AQA A-Level Physics: Astrophysics (7408) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 3.9 Astrophysics of the AQA AS and A-level Physics specification (7407/7408, version 1.4, AS and A-level exams June 2016 onwards), sub-sections 3.9.1 to 3.9.3. Astrophysics is one of the five options (sections 3.9 to 3.13); you study one, assessed in Paper 3 Section B. It is A-level only.

Review the study guide and revision notes first; the course hub, printable checklist and free diagnostics help you plan.

Data: c = 3.00 × 10⁸ m s⁻¹; G = 6.67 × 10⁻¹¹ N m² kg⁻²; σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien constant 2.9 × 10⁻³ m K; 1 solar mass = 1.99 × 10³⁰ kg; 1 Mpc = 3.08 × 10²² m; 1 year = 3.15 × 10⁷ s; power of the Sun = 3.9 × 10²⁶ W.

Questions

1. An astronomical refracting telescope has an objective of focal length 0.90 m and an eyepiece of focal length 25 mm. It is used in normal adjustment.

(a) Calculate the angular magnification. [2] (b) State the separation of the lenses. [1] (c) A planet subtends 2.2 × 10⁻⁴ rad at the unaided eye. Calculate the angle subtended by its final image. [2]

2. (a) Describe the path of light from a distant star through a Cassegrain telescope to the eyepiece. [3] (b) Explain why a reflecting telescope does not suffer from chromatic aberration. [2]

3. A radio telescope has a dish of diameter 25 m and observes at a wavelength of 0.21 m.

(a) Calculate its minimum angular resolution. [2] (b) Two radio sources are 5.0 × 10⁻³ rad apart. State whether the dish can resolve them. [1] (c) Calculate the minimum angular resolution of a 0.20 m optical telescope at 550 nm. [1] (d) Calculate the ratio of the collecting power of the dish to that of the optical telescope. [2]

4. (a) Explain why radio telescopes can be ground-based but X-ray telescopes must be placed in space. [2] (b) Compare a CCD with the eye as a detector in terms of quantum efficiency and convenience of use. [2]

5. Star A has apparent magnitude 0.5 and star B has apparent magnitude 5.5.

(a) State which star appears brighter. [1] (b) Calculate the ratio of the intensity received from A to that from B. [2] (c) Star B is 25 pc from Earth. Calculate its absolute magnitude. [2]

6. A star’s black-body spectrum peaks at 290 nm. Its power output is 3.2 × 10²⁸ W.

(a) Calculate its surface temperature. [2] (b) State its spectral class and intrinsic colour. [1] (c) Calculate its radius. [3]

7. (a) Explain why hydrogen Balmer absorption lines are strongest in A-class stars. [3] (b) Describe the path on the HR diagram of a star like the Sun after it leaves the main sequence. [2]

8. (a) Give two reasons why exoplanets are difficult to detect directly. [2] (b) A transit reduces the intensity of a star of radius 7.0 × 10⁸ m by 0.85%. Calculate the radius of the planet. [2] (c) Describe the radial velocity method. [2]

9. (a) Calculate the Schwarzschild radius of a supermassive black hole of 4.0 × 10⁶ solar masses. [2] (b) A type 1a supernova reaches a peak apparent magnitude of 16.4. Its peak absolute magnitude is −19.3. Calculate its distance in parsecs. [3] (c) Explain how type 1a supernovae led to the proposal of dark energy. [2] (d) A gamma ray burst releases 2.0 × 10⁴⁴ J. Compare this with the energy the Sun releases over a lifetime of 1.0 × 10¹⁰ years. [2]

10. A binary star system is viewed in the plane of its orbit. A line of rest wavelength 486.1 nm in one star’s spectrum shifts by up to ±0.042 nm, with a period of 6.5 days.

