A Level Physics 25.3 Hubble’s Law and the Big Bang Theory MCQs – 30 Practice Questions with Answers (Cambridge 9702)

This page has 30 original practice MCQs on Section 25.3 of the Cambridge AS & A Level Physics 9702 syllabus: redshift and recession velocity, Hubble’s law, and the evidence for the Big Bang theory. Section 25.3 is an A Level (A2) topic, so these questions are aimed at students in the second year of the course.

Throughout this page, use the speed of light c = 3.00 × 108 m s−1, the Hubble constant H0 = 2.2 × 10−18 s−1 and 1 year = 3.16 × 107 s. Tap “Show Answer” under any question to reveal the answer and a fully worked explanation.

Formula recap: redshift z = Δλ / λ = Δf / f = v / c (for v much less than c) · Hubble’s law: v = H0 d · estimated age of the Universe ≈ 1 / H0. For the full set of equations, see the A Level Physics Formula Sheet.

Redshift & Recession Velocity

Q1. The light from a distant galaxy is analysed and a known spectral line is found at a longer wavelength than the same line produced in a laboratory on Earth. This effect is called

  • (A) diffraction
  • (B) polarisation
  • (C) redshift
  • (D) dispersion
Show Answer

Answer: C – A shift of spectral lines towards longer wavelengths (towards the red end of the visible spectrum) is called a redshift. It is the key observation that tells us distant galaxies are moving away from us.

Q2. The light from almost all distant galaxies is redshifted. The explanation used in the 9702 syllabus is that

  • (A) the galaxies are receding from us as space itself expands
  • (B) the light loses energy by scattering off dust as it travels
  • (C) the galaxies are rotating very rapidly
  • (D) the light is refracted by the Earth’s atmosphere
Show Answer

Answer: A – The redshift is a Doppler-type effect caused by the galaxies receding from us. At a basic level this is described as the expansion of space itself: the wavelength of the light is stretched as the Universe expands while the light travels to us.

Q3. The redshift z of a galaxy is defined by z = Δλ / λ. If a galaxy has z = 0.020, this means its spectral lines are shifted by

  • (A) 0.020% of their original wavelength
  • (B) 2.0% of their original wavelength
  • (C) 20% of their original wavelength
  • (D) 0.020 nm, whatever the original wavelength
Show Answer

Answer: B – z is a fraction, not a percentage or a fixed length. z = Δλ / λ = 0.020 means Δλ is 0.020 (2.0%) of the emitted wavelength λ. Every line in the spectrum is stretched by the same fraction.

Q4. A spectral line emitted at 500 nm is observed at 505 nm in the light from a galaxy. The redshift z is

  • (A) 0.0010
  • (B) 0.0050
  • (C) 0.050
  • (D) 0.010
Show Answer

Answer: D – Δλ = 505 − 500 = 5 nm. z = Δλ / λ = 5 / 500 = 0.010. Note the emitted (laboratory) wavelength is used in the denominator.

Q5. For the galaxy in Q4, the recession velocity v is given by v = zc. Its value is

  • (A) 3.0 × 105 m s−1
  • (B) 3.0 × 106 m s−1
  • (C) 3.0 × 107 m s−1
  • (D) 1.0 × 106 m s−1
Show Answer

Answer: B – v = zc = 0.010 × 3.00 × 108 = 3.0 × 106 m s−1. This is only 1% of the speed of light, so the approximate relation v = zc is valid.

Q6. A line emitted at 656 nm is observed at 672 nm in a galaxy’s spectrum. The recession velocity of the galaxy is approximately

  • (A) 7.3 × 106 m s−1
  • (B) 2.4 × 106 m s−1
  • (C) 7.3 × 107 m s−1
  • (D) 1.6 × 107 m s−1
Show Answer

Answer: A – z = (672 − 656) / 656 = 16 / 656 = 0.024. Then v = zc = 0.024 × 3.00 × 108 = 7.3 × 106 m s−1.

Q7. The simple relation z = v / c used at A Level is a good approximation only when

  • (A) the galaxy is very large
  • (B) the redshift is measured in space, not on Earth
  • (C) v is much less than c
  • (D) the galaxy is moving towards us
Show Answer

Answer: C – z = v / c is the low-speed (non-relativistic) approximation. It works well for v << c, but for galaxies receding at a sizeable fraction of c a relativistic formula is needed, so the simple relation would give the wrong velocity.

