A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Doppler Effect in Astrophysics — mark scheme explained
The short answer
The Doppler effect is a fundamental concept in astrophysics that describes how the frequency or wavelength of light changes when the source and observer are moving relative to each other. This phenomenon is crucial for understanding the motion of celestial objects, such as binary stars, galaxies, and quasars.
The question
A star has a redshift of z = 0.02 . Calculate its velocity relative to the observer.
[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
Marks are typically awarded for correct application of formulae, accurate calculations, and clear explanations. Partial marks may be given for showing working and understanding the underlying principles, even if the final answer is incorrect.
What the command words demand
- Calculate
- Perform a numerical calculation using given data and appropriate formulae.
- Determine
- Find the value of a quantity or parameter by applying relevant principles or equations.
- Explain
- Provide a clear and detailed account of how something works or why it happens, including any necessary reasoning or evidence.
- Discuss
- Consider multiple aspects of a topic, providing arguments for and against different viewpoints or interpretations.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: For a 6-mark question on this topic, aim to spend about 4-5 minutes. Ensure you read the question carefully, identify the required formulae, perform calculations step-by-step, and provide clear explanations where necessary.
- Use the formula for redshift: z = v / c1 mark
- Rearrange the formula to solve for velocity: v = z × c1 mark
- Substitute the given values: v = 0.02 × 3 × 10 8 m/s1 mark
- Calculate the velocity: v = 6 × 10 6 m/s1 mark
Final answer: 6 × 10 6 m/s
Work through every step correctly and you earn all 4 marks.
Another worked example
A binary star system has a spectral line at rest with a wavelength of λ 0 = 550 nm . The observed wavelength is λ obs = 552 nm . Calculate the redshift and the velocity of the star.
- Use the formula for redshift: z = (λ obs - λ 0 ) / λ 01 mark
- Substitute the given values: z = (552 - 550) / 5501 mark
- Calculate the redshift: z ≈ 0.00361 mark
- Use the velocity formula: v = z × c1 mark
- Substitute the values: v = 0.0036 × 3 × 10 8 m/s0 marks
- Calculate the velocity: v ≈ 1.08 × 10 6 m/s1 mark
Final answer: z ≈ 0.0036, v ≈ 1.08 × 10 6 m/s
Work through every step correctly and you earn all 5 marks.
Common mistakes
Confusing redshift and blueshift
Why it happens: Students often mix up the signs of velocity in the Doppler effect formulae, leading to incorrect interpretations of whether an object is moving towards or away from the observer.
Fix: Always double-check the sign of the velocity. A positive redshift indicates the source is moving away, while a negative redshift (blueshift) indicates it is moving towards the observer.
Misinterpreting the sign of velocity in the equations
Why it happens: Students sometimes forget that the sign of velocity depends on whether the source or observer is moving towards or away from each other, leading to incorrect calculations.
Fix: Ensure you correctly identify the direction of motion and use the appropriate sign for velocity in the Doppler effect formulae.
Forgetting to convert units consistently
Why it happens: Students often forget to convert wavelengths from nanometers (nm) to meters (m) when using the speed of light in calculations, leading to incorrect results.
Fix: Always check that all units are consistent before performing calculations. Convert wavelengths to meters if necessary.
Using incorrect values for the speed of light
Why it happens: Students sometimes use approximate or incorrect values for the speed of light, leading to significant errors in their calculations.
Fix: Always use the standard value for the speed of light: c ≈ 3 × 10 8 m/s .
Not considering the relative motion of both source and observer
Why it happens: Students often overlook the fact that both the source and observer can be in motion, leading to incomplete or incorrect application of the Doppler effect formulae.
Fix: Consider the velocities of both the source and observer when applying the Doppler effect formulae. Use the appropriate form of the equation based on the relative motion.
Misapplying the redshift formula for high velocities
Why it happens: Students sometimes use the simplified redshift formula z = v / c for objects moving at significant fractions of the speed of light, where relativistic effects become important.
Fix: For high velocities (where v ≈ c ), use the relativistic Doppler effect formula to account for time dilation and other relativistic effects.
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 Velocity From Redshift | Use the redshift relation to find a star's recession velocity from its z value. | 4 |
| Calculate Redshift Velocity | Find the redshift from wavelengths, then calculate the star's recessional velocity. | 5 |
| Redshift Velocity Calculation | Calculate a galaxy's recession velocity from its redshift and interpret its motion. | 6 |
| Calculate Redshift Velocity | Use the redshift equation to find a galaxy's recession velocity and interpret its motion. | 6 |
| Total across these question types | 21 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.