(a) Explain why the line shifts periodically. [1] (b) Calculate the star’s orbital speed. [2] (c) Calculate the radius of its circular orbit. [2]

11. A line of rest wavelength 393.4 nm is observed at 410.9 nm in a galaxy’s spectrum. Take H = 68 km s⁻¹ Mpc⁻¹.

(a) Calculate z. [1] (b) Calculate the recession speed. [1] (c) Calculate the distance to the galaxy in Mpc. [2] (d) Estimate the age of the Universe in years, assuming H is constant. [3] (e) State two other pieces of evidence for the Big Bang. [2]

12. A quasar has z = 0.16 and the intensity of its radiation at Earth is 5.0 × 10⁻¹³ W m⁻². Take H = 68 km s⁻¹ Mpc⁻¹.

(a) State how quasars were first discovered. [1] (b) Calculate the distance to the quasar in metres. [2] (c) Estimate its power output. [2] (d) Compare this with the power of the Sun. [1]

Answers

1. (a) M = fₒ/fₑ = 0.90/0.025 [1] = 36 [1] (b) fₒ + fₑ = 0.925 m [1] (c) β = Mα = 36 × 2.2 × 10⁻⁴ [1] = 7.9 × 10⁻³ rad [1] Examiner insight: Convert 25 mm to 0.025 m before dividing; a power-of-ten slip in (a) carries into (c), though the method in (c) can still earn credit.

2. (a) Light reflects off the parabolic concave primary mirror towards its focus [1]; a convex secondary mirror reflects it back [1]; through a hole in the primary to the eyepiece [1]. (b) Chromatic aberration comes from refraction, which differs with wavelength [1]; mirrors reflect all wavelengths at the same angle, so all colours focus at one point [1]. Examiner insight: Name the mirror shapes; “a big mirror and a small mirror” is not enough.

3. (a) θ ≈ λ/D = 0.21/25 [1] = 8.4 × 10⁻³ rad [1] (b) No: 5.0 × 10⁻³ rad is smaller than 8.4 × 10⁻³ rad [1]. (c) θ ≈ 550 × 10⁻⁹/0.20 = 2.75 × 10⁻⁶ rad [1] (d) Collecting power ∝ D² [1]; (25/0.20)² = 1.6 × 10⁴ [1] Examiner insight: In (b), quote both numbers in your comparison; a bare “no” gives no reason for the judgement.

4. (a) The atmosphere is transparent to most radio wavelengths, so radio waves reach the ground [1]; X-rays are absorbed by the atmosphere, so the telescope must be above it [1]. (b) A CCD has a much higher quantum efficiency than the eye, detecting a larger fraction of incident photons [1]; it can integrate over long exposures and store a digital image for processing, unlike the eye [1]. Examiner insight: “Compare” needs both detectors in each point; describing only the CCD is incomplete.

5. (a) Star A (lower magnitude) [1] (b) Ratio = 2.51^(5.5 − 0.5) = 2.51⁵ [1] = 99.6 (about 100) [1] (c) 5.5 − M = 5 log(25/10) [1]; M = 5.5 − 1.99 = 3.5 [1] Examiner insight: Keep d in parsecs inside the logarithm; converting to metres first gives a nonsense magnitude.

6. (a) T = 2.9 × 10⁻³/290 × 10⁻⁹ [1] = 1.0 × 10⁴ K [1] (b) Class A, blue-white [1] (c) A = P/σT⁴ = 3.2 × 10²⁸/(5.67 × 10⁻⁸ × (1.0 × 10⁴)⁴) [1]; r = √(A/4π) [1] = 2.1 × 10⁹ m [1] Examiner insight: Raise T to the fourth power and remember A = 4πr²; stopping at A gives an area, not a radius.

7. (a) Balmer lines need hydrogen atoms with electrons in the n = 2 state [1]; in cooler stars few atoms are excited to n = 2 [1]; in the hottest stars most hydrogen is ionised, so A stars have the most atoms in n = 2 [1]. (b) It expands and cools, moving up and to the right to become a red giant [1]; it then moves left and down to become a white dwarf [1]. Examiner insight: Both temperature limits are needed in (a); explaining only why cool stars have weak lines leaves the argument half done.

