium correctly predicts the observed fringe spacing in (b), showing it captures the essential interference physics - M2: limiting consideration: however, once the field ionizes/polarizes the medium the refractive index is no longer uniform or static, so the wave model can only describe this regime by adding ad-hoc coupling between the field (D.2) and the optical phase — a limitation the simple model in (b) does not contain ### Marker notes - (b)(i): accept answers 3.2–3.4 mm; penalise missing units once only across paper. - (b)(ii): ECF — if student used incorrect fringe-spacing equation in (b)(i), still award full marks here for λ/2 reasoning and correct numerical value 275 nm. - (c): accept equivalent descriptions invoking density fluctuations, scintillation, or randomly-varying optical path; M2 requires explicit link between charged-particle motion in the field and an optical-medium property; M3 requires explicit link between random phase and loss of visibility. - (d) accept any of: medium is not truly uniform once ionized; refractive index becomes field-dependent (Kerr-type response); scattering by ions reduces coherence; thermal motion from ion–neutral collisions broadens phase distribution.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ correctly implements the cognitive ladder: Part (a) is AO1 (State), parts (b)(i)–(b)(ii) are AO2 (Calculate/Determine), part (c) is AO3 (Explain with causal chain), and part (d) is AO3 (Evaluate with judgement + supporting + limiting). The progression is strict, properly sequenced, and each tier uses appropriate command terms.
command_structure fail

Part (c) fails the Explain command-term structure per §4.4.1. While M1 and M2 establish a causal chain (F = qE causes acceleration → fluctuating optical path length → random phase offset), M3 does not function as an explicit 'therefore Y' linking point; instead it restates consequences. The marking scheme lacks a single causal-chain bullet that reads 'X therefore Y' showing how random phase changes directly cause fringe visibility reduction. Part (d) also fails: M1 and M2 are listed as 'supporting' and 'limiting' but do not follow the required structure of 'position + supporting consideration + limiting consideration'; instead they are presented as two separate perspectives without a clear evaluative position statement that integrates both.

FIX: Part (c): Restructure to M1 (force accelerates ions) → M2 (acceleration causes fluctuating refractive index/optical path) → M3 (random phase differences acquired by each slit therefore prevent fixed constructive/destructive interference; consequently fringe visibility is lost). Part (d): Rewrite as M1 (position: the wave model is adequate only when the medium is uniform and undisturbed), M2 (supporting: it predicts fringe spacing correctly in the field-free case), M3 (limiting: once charges are driven by E, the model fails because it neglects light–charge electromagnetic coupling and scattering, which are essential to explain coherence loss).
cross_theme pass

Both C.2 (wave model: coherence, interference, fringe visibility) and D.2 (electric and magnetic fields: force on charges, field-induced motion) are genuinely integrated throughout. Part (c) is the key: it requires understanding how the electric field (D.2) accelerates ions/electrons, causing random phase fluctuations that destroy the interference pattern predicted by wave theory (C.2). Neither topic is name-checked in isolation; both are causally linked in the explanation of coherence loss.
discriminator pass

Part (d) explicitly asks students to 'Evaluate the assumption that, in this experiment, light can be treated as a pure classical wave when the path between the slits and screen contains charged particles driven by the electric field.' This is a genuine model-critique dimension: it requires judgment about validity, supporting reasoning (wave model works in undisturbed medium), and limiting considerations (model breaks down with charged particles present). The mark scheme confirms this by awarding marks for both supporting and limiting considerations, not calculations.
rule_of_one pass

Each part's mark allocation matches the number of distinct award criteria. Part (a) 2 marks / 2 bullets; (b)(i) 3 marks / 3 bullets (formula, arithmetic, answer); (b)(ii) 2 marks / 2 bullets; (c) 3 marks / 3 bullets (force, optical path/phase change, loss of coherence); (d) 2 marks / 2 bullets (supporting + limiting). The dimension is satisfied.
topic pass

The ERQ genuinely integrates both topics. C.2 Wave model is primary (parts a, b, and core fringe physics), while D.2 Electric and magnetic fields is secondary but essential: part (c) requires explaining how the electric field force on charged particles causes random phase changes that destroy interference, and part (d) evaluates the validity of the classical wave model when electromagnetic interactions with charged particles become significant. Neither topic is merely nominal; the physical scenario demands both the wave interference framework and the electric field effects to make sense of the phenomenon.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly follows the cognitive ladder: (a) AO1 State with command term; (b)(i)–(ii) AO2 Calculate/Determine with computational tasks; (c) AO3 Explain with causal chain requiring synthesis; (d) AO3 Evaluate with critical assessment of assumptions. Each tier is clearly differentiated and builds appropriately.
command_structure fail

