A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Line Spectra and Energy Level Transitions in Atoms — mark scheme explained
The short answer
Line spectra, such as those observed for atomic hydrogen, provide strong evidence for the quantized nature of energy levels within atoms. This section delves into how these line spectra arise from transitions between discrete energy levels and how they can be observed using a diffraction grating.
The question
Calculate the wavelength of light emitted when an electron in a hydrogen atom transitions from the n = 3 level to the n = 2 level.
[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 numerical calculations, marks are typically awarded for identifying the correct formula, substituting values correctly, performing the calculation accurately, and providing the final answer with appropriate units. For explanations, marks are given for clarity, accuracy, and completeness of the response.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Explain
- Provide a clear and concise explanation of a concept or phenomenon.
- Identify
- Recognize and name the correct answer from a set of options.
- Determine
- Find out or establish something with certainty, often through calculation.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 5-7 minutes per question to ensure you have enough time to carefully read the question, identify the required steps, perform calculations, and check your work.
- 1. Identify the energy levels involved: n 1 = 2 and n 2 = 3.0 marks
- 2. Use the Rydberg formula to find the wavelength: 1/λ = R(1/n 1 2 - 1/n 2 2 ).1 mark
- 3. Substitute the values: 1/λ = 1.097 × 10 7 m -1 (1/2 2 - 1/3 2 ).1 mark
- 4. Simplify the expression: 1/λ = 1.097 × 10 7 m -1 (1/4 - 1/9).0 marks
- 5. Calculate the difference: 1/λ = 1.097 × 10 7 m -1 (0.25 - 0.1111) ≈ 1.097 × 10 7 m -1 × 0.1389.1 mark
- 6. Find the wavelength: λ = 1 / (1.097 × 10 7 m -1 × 0.1389) ≈ 6.56 × 10 -7 m or 656 nm.1 mark
Final answer: 656 nm
Work through every step correctly and you earn all 4 marks.
Another worked example
An electron in a hydrogen atom transitions from the n = 4 level to the n = 2 level. Calculate the energy of the emitted photon in joules.
- 1. Identify the energy levels involved: n 1 = 2 and n 2 = 4.0 marks
- 2. Use the energy level equation to find the energies: E n = -13.6 eV / n 2 .1 mark
- 3. Calculate the energy of the n = 2 level: E 2 = -13.6 eV / 2 2 = -3.4 eV.1 mark
- 4. Calculate the energy of the n = 4 level: E 4 = -13.6 eV / 4 2 = -0.85 eV.1 mark
- 5. Find the energy difference: E photon = E 4 - E 2 = -0.85 eV - (-3.4 eV) = 2.55 eV.1 mark
- 6. Convert the energy to joules: E photon = 2.55 eV × 1.602 × 10 -19 J/eV ≈ 4.08 × 10 -19 J.1 mark
Final answer: 4.08 × 10 -19 J
Work through every step correctly and you earn all 5 marks.
Common mistakes
Confusing the energy level equation with the Rydberg formula.
Why it happens: Students may mix up the equations for energy levels and wavelengths, leading to incorrect calculations.
Fix: Review the specific equations: E n = -13.6 eV / n 2 for energy levels and 1/λ = R(1/n 1 2 - 1/n 2 2 ) for wavelengths.
Using the wrong units for energy levels and photon energies.
Why it happens: Students may forget to convert between joules and electronvolts, leading to incorrect answers.
Fix: Always check the units required in the question and use the conversion factor 1 eV = 1.602 × 10 -19 J when necessary.
Forgetting to include the negative sign in energy level calculations.
Why it happens: Students may overlook the negative sign, which indicates that the electron is bound to the atom.
Fix: Always include the negative sign when using the energy level equation E n = -13.6 eV / n 2 .
Incorrectly identifying the higher and lower energy levels in transitions.
Why it happens: Students may confuse which level is higher or lower, leading to incorrect energy differences.
Fix: Always identify the higher (n 2 ) and lower (n 1 ) energy levels clearly before calculating the energy difference.
Using the wrong value for Planck's constant or the Rydberg constant.
Why it happens: Students may use incorrect values for constants, leading to significant errors in calculations.
Fix: Memorize and double-check the values of important constants: h = 6.626 × 10 -34 J·s and R = 1.097 × 10 7 m -1 .
Misinterpreting the diffraction grating equation.
Why it happens: Students may confuse the variables in the grating equation, leading to incorrect angles of diffraction.
Fix: Review the grating equation d sin(θ) = mλ and ensure you correctly identify d (grating spacing), θ (angle of diffraction), m (order), and λ (wavelength).
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 Wavelength | Use the Rydberg formula to find the wavelength of light emitted in a hydrogen transition. | 4 |
| Calculate Photon Energy | Find the emitted photon's energy in joules for a hydrogen electron transition between levels. | 5 |
| Diffraction Grating Wavelength | Find the emitted wavelength from an energy transition, then calculate the first-order diffraction angle. | 6 |
| Calculate Energy Level Difference | Find the energy gap between two hydrogen energy levels and convert to electronvolts. | 4 |
| Total across these question types | 19 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.