OCR A Level Physics A: Distances, redshift, Hubble's law and the Big Bang (H556) – 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 5.5.3 (Cosmology) of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), for first assessment in 2017. Where data are not given, use c = 3.00 × 10⁸ m s⁻¹, 1 ly = 9.46 × 10¹⁵ m, 1 pc = 3.09 × 10¹⁶ m, 1 Mpc = 3.09 × 10²² m, 1 year = 3.16 × 10⁷ s. Start with the study guide or the revision notes. Course links: OCR A Level Physics hub and printable checklist.

Questions

1. Define the astronomical unit, the light-year and the parsec. [3]

2. A star is 2.6 pc from the Sun. Calculate its distance in metres and in light-years. [2]

3. A nearby star has a parallax of 0.045 seconds of arc.

(a) Calculate its distance in pc and in ly. [2] (b) Describe how the parallax of a star is measured. [3] (c) Suggest why the method cannot be used for very distant stars. [1]

4. State the Cosmological principle. [3]

5. The calcium K line has a laboratory wavelength of 393.4 nm. In the light from a galaxy it is measured as 405.1 nm.

(a) Calculate the speed at which the galaxy is moving relative to the Earth. [3] (b) A star in our own galaxy approaches the Earth at 25 km s⁻¹. Calculate the change in wavelength of a 500 nm line from it. [2]

6. The table shows recession speeds for five galaxies.

d / Mpc	30	60	90	130	170
v / km s⁻¹	2250	4300	6500	9200	11 900

(a) State the shape of a graph of v against d that agrees with Hubble’s law. [1] (b) Use the data to find a value for the Hubble constant, in km s⁻¹ Mpc⁻¹. [2] (c) Convert your value to s⁻¹. [2] (d) Use H0 = 71 km s⁻¹ Mpc⁻¹ to estimate the age of the universe in years. [2]

7. Explain how the red shift of light from distant galaxies supports a model of an expanding universe, and why this does not mean that the Earth is at the centre. [5]

8. The cosmic microwave background radiation has a temperature of 2.7 K. Describe this radiation and explain why it is evidence for the Big Bang theory. [4]

9. A measurement gives H0 = 2.4 × 10⁻¹⁸ s⁻¹. Calculate the estimated age of the universe in seconds and in years, and state one reason why the estimate may be wrong. [4]

10. Describe, in the correct order, three stages in the history of the universe between the first few minutes and the formation of the first stars. [4]

11.

(a) State the approximate percentages of dark energy, dark matter and ordinary matter in the universe. [2] (b) Give one observation that suggests dark matter exists. [1] (c) State what dark energy is associated with. [1]

12. In the light from a galaxy, a spectral line is measured with Δλ/λ = 0.0085. Take H0 = 68 km s⁻¹ Mpc⁻¹.

(a) Calculate the recession speed of the galaxy. [2] (b) Calculate the distance to the galaxy in Mpc. [2] (c) Show that this distance is about 1.2 × 10⁸ ly. [2] (d) Explain why the Doppler equation is suitable here. [1] (e) Compare the time the light has travelled with the age of the universe, taken as 1.4 × 10¹⁰ years. [2]

Answers

1. AU: the mean distance from the Earth to the Sun [1]. Light-year: the distance light travels in a vacuum in one year [1]. Parsec: the distance at which a star shows a parallax of one second of arc (an AU subtends one second of arc) [1]. [3] Examiner insight: A light-year must be described as a distance travelled by light in a vacuum in one year. Writing only “how far light goes in a year” is vague, and “a time” loses the idea completely.

2. Distance = 2.6 × 3.09 × 10¹⁶ = 8.0 × 10¹⁶ m [1]. In ly: 8.03 × 10¹⁶ / 9.46 × 10¹⁵ = 8.5 ly [1]. [2] Examiner insight: Keep the unrounded value from the first conversion for the second, and give units on both answers. A number with no unit is not a complete answer.

3. (a) d = 1/p = 1/0.045 = 22 pc [1]. In ly: 22.2 × 3.09 × 10¹⁶ / 9.46 × 10¹⁵ = 73 ly [1]. (b) Measure the position of the star relative to very distant stars [1]. Measure again six months later, when the Earth is on the opposite side of its orbit [1]. The parallax angle is half the angular shift in position between the two observations [1]. (c) For distant stars the parallax angle is too small to measure [1]. [6] Examiner insight: For the method, state both observation times and say “half” of the shift. The commonest slip is giving the full shift as p.

4. On a large scale the universe is homogeneous (the same average density and structure everywhere) [1]. It is isotropic (it looks the same in every direction) [1]. The laws of physics are the same everywhere (universal) [1]. [3] Examiner insight: Explain each word rather than only naming it. Writing “uniform” for both homogeneous and isotropic does not separate them.

5. (a) Δλ = 405.1 − 393.4 = 11.7 nm [1]. v = c Δλ/λ = 3.00 × 10⁸ × 11.7 / 393.4 [1]. v = 8.9 × 10⁶ m s⁻¹ (the galaxy is receding) [1]. (b) Δλ = λ v/c = 500 × 25 × 10³ / 3.00 × 10⁸ [1]. Δλ = 0.042 nm, a decrease (blue shift) [1]. [5] Examiner insight: Convert km s⁻¹ to m s⁻¹ before using c. State the direction of the shift as well as its size, since the question gave a direction of motion.

