A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Ultraviolet Catastrophe and Black-Body Radiation — mark scheme explained
The short answer
The ultraviolet catastrophe and black-body radiation are pivotal concepts in the development of quantum mechanics, marking a significant departure from classical physics. This section explores these phenomena, Planck's interpretation in terms of quanta, the failure of classical wave theory to explain photoelectricity, and Einstein’s revolutionary explanation.
The question
A metal surface has a work function of 4.2 eV. Calculate the minimum frequency of light required to eject electrons from this metal.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For explanation questions, marks are typically awarded for correct use of scientific terminology, logical reasoning, and clear communication. For derivation and calculation questions, marks are given for each step in the process, including units and significant figures.
What the command words demand
- Explain
- Provide a detailed account of why or how something happens, using appropriate scientific terminology and examples.
- Derive
- Show the steps involved in deriving a formula or equation from first principles.
- Calculate
- Perform numerical calculations to find a specific value, showing all working clearly.
- Describe
- Give a detailed account of the characteristics or features of a phenomenon without necessarily explaining why it happens.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 5-7 minutes per mark to ensure you have enough time to fully answer each question without rushing.
- 1. Convert the work function (φ) from electron volts to joules: φ = 4.2 eV × 1.602 × 10 -19 J/eV ≈ 6.73 × 10 -19 J.1 mark
- 2. Use the equation E = hν to find the minimum frequency (ν): ν = φ / h, where h is Planck's constant (6.626 × 10 -34 J·s).1 mark
- 3. Substitute the values: ν ≈ (6.73 × 10 -19 J) / (6.626 × 10 -34 J·s) ≈ 1.02 × 10 15 Hz.2 marks
Final answer: The minimum frequency of light required to eject electrons from the metal is approximately 1.02 × 10 15 Hz.
Work through every step correctly and you earn all 4 marks.
Another worked example
A black body at a temperature of 300 K emits radiation. Calculate the wavelength at which the intensity of this radiation is maximum using Wien's displacement law.
- 1. Recall Wien's displacement law: λ max = b / T, where λ max is the wavelength of maximum intensity, T is the temperature in Kelvin, and b is Wien's constant (2.897 × 10 -3 m·K).1 mark
- 2. Substitute the given values: λ max = (2.897 × 10 -3 m·K) / (300 K).1 mark
- 3. Calculate the result: λ max ≈ 9.66 × 10 -6 m or 9.66 μm.1 mark
Final answer: The wavelength at which the intensity of radiation is maximum for a black body at 300 K is approximately 9.66 μm.
Work through every step correctly and you earn all 3 marks.
Common mistakes
Confusing the work function with the kinetic energy of ejected electrons.
Why it happens: Students often mix up the concepts, thinking that the work function is the same as the kinetic energy. The work function is the minimum energy required to remove an electron from a metal, while the kinetic energy is what remains after this threshold is met.
Fix: Always remember that the kinetic energy of ejected electrons is given by K = hν - φ, where hν is the energy of the incident photon and φ is the work function.
Using classical wave theory to explain the photoelectric effect.
Why it happens: Students sometimes try to apply classical wave theory principles, which predict that increasing the intensity of light should increase the kinetic energy of ejected electrons. However, this is incorrect; only the frequency of the light affects the kinetic energy.
Fix: Understand and use Einstein’s quantum explanation: the energy of a photon (E = hν) must exceed the work function to eject an electron, and any excess energy becomes the kinetic energy of the electron.
Forgetting to convert units between joules and electron volts.
Why it happens: Students often forget to convert between these units when solving problems involving the photoelectric effect or black-body radiation. This can lead to incorrect answers.
Fix: Always check the units of the given values and ensure they are consistent before performing calculations. Use the conversion factor 1 eV = 1.602 × 10 -19 J when necessary.
Misapplying Wien's displacement law to calculate intensity instead of peak wavelength.
Why it happens: Students sometimes use Wien's displacement law (λ max = b / T) to find the intensity of black-body radiation, which is incorrect. This law only gives the peak wavelength.
Fix: Use Wien's displacement law to find the peak wavelength of black-body radiation and other formulas for intensity calculations.
Confusing Planck’s constant with Boltzmann’s constant.
Why it happens: Both constants are used in thermodynamics and quantum mechanics, leading to confusion. Planck’s constant (h) is related to the energy of photons, while Boltzmann’s constant (k B ) is related to thermal energy.
Fix: Memorize the definitions and symbols for each constant: h = 6.626 × 10 -34 J·s and k B = 1.38 × 10 -23 J/K.
Forgetting that the ultraviolet catastrophe is a classical prediction, not an experimental observation.
Why it happens: Students sometimes confuse the theoretical prediction of the ultraviolet catastrophe with actual experimental results. The ultraviolet catastrophe was a failure of classical physics to match experimental data.
Fix: Understand that the ultraviolet catastrophe refers to the incorrect prediction by classical wave theory that energy density would diverge at short wavelengths, which contradicts experimental observations.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Threshold Frequency | Find the minimum frequency of light needed to release electrons from the metal. | 4 |
| Calculate Peak Wavelength | Use Wien's displacement law to find the wavelength of maximum intensity for a black body. | 3 |
| Photoelectric Effect Calculation | Use the photoelectric equation to find the ejected electron's maximum kinetic energy. | 3 |
| Wien's Law Calculation | Find peak wavelength using Wien's displacement law and compare it across two temperatures. | 4 |
| Photoelectric Effect Calculation | Use Einstein's photoelectric equation to find the maximum kinetic energy of ejected electrons. | 3 |
| Total across these question types | 17 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.