Part (c) violates §4.4.1 Explain structure: while M1 and M2 contain explicit causal linkage ('The electric field... causes oscillation, Therefore the refractive index fluctuates'), M3 uses 'Consequently... therefore' but lacks a single clear 'X therefore Y' chain—it conflates two separate causal steps ('phase difference is no longer constant' → 'time-averaged fringes wash out' AND separately 'visibility is reduced') without explicit warrant connecting the constancy of phase difference to fringe washing. The 'therefore' appears twice in M3 creating ambiguity about which is the primary causal link. Part (d) also fails: M1 states 'the model is adequate only when the medium is undisturbed' as position + supporting, but does not explicitly state a limiting consideration in M2—instead M2 re-explains why the model fails, without contrasting this against a residual strength or domain where it *does* apply. §4.4.1 requires Evaluate to show 'position + supporting consideration + limiting consideration' as distinct weighted elements; this mark scheme only shows 'position/supporting' then 'why it fails' without true evaluative tension.

FIX: Part (c): Rewrite M3 as: 'Consequently, the phase relationship between the two beams becomes random in time, therefore the observed fringes (from time-averaging) lose contrast and visibility diminishes.' This creates one clear causal chain. Alternatively, break into two separate marks: M3a = 'Therefore phase difference becomes random', M3b = 'Therefore fringe visibility is lost.' Part (d): Revise M2 to explicitly contrast: 'However, the wave model *does* correctly predict fringe spacing in the undisturbed case, showing it captures the essential interference physics; its limitation is that it cannot account for medium modification by external fields without introducing ad-hoc coupling terms.' This creates genuine evaluative tension between what the model succeeds and fails to explain.
cross_theme pass

The ERQ successfully integrates both C.2 (Wave model) and D.2 (Electric and magnetic fields). Part (c) requires students to explain how the electric field (D.2) causes ionization and refractive index fluctuations that destroy the interference pattern (C.2), creating a genuine causal mechanism linking both topics. Part (d) further deepens this integration by evaluating the limits of the wave model when electromagnetic coupling becomes important. Both topics are essential to answering the question, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to 'Evaluate the assumption that light in this experiment can be treated purely as a classical wave'. The mark scheme requires students to take a position on the wave model's validity (M1: adequate only when medium is undisturbed; M2: incomplete once field ionizes air), and to identify what the model neglects (electromagnetic coupling, scattering, phase randomisation). This is genuine model critique, not a calculation.
rule_of_one fail

Part (c) is marked [3 marks] but contains 4 distinct award criteria (M1, M2, M3, and an implicit M4 within M3's 'therefore' clause). The mark scheme violates the dimensional contract: a 3-mark Explain part must have exactly 3 award bullets, not 4. The split of M3 into two logically separate steps (phase difference becomes non-constant → fringes wash out) inflates the criterion count.

FIX: Consolidate Part (c) M3 into a single criterion by combining the cause ('phase difference is no longer constant') with its single effect ('fringes wash out and visibility is reduced'), removing the embedded second 'therefore'. Alternatively, if the marker intends 4 steps, change Part (c) to [4 marks]. As written, the 3-mark / 4-criterion mismatch must be corrected.
topic fail

Part (c) and (d) nominally invoke D.2 (electric and magnetic fields) but the physics required is superficial. The question states that an electric field is applied, but students need only know F = qE and that free charges accelerate—this is basic electrostatics, not genuinely from D.2 (which covers field properties, motion of charged particles in fields, electromagnetic induction, etc.). The core of parts (c)–(d) is entirely about wave coherence, interference visibility, and the wave model's limitations (C.2). D.2 is merely the mechanism that *destroys* the wave pattern, not a topic requiring its own conceptual depth. The ERQ does not require understanding of D.2 concepts such as field superposition, potential, or the relationship between E and B fields.

FIX: Restructure part (c) to require explicit D.2 knowledge: e.g., ask students to calculate the force on ionized particles using F = qE, determine their acceleration and drift velocity in the field, or explain how the induced dipole moment in neutral molecules depends on field strength. Alternatively, replace the ionization scenario with one requiring magnetic deflection (Lorentz force, F = qv×B), which would authentically integrate C.2 (wave propagation direction/polarization affected by field) with D.2 (magnetic field effects on charged particle motion). Without such restructuring, the primary topic remains C.2 alone, with D.2 as mere decoration.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder strictly: part (a) is AO1 with State command; parts (b)(i)–(b)(ii) are AO2 with Calculate/Determine; parts (c)–(d) are AO3 with Explain/Evaluate. Each tier builds correctly on lower tiers and no tiers are inverted or missing.
command_structure fail

Part (c) mark scheme violates §4.4.1 AO3 'Explain' structure. M1 states a fact (ions are accelerated) but does not establish the opening of an explicit causal chain. M2 claims to provide a 'therefore' link, but it actually introduces a new intermediate mechanism (refractive-index fluctuation) without first establishing why F=qE work on ions necessarily produces this effect. The chain should run: F=qE does work → ions gain KE and move → moving charges scatter/polarize medium → local n(r,t) changes → optical path varies → phase shifts randomly → visibility lost. The current scheme jumps from work-done to refractive-index change without the intervening physics, breaking the required explicit causal chain.