6. (a) A straight line through the origin [1]. (b) v/d values are 75, 71.7, 72.2, 70.8 and 70.0, or a best-fit line through the origin [1]. H0 ≈ 71 km s⁻¹ Mpc⁻¹ (accept about 70 to 72) [1]. (c) 1 Mpc = 3.09 × 10¹⁹ km, so H0 = 71 / 3.09 × 10¹⁹ [1] = 2.3 × 10⁻¹⁸ s⁻¹ [1]. (d) t = 1/H0 = 1 / 2.30 × 10⁻¹⁸ = 4.35 × 10¹⁷ s [1]. In years: 4.35 × 10¹⁷ / 3.16 × 10⁷ = 1.4 × 10¹⁰ years [1]. [7] Examiner insight: A single end point is a weak basis for a gradient. Show that you used all the data, either by a best-fit line or by averaging the ratios. Carry the unrounded H0 into part (d).

7. The light from distant galaxies is shifted to longer wavelength (red shift) [1]. This is interpreted as the galaxies moving away from us [1]. The shift, and so the speed, increases with distance (Hubble’s law) [1]. This is what a uniform expansion of space gives, as all separations grow [1]. Observers in any other galaxy would see the same pattern, so the Earth is not at a centre; the expansion has no centre [1]. [5] Examiner insight: Go beyond the observation to the reasoning. Stating that every observer would see the same pattern is the point to include.

8. The CMB is microwave radiation reaching the Earth equally from all directions [1]. It has a spectrum corresponding to a temperature of 2.7 K [1]. At the start the universe was extremely hot, packed tightly and full of radiation [1]. Expansion stretched the wavelength of this radiation and cooled it, which gives the observed low temperature; this matches a prediction of the Big Bang theory [1]. [4] Examiner insight: Link the observation to the theory. Describing the CMB without explaining why a hot early universe predicts it gives only part of the credit available.

9. t = 1/H0 = 1 / 2.4 × 10⁻¹⁸ [1] = 4.2 × 10¹⁷ s [1]. In years: 4.17 × 10¹⁷ / 3.16 × 10⁷ = 1.3 × 10¹⁰ years [1]. The estimate assumes a constant expansion rate (the rate may have changed), or H0 has experimental uncertainty [1]. [4] Examiner insight: Give a reason that is specific to this calculation. “Human error” is not a reason about the physics.

10. A model answer has three stages in the right order. After a few minutes, fusion forms light nuclei, mainly hydrogen and helium [1]. After a few hundred thousand years, the universe cools enough for electrons to join nuclei and form atoms [1]; radiation can then travel freely, and this is the cosmic microwave background [1]. Over the following hundreds of millions of years, gravity pulls gas together to form the first stars and galaxies [1]. [4] Examiner insight: Use time-ordering words and approximate timescales. A list of events without an order, or with a wrong order, shows fewer correct points.

11. (a) Dark energy about 68% [1], dark matter about 27% and ordinary matter about 5% [1]. (b) Galaxies rotate faster than the visible matter alone can explain (or similar gravitational evidence) [1]. (c) The accelerating expansion of the universe [1]. [4] Examiner insight: Percentages need to be about right and in the right order. Do not say that dark energy and dark matter are the same thing.

12. (a) v = c Δλ/λ = 0.0085 × 3.00 × 10⁸ [1] = 2.6 × 10⁶ m s⁻¹ (2550 km s⁻¹) [1]. (b) d = v/H0 = 2550 / 68 [1] = 38 Mpc (37.5) [1]. (c) 37.5 × 10⁶ pc × 3.26 ly per pc [1] = 1.22 × 10⁸ ly, about 1.2 × 10⁸ ly [1]. (d) The speed is about 0.85% of c, so v is much less than c [1]. (e) The light travelled for about 1.2 × 10⁸ years [1], which is 0.9% of the age of the universe (1.2 × 10⁸ / 1.4 × 10¹⁰), a small fraction [1]. [9] Examiner insight: In a “show that” part, show the unrounded value before the given figure. Keep distances and speeds in consistent units: km s⁻¹ with Mpc, then Mpc to ly.

Where marks are usually lost

• Not converting km s⁻¹ to m s⁻¹ before using v/c.
• Quoting distances without units, or mixing pc, ly and m.
• Using the full shift instead of half the shift for parallax.
• Taking a gradient from one point rather than all the data.
• Leaving H0 in km s⁻¹ Mpc⁻¹ in t = 1/H0.
• Describing expansion as galaxies moving through space from a centre.
• Describing the CMB without linking it to the hot early universe.
• Mixing up dark matter and dark energy.

Next steps

• Re-read the study guide and the revision notes.
• Go to the OCR A Level Physics hub and tick off the printable checklist.
• Try the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

OCR Advanced GCE in Physics A (H556), Version 3.0 (March 2026), first assessment 2017, published by OCR. Section 5.5.3, Cosmology.