Q8. Galaxy X has a redshift of 0.008 and galaxy Y has a redshift of 0.040. Compared with galaxy X, galaxy Y is

  • (A) receding five times faster
  • (B) receding five times slower
  • (C) five times closer
  • (D) five times larger
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Answer: A – Since v = zc, the recession velocity is proportional to z. vY / vX = 0.040 / 0.008 = 5. A larger redshift always means a faster recession (and, by Hubble’s law, a greater distance).

Q9. A galaxy emits radiation of frequency 6.00 × 1014 Hz and has a redshift z = 0.020. The frequency observed on Earth is

  • (A) 6.12 × 1014 Hz
  • (B) 6.00 × 1014 Hz
  • (C) 3.00 × 1014 Hz
  • (D) 5.88 × 1014 Hz
Show Answer

Answer: D – For redshift, z = Δf / f where Δf is the size of the DECREASE in frequency. Δf = 0.020 × 6.00 × 1014 = 1.2 × 1013 Hz, so fobserved = 6.00 × 1014 − 1.2 × 1013 = 5.88 × 1014 Hz. The frequency falls because the wavelength is stretched (f = c / λ).

Q10. Which statement about the redshifts of galaxies is correct?

  • (A) About half of all distant galaxies are blueshifted
  • (B) Distant galaxies all show redshift, and the redshift generally increases with distance
  • (C) Only the most distant galaxies show any shift
  • (D) Redshift is larger for galaxies in one direction of the sky only
Show Answer

Answer: B – Observations show that essentially every galaxy beyond our local neighbourhood is redshifted, in every direction, and more distant galaxies have larger redshifts. This pattern is the evidence that the whole Universe is expanding, not that we sit at the centre of an explosion.

Hubble’s Law

Q11. Hubble’s law states that the recession velocity v of a galaxy is

  • (A) inversely proportional to its distance d
  • (B) proportional to the square of its distance d
  • (C) directly proportional to its distance d
  • (D) the same for all galaxies
Show Answer

Answer: C – Hubble’s law is v = H0 d: the further away a galaxy is, the faster it recedes from us. The constant of proportionality H0 is the Hubble constant.

Q12. A graph of recession velocity v against distance d for many galaxies is a straight line through the origin. The gradient of this line is

  • (A) the speed of light c
  • (B) the Hubble constant H0
  • (C) the age of the Universe
  • (D) the redshift z
Show Answer

Answer: B – Comparing v = H0 d with y = mx, the gradient of the v-d graph is H0. This is how the Hubble constant is measured in practice: recession speeds come from redshifts and distances are measured by independent methods.

Q13. Using H0 = 2.2 × 10−18 s−1, a galaxy receding at 6.6 × 106 m s−1 is at a distance of

  • (A) 3.0 × 1022 m
  • (B) 1.5 × 1025 m
  • (C) 3.3 × 10−25 m
  • (D) 3.0 × 1024 m
Show Answer

Answer: D – d = v / H0 = 6.6 × 106 / 2.2 × 10−18 = 3.0 × 1024 m.

Q14. A galaxy is at a distance of 5.0 × 1024 m. Using H0 = 2.2 × 10−18 s−1, its recession velocity is

  • (A) 1.1 × 107 m s−1
  • (B) 2.3 × 106 m s−1
  • (C) 4.4 × 10−43 m s−1
  • (D) 1.1 × 106 m s−1
Show Answer

Answer: A – v = H0 d = 2.2 × 10−18 × 5.0 × 1024 = 1.1 × 107 m s−1.

Q15. The SI unit of the Hubble constant H0 is

  • (A) m s−1
  • (B) s
  • (C) s−1
  • (D) m−1
Show Answer

Answer: C – From v = H0 d, H0 = v / d, so its unit is (m s−1) / m = s−1. This is why 1 / H0 has the unit of time, seconds.

