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

Machine-verifiedchecked against the AQA A-Level Physics specificationlast verified 2 July 2026

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

What each mark is really for — in plain English — and the wording trap that loses it.

S1
Use the formula: m – M = 5 log 10 (d) – 5
S2
Substitute the given values: 2.5 – (-3.0) = 5 log 10 (d) – 5
S3
Simplify: 5.5 + 5 = 5 log 10 (d)
S4
10.5 = 5 log 10 (d)
S5
2.1 = log 10 (d)
S6
Therefore: d = 10 2.1
S7
Calculate the distance: d ≈ 125.89 parsecs

Model answer

Worked through, with each step tagged to the mark it earns.

S1
Use the formula: m – M = 5 log 10 (d) – 5
S2
Substitute the given values: 2.5 – (-3.0) = 5 log 10 (d) – 5
S3
Simplify: 5.5 + 5 = 5 log 10 (d)
S4
10.5 = 5 log 10 (d)
S5
2.1 = log 10 (d)
S6
Therefore: d = 10 2.1
S7
Calculate the distance: d ≈ 125.89 parsecs
Final answer: 126 parsecs

Common mistakes

Confusing parsec and light year as units of time. — 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. — 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. — Emphasize the importance of the constant term in the formula and practice using it in various scenarios.
Incorrectly applying logarithmic rules. — Review basic logarithmic properties and practice problems involving logarithms.
Using the wrong base for logarithms. — 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. — 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

Full worked solution (all marking points)4 marks