Year 12 Physics Module 8 ⏱ ~40 min 5 MC · 2 Short Answer Lesson 1 of 17

The Big Bang Theory

In 1964, Arno Penzias and Robert Wilson at Bell Labs in Holmdel, New Jersey were calibrating a 6 m horn antenna for satellite communications when they detected an isotropic microwave noise at 2.725 K that could not be explained by any local source. Colleagues at Princeton identified it as the Cosmic Microwave Background (CMB), relic radiation predicted by Alpher and Gamow in 1948 as the afterglow of the Big Bang. Penzias and Wilson were awarded the Nobel Prize in Physics in 1978.

Today's hook: In 1965, Arno Penzias and Robert Wilson at Bell Labs pointed a 6 m horn antenna at the sky and measured a persistent microwave hiss at 2.725 K coming equally from every direction, day and night, even after scrubbing pigeon droppings from the dish. Their Princeton colleagues calculated it corresponded to a blackbody with a wavelength peak at 1.9 mm. What did this faint, uniform glow tell us about the origin of the universe?
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Orient and predict

Set up the vocabulary of expansion, temperature and redshift, then commit to a prediction about what running the expansion backwards would do.

Worksheets

Practise this lesson

Four printable worksheets that build from the foundations up to exam-style questions, start at whatever level suits you.

Build Foundations & guided practice Apply Application & data response Master Mastery tasks Exam Exam-style questions
Before you read, predict

Imagine the universe is expanding, and galaxies are moving apart from each other.

Before reading on, answer:

  1. If you reverse time, what happens to the size of the universe?
  2. What would happen to the temperature of the universe as it shrinks?
  3. Does the expansion mean Earth is at the centre of the universe?

Warm-up, approximately how old is the universe according to the Big Bang model?

Learning Intentions
goals

Know, The Big Bang Model

  • Universe began ~13.8 billion years ago
  • Space itself expands, not an explosion into empty space
  • CMB released at recombination (~380,000 years)

Understand, Cosmic Evolution

  • Universe cooled as it expanded: $T \propto 1/a$
  • Formation of fundamental particles and atoms over time
  • Cosmological redshift: $\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$

Can Do, Analyse Cosmological Data

  • Calculate the expansion factor from CMB temperatures
  • Interpret the timeline of key events after the Big Bang
  • Evaluate the cosmological redshift formula
Scan these before reading
vocab
Big BangThe cosmological model describing the expansion of the universe from an extremely hot, dense initial state approximately 13.8 billion years ago.
Cosmic Microwave Background (CMB)Thermal radiation left over from the Big Bang, now cooled to 2.725 K, filling the universe uniformly from all directions.
Cosmological redshiftThe stretching of light wavelengths due to the expansion of space itself: $\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$.
RecombinationThe epoch (~380,000 years after the Big Bang) when electrons bound to nuclei forming neutral hydrogen, making the universe transparent and releasing the CMB.
Scale factor ($a$)A dimensionless quantity describing the relative size of the universe at a given time; temperature scales as $T \propto 1/a$.
Cross-lesson links: Module 8 opens with the largest physical question, the origin of the universe. The Big Bang model is grounded in three independent lines of evidence (CMB, Hubble expansion, nucleosynthesis ratios) that you will examine in L01–L03. Each line of evidence uses physics you have studied: wave properties (M7), spectroscopy (M7 L09), and nuclear physics (L14–L15).

Core Content

2

Trace the model's timeline

Work through the stages the model describes, from the earliest extrapolated moments to the first stars, and see why "expansion of space" is not "explosion in space".

Beyond the syllabus. The hot dense early Universe, the radiation-to-matter sequence and qualitative expansion are core. The Planck-time/inflation chronology, scale-factor thermodynamics and quantitative CMB expansion calculations are extension — the exam wants the Big Bang story and its evidence.
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The Big Bang Model
+5 XP

The expanding universe

In 1965, Arno Penzias and Robert Wilson at Bell Labs measured a faint microwave hiss of 2.725 K arriving equally from every direction in the sky. No matter where they pointed their 6 m antenna, toward or away from the Milky Way, at any time of day or night, the signal remained constant. Their Princeton colleagues showed this matched the blackbody radiation predicted by Alpher and Gamow as the cooled afterglow of an ancient hot, dense universe: the Cosmic Microwave Background (CMB). This observation is the central evidence for the Big Bang theory the cosmological model stating the universe began approximately 13.8 billion years ago in an extremely hot, dense state and has been expanding and cooling ever since.