8. (a) The planet is very faint compared with its star [1]; the angular separation is too small to resolve [1]. (b) Fractional dip = (r_p/r_s)², so r_p = 7.0 × 10⁸ × √0.0085 [1] = 6.5 × 10⁷ m [1] (c) The star and planet orbit their common centre of mass [1]; the star’s spectral lines show a periodic Doppler shift with the planet’s orbital period [1]. Examiner insight: Convert 0.85% to 0.0085 before taking the square root; using 0.85 gives a planet almost as large as the star.

9. (a) Rs = 2GM/c² = 2 × 6.67 × 10⁻¹¹ × 7.96 × 10³⁶/(3.00 × 10⁸)² [1] = 1.2 × 10¹⁰ m [1] (b) m − M = 16.4 − (−19.3) = 35.7 [1]; d = 10 × 10^(35.7/5) [1] = 1.4 × 10⁸ pc [1] (c) All type 1a supernovae reach about the same peak absolute magnitude, so they act as standard candles [1]; distant ones appeared fainter than expected, suggesting accelerating expansion, attributed to dark energy [1]. (d) Sun: 3.9 × 10²⁶ × 1.0 × 10¹⁰ × 3.15 × 10⁷ = 1.2 × 10⁴⁴ J [1]; the burst releases about 1.6 times the Sun’s lifetime output [1]. Examiner insight: In (b) the double negative matters: m − M is 16.4 + 19.3, and a sign slip changes d by many orders of magnitude.

10. (a) The star moves alternately towards and away from Earth as it orbits [1]. (b) v = cΔλ/λ = 3.00 × 10⁸ × 0.042/486.1 [1] = 2.6 × 10⁴ m s⁻¹ [1] (c) T = 6.5 × 86 400 = 5.62 × 10⁵ s; r = vT/2π [1] = 2.3 × 10⁹ m [1] Examiner insight: Convert days to seconds before using r = vT/2π; units must be consistent for the final answer.

11. (a) z = (410.9 − 393.4)/393.4 = 0.0445 [1] (b) v = zc = 1.33 × 10⁷ m s⁻¹ [1] (c) d = v/H = 13 300 km s⁻¹/68 km s⁻¹ Mpc⁻¹ [1] = 196 Mpc [1] (d) H = 68 × 10³/3.08 × 10²² = 2.21 × 10⁻¹⁸ s⁻¹ [1]; 1/H = 4.53 × 10¹⁷ s [1] = 1.4 × 10¹⁰ years [1] (e) Cosmological microwave background radiation [1]; relative abundance of hydrogen and helium [1]. Examiner insight: In (c), match units: v in km s⁻¹ with H in km s⁻¹ Mpc⁻¹ gives Mpc directly.

12. (a) As bright radio sources [1]. (b) v = 0.16 × 3.00 × 10⁸ = 4.8 × 10⁷ m s⁻¹; d = 48 000/68 = 706 Mpc [1] = 2.2 × 10²⁵ m [1] (c) P = 4πd²I = 4π × (2.17 × 10²⁵)² × 5.0 × 10⁻¹³ [1] = 3.0 × 10³⁹ W [1] (d) About 7.6 × 10¹² times the Sun’s power [1]. Examiner insight: Convert d from Mpc to metres before using I = P/4πd², or the power comes out wrong by a huge factor.

Where marks are usually lost

• Quoting M = fₑ/fₒ or omitting fₑ from the lens separation.
• Comparing an angle in degrees with λ/D in radians.
• Calling the higher-magnitude star brighter.
• Putting d in metres into m − M = 5 log(d/10).
• Forgetting the fourth power of T, or not square-rooting to get r.
• Using the percentage dip without converting it to a fraction.
• Leaving H in km s⁻¹ Mpc⁻¹ when computing 1/H in seconds.

Next steps

• Astrophysics revision notes
• Astrophysics study guide
• AQA A-Level Physics course hub
• Printable checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

AQA AS and A-level Physics specification (7407/7408), version 1.4, July 2026, AS and A-level exams June 2016 onwards: section 3.9 Astrophysics (A-level only).