Q16. Galaxy P is 2.0 × 1024 m away and galaxy Q is 4.0 × 1024 m away. If both obey Hubble’s law, then

  • (A) Q recedes at the same speed as P
  • (B) Q recedes at twice the speed of P
  • (C) Q recedes at four times the speed of P
  • (D) Q recedes at half the speed of P
Show Answer

Answer: B – v is directly proportional to d. Q is twice as far away as P, so vQ = 2 vP. (In numbers: vP = 2.2 × 10−18 × 2.0 × 1024 = 4.4 × 106 m s−1 and vQ = 8.8 × 106 m s−1.)

Q17. The Andromeda galaxy, a near neighbour of the Milky Way, shows a small BLUESHIFT. This is because

  • (A) Hubble’s law is wrong
  • (B) Andromeda is young and still forming
  • (C) the light from Andromeda is not redshifted by dust
  • (D) at small distances, the gravitational pull between the galaxies gives a motion towards us that is bigger than the expansion effect
Show Answer

Answer: D – Hubble’s law describes the large-scale expansion, but nearby galaxies also have their own local motions. Andromeda is close enough that mutual gravity is pulling it towards the Milky Way faster than space between us expands, so its light is blueshifted. The law only dominates at large distances.

Q18. A galaxy has a recession velocity of 2.2 × 104 km s−1. Its distance, using H0 = 2.2 × 10−18 s−1, is

  • (A) 1.0 × 1025 m
  • (B) 1.0 × 1022 m
  • (C) 2.2 × 1024 m
  • (D) 1.0 × 1028 m
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Answer: A – First convert to SI: v = 2.2 × 104 km s−1 = 2.2 × 107 m s−1. Then d = v / H0 = 2.2 × 107 / 2.2 × 10−18 = 1.0 × 1025 m. Forgetting the km-to-m conversion gives the wrong answer (B).

Q19. To find the value of H0 from observations of a single galaxy, astronomers need to measure

  • (A) only the galaxy’s redshift
  • (B) only the galaxy’s distance
  • (C) both the recession velocity (from the redshift) and the distance, measured independently
  • (D) the galaxy’s mass and diameter
Show Answer

Answer: C – H0 = v / d. The velocity v comes from the redshift (v = zc), but the distance d must be found by a separate method (for example, using standard candles). Using many galaxies and taking the gradient of the v-d graph gives the most reliable value.

Q20. If the true value of H0 were larger than 2.2 × 10−18 s−1, then for a galaxy with a measured recession velocity, Hubble’s law would give

  • (A) a larger distance
  • (B) a smaller distance
  • (C) the same distance
  • (D) a larger redshift
Show Answer

Answer: B – d = v / H0. With v fixed, a larger H0 means a smaller d. A larger H0 also means a smaller value of 1 / H0, i.e. a younger estimated age for the Universe.


The Age of the Universe & Big Bang Evidence

Q21. If a galaxy at distance d has always receded at the constant speed v, the time since all galaxies were together is d / v. Using Hubble’s law this time is approximately

  • (A) H0
  • (B) 1 / H0
  • (C) H02
  • (D) c / H0
Show Answer

Answer: B – t = d / v, and Hubble’s law gives v = H0 d, so t = d / (H0 d) = 1 / H0. This is called the Hubble time, and it gives an estimate of the age of the Universe whatever galaxy is chosen.

Q22. Using H0 = 2.2 × 10−18 s−1, the Hubble time 1 / H0 is

  • (A) 2.2 × 1018 s
  • (B) 6.6 × 1017 s
  • (C) 4.5 × 1017 s
  • (D) 4.5 × 1015 s
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Answer: C – 1 / H0 = 1 / (2.2 × 10−18) = 4.5 × 1017 s.

Q23. The value from Q22 expressed in years (1 year = 3.16 × 107 s) is approximately

  • (A) 1.4 × 108 years
  • (B) 1.4 × 109 years
  • (C) 1.4 × 1011 years
  • (D) 1.4 × 1010 years
Show Answer

Answer: D – t = 4.5 × 1017 / 3.16 × 107 = 1.4 × 1010 years, about 14 billion years. This agrees well with the accepted age of the Universe.

