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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Use the formula for redshift: z = v / c
- S2
Rearrange the formula to solve for velocity: v = z × c
- S3
Substitute the given values: v = 0.02 × 3 × 10 8 m/s
- S4
Calculate the velocity: v = 6 × 10 6 m/s
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Use the formula for redshift: z = v / c
- S2
Rearrange the formula to solve for velocity: v = z × c
- S3
Substitute the given values: v = 0.02 × 3 × 10 8 m/s
- S4
Calculate the velocity: v = 6 × 10 6 m/s
Final answer: 6 × 10 6 m/s
Common mistakes
- Confusing redshift and blueshift — 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 — 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 — Always check that all units are consistent before performing calculations. Convert wavelengths to meters if necessary.
- Using incorrect values for the speed of light — 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 — 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 — 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
- Full worked solution (all marking points)4 marks