AQA A-Level Physics Paper 3 (3BD), June 2025: Question 2

✅ Correct Answer & Mark Scheme

Any three points from the following (can be awarded via written explanation or clearly labelled curves):

• Agreement at long wavelengths: Theoretical predictions and experimental results match well at high (long) wavelengths (λ).
• Peak intensity: Experimental results exhibit a distinct peak intensity at a specific wavelength, whereas classical theory predicted no peak.
• Low wavelength cut-off: Experimental curve drops to zero (or touches the λ-axis) as wavelength approaches zero, while theory predicts no cut-off.
• Divergence as λ → 0: Classical theory predicts intensity tends to infinity as wavelength approaches 0 (UV region), which contradicts experiment. (Note: intensity tending to infinity requires a written comment).

💡 Key Knowledge

• Classical prediction (Rayleigh-Jeans Law): Assumed EM energy is emitted continuously by standing waves in the cavity. Energy density is proportional to 1 / λ⁴ . As λ → 0 , intensity I → ∞ .
• Experimental Curve: A continuous distribution that peaks at λ_max and approaches 0 as λ → 0 and as λ → ∞ .
• The "Catastrophe": Classical physics predicted that any heated cavity should emit an infinite amount of energy in the ultraviolet/shorter wavelength range.

🧠 Exam Technique & Diagram Guide

Drawing on Figure 4 is the quickest way to pick up the majority of marks, provided you label the curves clearly:

❌ Common Errors

• Unlabelled curves: Drawing two curves without identifying which is theoretical and which is experimental awards 0 marks.
• Non-EM references: Referring to particles, electrons, or matter waves caps the mark for this question to a maximum of 2 marks.
• Vague descriptions: Saying "they disagree at the start" without specifying that the disagreement occurs at low wavelengths or high frequencies.
• Failing to state divergence: Forgetting that an asymptotic curve on a small graph doesn't automatically convey "approaches infinity" without an explanatory note.

✅ Correct Answer

Electromagnetic radiation / light is emitted in discrete packets called quanta, where the energy of each quantum is proportional to its frequency ( E = hf ).

💡 Key Knowledge

• Max Planck (1900): Proposed that atomic oscillators in black-body cavity walls could only absorb or emit energy in discrete amounts: E = nhf (where n = 1, 2, 3... ).
• At short wavelengths (high frequencies), the energy required to emit a single quantum ( hf ) is very large. Therefore, high-frequency oscillations are rarely excited at ordinary temperatures, resolving the ultraviolet catastrophe.

🧠 Exam Technique: Two Halves to 1 Mark

Notice that this single mark has two compulsory components in the mark scheme:

1. Energy is emitted in discrete packets / quanta.
2. Energy is directly proportional to frequency ( E ∝ f or E = hf ).

Missing either part results in zero marks!

❌ Common Errors & Examiner Traps

• Writing "photons": Do NOT write "photons" or "particles of light". The mark scheme explicitly states: "Do NOT accept photons / particles". The concept of the photon as a localized particle of light was introduced later by Einstein in 1905 (for the photoelectric effect), not by Planck's original 1900 proposal.
• Leaving out frequency: Stating only that energy is quantized without mentioning that quantum energy depends on frequency ( E ∝ f ).