Early universe Expands Present-day universe

Figure 1, Balloon analogy: galaxies (dots) move apart as space (balloon surface) expands, there is no centre

Key events in the timeline:

  • Earliest extrapolation: Classical general relativity extrapolates toward a singularity, but the model is not reliable at $t = 0$; a tested quantum theory of gravity would be needed to describe that limit.
  • $t \approx 10^{-43}$ s (Planck time): Gravity separates from other forces. Temperature ~$10^{32}$ K.
  • $t \approx 10^{-35}$ s: Inflation, universe expands exponentially by factor of ~$10^{26}$ in $10^{-32}$ s.
  • $t \approx 10^{-6}$ s: Quarks combine to form protons and neutrons.
  • $t \approx 3$ min: Nucleosynthesis, protons and neutrons fuse into hydrogen, helium and trace lithium.
  • $t \approx 380{,}000$ years: Recombination, electrons bind to nuclei, forming neutral atoms. Universe becomes transparent. CMB released.
  • $t \approx 200$ million years: First stars form.
  • $t \approx 9$ billion years: Expansion begins to accelerate.
  • Present ($t \approx 13.8$ Gyr): Accelerating expansion continues.
Stop & Check

If the universe is 13.8 billion years old, what is the maximum distance light could have travelled since the Big Bang? Why might galaxies be farther apart than this distance?

The Big Bang is the expansion of space itself from an extremely hot, dense state ~13.8 billion years ago, not an explosion into pre-existing space. The universe evolved through key stages: singularity → inflation → quarks/hadrons → nucleosynthesis (~3 min) → recombination (~380,000 yr, CMB released) → first stars (~200 Myr).

Pause, copy the highlighted definition into your book before moving on.

The Big Bang is best described as:

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Read the CMB, the model's testable prediction

See why a hot early universe must leave an afterglow, what recombination changed, and how 3000 K becomes 2.725 K.

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The Cosmic Microwave Background
+5 XP

The afterglow of the Big Bang

We just saw that the Big Bang describes the expansion of space from an extremely hot, dense state ~13.8 billion years ago. That raises a question: if the early universe was so hot and opaque, can we actually observe any relic of it today? This card answers it → yes, the Cosmic Microwave Background is that relic, released when the universe first became transparent.

Before recombination (~380,000 years after the Big Bang), the universe was an opaque plasma of charged particles. Photons could not travel freely, they scattered constantly off electrons. When the universe cooled enough for electrons to bind to nuclei, forming neutral hydrogen, the universe became transparent. The last-scattering photons have been travelling ever since, stretched by cosmic expansion from visible light to microwave wavelengths. This radiation, the Cosmic Microwave Background (CMB) is the most direct observational evidence of the hot early universe.

Key properties of the CMB:

  • It has a perfect black-body spectrum with temperature 2.725 K ($-270.4°$C).
  • It is extraordinarily uniform the same temperature in all directions to about 1 part in 100,000.
  • The tiny anisotropies (temperature fluctuations $\Delta T/T \sim 10^{-5}$) are the seeds of all large-scale structure, galaxies, clusters, and voids.
Cosmological Equations

$T \propto 1/a$    (temperature inversely proportional to scale factor)

$\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$    (cosmological redshift)

$v = H_0 d$    (Hubble's law, $H_0 \approx 70$ km/s/Mpc)

Opaque plasma Photons scatter off electrons Light cannot travel freely → Recombination ~380,000 yr Transparent universe Electrons bind to nuclei CMB photons travel freely CMB released here → now observed at 2.725 K (stretched by expansion)

Figure 2, At recombination the universe became transparent; CMB photons released then have been travelling and cooling ever since

Stop & Check

The CMB was emitted at ~3000 K. It is now observed at 2.725 K. Calculate the factor by which the universe has expanded since recombination. If a CMB photon had wavelength 500 nm when emitted, what is its wavelength now?

The CMB is relic black-body thermal radiation released at recombination (~380,000 yr after Big Bang) when the universe first became transparent; it now has temperature 2.725 K, is isotropic to 1 part in 100,000, and the expansion factor since recombination is $T_{emit}/T_{now} = 3000/2.725 \approx 1100$ (from $T \propto 1/a$).

Add the highlighted principle to your notes before the check below.

The CMB temperature is 2.725 K and was emitted at approximately 3000 K. The universe has expanded by a factor of approximately:

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Separate the redshift types, and mark the limits

Distinguish cosmological from Doppler and gravitational redshift, then note where the $v = cz$ shortcut stops being safe.