Q24. The value 1 / H0 is only an ESTIMATE of the age of the Universe because

  • (A) the speed of light has changed over time
  • (B) the expansion rate has not stayed constant: gravity slowed the expansion in the past and the expansion is now accelerating
  • (C) galaxy distances cannot be measured at all
  • (D) redshift can only be measured for a few galaxies
Show Answer

Answer: B – The calculation assumes every galaxy has always moved at today’s speed. In reality the expansion was slowed by gravity for most of the Universe’s history and has recently started to accelerate, so the true age differs somewhat from 1 / H0 – but it is the correct order of magnitude.

Q25. The cosmic microwave background radiation is

  • (A) radiation given out by the Sun’s corona
  • (B) interference from radio telescopes on Earth
  • (C) X-rays from black holes at the centres of galaxies
  • (D) microwave radiation arriving uniformly from all directions, corresponding to a temperature of about 2.7 K
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Answer: D – Detectors pick up faint microwave radiation coming equally from every direction in the sky, matching a black-body temperature of about 2.7 K. It is found everywhere and cannot be linked to any single source, which is why it is called a background.

Q26. The cosmic microwave background supports the Big Bang theory because it is interpreted as

  • (A) the cooled remnant of the intense radiation of the early, hot Universe, stretched to microwaves by the expansion
  • (B) light from the very first stars
  • (C) heat radiated by dark matter today
  • (D) radiation produced when galaxies collide
Show Answer

Answer: A – In the Big Bang model the early Universe was extremely hot and filled with high-energy radiation. As space expanded, that radiation’s wavelength was stretched (redshifted) into the microwave region and its temperature fell to about 2.7 K. The existence of this background, predicted by the theory and then discovered, is powerful evidence for a hot beginning.

Q27. The observed composition of the Universe – roughly 75% hydrogen and 25% helium by mass, with only traces of lithium and other light elements – supports the Big Bang theory because

  • (A) stars cannot produce any helium
  • (B) these proportions match the amounts predicted to have been made by nuclear reactions in the hot early Universe
  • (C) hydrogen and helium are the heaviest elements
  • (D) the proportions are the same inside every star
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Answer: B – Calculations of the nuclear reactions (Big Bang nucleosynthesis) that took place in the first few minutes predict about 75% hydrogen and 25% helium-4, plus tiny amounts of lithium. These match observations even in the oldest, least-processed gas clouds, where stars have not had time to change the mix.

Q28. If the expansion of the Universe is “run backwards” in our imagination, Hubble’s law and the redshift evidence imply that

  • (A) the Universe has always existed in its present state
  • (B) galaxies will eventually start to approach each other
  • (C) the Universe began a finite time ago in a very hot, dense state
  • (D) the Universe is shrinking
Show Answer

Answer: C – Galaxies are moving apart now, so in the past they must have been closer together. Running the expansion back far enough, all matter and energy were concentrated in an extremely hot, dense state about 1.4 × 1010 years ago – the starting point described by the Big Bang theory.

Q29. A galaxy is 3.0 × 1024 m away and recedes at 6.6 × 106 m s−1. Assuming its speed has never changed, the time since it was at our position is

  • (A) 4.5 × 1017 s
  • (B) 2.0 × 1031 s
  • (C) 2.2 × 10−18 s
  • (D) 5.0 × 1016 s
Show Answer

Answer: A – t = d / v = 3.0 × 1024 / 6.6 × 106 = 4.5 × 1017 s. This is exactly the Hubble time 1 / H0 from Q22 – any galaxy obeying Hubble’s law gives the same answer, which is why it estimates the age of the Universe.

Q30. Which combination correctly lists pieces of evidence for the Big Bang theory?

  • (A) The phases of Venus and the retrograde motion of Mars
  • (B) Fossils in rocks and continental drift
  • (C) The solar eclipse observations and bending of starlight
  • (D) Galaxy redshifts following Hubble’s law, the cosmic microwave background, and the abundances of the light elements
Show Answer

Answer: D – The three classic lines of evidence are: (i) distant galaxies are redshifted with recession speed proportional to distance (Hubble’s law), showing the Universe is expanding from a denser past; (ii) the cosmic microwave background at about 2.7 K, the cooled remnant of the early radiation; (iii) the observed proportions of hydrogen, helium and lithium matching Big Bang nucleosynthesis predictions.

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