FIX: Restructure Part (c) marking points to establish a complete causal chain: M1 should be 'F = qE does work W on ions, imparting kinetic energy and random velocities (since ion positions/creation times are random)'; M2 should be 'these moving charged particles locally perturb the medium's electromagnetic polarisability, causing the refractive index n(r,t) to fluctuate randomly in space and time'; M3 should be 'consequently, the optical path length L = ∫n(r,t)dr differs randomly between the two slit paths, so the phase difference φ₁ − φ₂ = 2π(L₁−L₂)/λ becomes a random time-varying quantity; on averaging over the ion-motion timescale, constructive and destructive interference conditions wash out and fringe contrast → 0'.
cross_theme pass

The ERQ genuinely integrates both C.2 (Wave model) and D.2 (Electric and magnetic fields). Part (c) requires students to use the electric force F = qE from D.2 to explain how field-accelerated ions alter the optical medium's refractive index, directly causing loss of fringe visibility predicted by C.2 wave theory. Both concepts are essential to solving the problem; D.2 is not merely name-checked or confined to assumptions.
discriminator pass

Part (d) explicitly asks the student to 'Evaluate the assumption' that air can be treated as an undisturbed optical medium. This is a clear model-critique task: the mark scheme requires students to justify the assumption in the field-free case (M1) and then identify its breakdown when the field is applied (M2), making this a genuine evaluation of model validity and limitations. The dimension is satisfied.
rule_of_one fail

Part (c) lists 3 marks but the mark scheme provides 3 distinct award criteria (M1: fact, M2: linking, M3: linking + consequence). However, the dimensional mismatch arises in Part (d): it is allocated 2 marks but the scheme lists only 2 criteria (M1: position+supporting, M2: limiting), yet M1 itself combines two distinct operations (state position AND provide supporting evidence from part b), violating the strict 1:1 correspondence between mark count and distinct award bullets. For an Evaluate [2 marks] part, the scheme should either split M1 into separate bullets or explicitly clarify that one bullet encompasses both operations. The current structure is ambiguous.

FIX: Revise Part (d) mark scheme to either: (i) split M1 into two separate bullets: 'M1: states the assumption is justified for the evacuated/field-free case' and 'M2: provides supporting evidence (e.g., predicted fringe spacing matches observation)' and 'M3: identifies a limiting consideration (medium becomes non-uniform/field-dependent once ionized)', OR (ii) if maintaining 2 marks, explicitly combine M1 and M2 into a single bullet 'M1: [position + supporting + limiting consideration]' and add a second bullet 'M2: [alternative limiting consideration or depth of reasoning]'. Current scheme conflates position+supporting+limiting into single bullets without clear award demarcation.
topic pass

The ERQ authentically integrates both topics. Part (c) requires understanding wave interference (C.2: coherence, phase, fringe visibility) AND electric fields and charged-particle dynamics (D.2: F=qE, work, kinetic energy). The causal mechanism—field accelerates ions → refractive index fluctuates → phase randomizes → fringes wash out—genuinely demands both topics' concepts. Parts (a)–(b) establish C.2 foundations; part (c) then bridges into D.2 physics; part (d) reflects on the model's limits. Neither topic is nominal.

Planner output (stage 1)

Archetype: experimental setup
Scenario: A student performs a double-slit interference experiment using visible light, observing a pattern on a distant screen. The experiment is then repeated with the addition of a uniform electric field perpendicular to the slits, which ionizes some air molecules in the light path. The student notices that the interference pattern becomes blurred and eventually disappears as the field strength increases. The task involves analyzing the wave behavior of light, calculating fringe spacing, and evaluating how the electric field's interaction with charged particles disrupts coherence.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State the conditions necessary for a clear double-slit interference pattern to be observed.
b(i)	3	AO2	Calculate the fringe spacing on the screen for light of wavelength 550 nm, slit separation 0.25 mm, and screen distance 1.5 m.
b(ii)	2	AO2	Determine the path difference between rays from the two slits at the first minimum.
c	3	AO3	Explain how the presence of a uniform electric field perpendicular to the slits causes ionized air molecules to acquire a random phase as they move between the slits, and discuss how this reduces the visibility of the interference pattern.
d	2	AO3	Evaluate the assumption that light behaves purely as a wave in this scenario, considering the interaction between the electric field and charged particles in the medium.

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