A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Parsec and Light Year, Definition of M and m: m – M = 5 log 10 (d/10) — mark scheme explained
The short answer
In astrophysics, understanding the vast distances between celestial objects is crucial. Two common units used to measure these distances are the parsec (pc) and the light year (ly).
The question
A star has an apparent magnitude of 2.5 and an absolute magnitude of -3.0. Calculate the distance to the star in parsecs.
[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 questions involving calculations, marks are typically awarded for correct substitution into the formula, correct use of logarithms, and the final answer. For conceptual questions, marks are awarded for accurate definitions and explanations.
What the command words demand
- Calculate
- Perform the necessary mathematical operations to find the answer.
- Determine
- Find the value of a specific quantity using given data and formulas.
- Explain
- Provide a clear and concise explanation of a concept or process.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 2-3 minutes per mark to ensure you have enough time to carefully substitute values, perform calculations, and check your work.
- Use the formula: m – M = 5 log 10 (d) – 51 mark
- Substitute the given values: 2.5 – (-3.0) = 5 log 10 (d) – 51 mark
- Simplify: 5.5 + 5 = 5 log 10 (d)0 marks
- 10.5 = 5 log 10 (d)0 marks
- 2.1 = log 10 (d)0 marks
- Therefore: d = 10 2.11 mark
- Calculate the distance: d ≈ 125.89 parsecs1 mark
Final answer: 126 parsecs
Work through every step correctly and you earn all 4 marks.
Another worked example
A star is observed to have an apparent magnitude of 6.0 and is known to be at a distance of 50 parsecs. Calculate the absolute magnitude of the star.
- Use the formula: M = m – 5 log 10 (d) + 50 marks
- Substitute the given values: M = 6.0 – 5 log 10 (50) + 51 mark
- Calculate log 10 (50) : log 10 (50) ≈ 1.71 mark
- M = 6.0 – 5 × 1.7 + 50 marks
- M = 6.0 – 8.5 + 50 marks
- M = 2.51 mark
Final answer: 2.5
Work through every step correctly and you earn all 3 marks.
Common mistakes
Confusing parsec and light year as units of time.
Why it happens: Students often mix up the definitions of parsec and light year, thinking they are units of time rather than distance.
Fix: Reinforce that a parsec is defined by the angle subtended by one AU at a certain distance, and a light year is the distance light travels in one year.
Using incorrect values for 1 parsec or 1 light year.
Why it happens: Students may memorize approximate values but use them incorrectly in calculations.
Fix: Provide the exact values: 1 pc ≈ 3.26 ly and 1 ly ≈ 0.3066 pc, and ensure students use these consistently.
Forgetting to add or subtract 5 in the magnitude formula.
Why it happens: The formula m – M = 5 log 10 (d) – 5 can be confusing, and students might forget the constant term.
Fix: Emphasize the importance of the constant term in the formula and practice using it in various scenarios.
Incorrectly applying logarithmic rules.
Why it happens: Students may struggle with logarithmic operations, leading to errors in solving for distance or magnitude.
Fix: Review basic logarithmic properties and practice problems involving logarithms.
Using the wrong base for logarithms.
Why it happens: Students might use natural logarithms (ln) instead of common logarithms (log 10 ).
Fix: Clarify that the formula uses common logarithms and ensure students are familiar with using log 10 on their calculators.
Misinterpreting the meaning of apparent magnitude and absolute magnitude.
Why it happens: Students may confuse the definitions or think they are interchangeable.
Fix: Clearly define apparent magnitude as how bright a star appears from Earth and absolute magnitude as how bright it would appear at 10 parsecs.
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 Stellar Distance | Use the distance modulus formula with logarithms to find a star's distance in parsecs. | 4 |
| Calculate Absolute Magnitude | Use the distance modulus formula to find a star's absolute magnitude from its apparent magnitude and distance. | 3 |
| Calculate Stellar Distance | Use the distance modulus equation with magnitudes to find the star's distance in parsecs. | 4 |
| Calculate Absolute Magnitude | Use the distance modulus formula to find absolute magnitude from apparent magnitude and distance. | 3 |
| Total across these question types | 14 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.