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Cosmological Redshift and Hubble's Law
+5 XP

Space expanding stretches wavelengths

We just saw that the CMB is the relic afterglow of the Big Bang, with its wavelengths stretched by cosmic expansion. That raises a question: how do we actually measure this expansion for individual galaxies, and can we quantify the rate? This card answers it → via cosmological redshift $z$ and Hubble's law $v = H_0 d$.

As space expands, the wavelengths of photons travelling through it are stretched. This is cosmological redshift distinct from Doppler redshift (motion through space) and gravitational redshift (climbing out of a gravitational field). For distant galaxies, cosmological redshift dominates. The redshift $z$ is defined as $z = \Delta\lambda/\lambda_{\mathrm{rest}}$, and the observed wavelength is $\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$.

Edwin Hubble (1929) observed that more distant galaxies have greater redshifts. This is expressed in Hubble's law: $v = H_0 d$, where $H_0 \approx 70$ km/s/Mpc. For nearby galaxies, $v \approx cz$.

HSC Tip: Distinguishing Redshift Types

Three types of redshift appear in HSC Physics: Doppler redshift (relative motion through space), gravitational redshift (climbing out of a gravitational field), and cosmological redshift (expansion of space itself stretching wavelengths). For distant galaxies, cosmological redshift is dominant. The formula $z = \Delta\lambda/\lambda_{\mathrm{rest}}$ works for all three, but the physical cause differs. A common trap: treating cosmological redshift as a Doppler shift, for distant galaxies, space itself expands, so $v = cz$ is only an approximation valid for $z \ll 1$.

Emitted (early universe) λemit (short) → Space expands Observed (today) λobs (stretched, redshifted) λobs = λemit(1 + z)    where    z = Δλ / λrest

Figure 3, Cosmological redshift: as space expands, the wavelength of a photon travelling through it is stretched proportionally

Stop & Check

A galaxy has its hydrogen-alpha spectral line (rest wavelength 656 nm) observed at 720 nm. Calculate the redshift $z$ and, using Hubble's law ($H_0 = 70$ km/s/Mpc) with the approximation $v \approx cz$, estimate the galaxy's distance.

Cosmological redshift is the stretching of photon wavelengths by expanding space: $\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$, where $z = (\lambda_{\mathrm{obs}}-\lambda_{\mathrm{rest}})/\lambda_{\mathrm{rest}}$. Hubble's law $v = H_0 d$ ($H_0 \approx 70$ km/s/Mpc) relates recession velocity to distance; for $z \ll 1$, $v \approx cz$. This is distinct from Doppler shift, it is space itself expanding, not motion through space.

Pause, write the highlighted law and formula into your book before the check below.

The Big Bang was an explosion of matter into pre-existing empty space, with Earth located at the centre of the explosion.

During recombination, electrons combined with nuclei to form neutral atoms, allowing photons to travel freely and producing the CMB.

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Sequence the cosmic timeline yourself

Order the events, justify why the CMB waited ~380,000 years, and work with lookback time as a fraction of the model's age.

Activity 1, Timeline Construction
ApplyBand 4

Sequence the key events in cosmic evolution

  1. Place the following events in chronological order after the Big Bang, stating the approximate time for each: (a) first stars form, (b) quarks combine into protons/neutrons, (c) nucleosynthesis produces helium, (d) recombination and CMB release, (e) inflation.
  2. Explain why the CMB was not released until ~380,000 years after the Big Bang, even though the universe was extremely hot and full of photons from the very beginning.
  3. The universe is currently 13.8 billion years old. If a telescope observes a galaxy at a lookback time of 13 billion years, what fraction of the universe's current age had elapsed when that light was emitted?
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Apply it, from CMB temperatures to a redshift

Run the staged calculation from $T \propto 1/a$ to an observed wavelength and a redshift, then judge a claim about galaxy separations.

Activity 2, CMB Expansion Calculation
ApplyBand 5

Use $T \propto 1/a$ and $\lambda_{\mathrm{obs}} = \lambda_{\mathrm{emit}}(1+z)$

  1. The CMB was emitted at a temperature of ~3000 K and is now observed at 2.725 K. Use $T \propto 1/a$ to calculate the factor by which the universe has expanded since recombination.
  2. A CMB photon was emitted with wavelength 500 nm at recombination. Calculate its observed wavelength today, and confirm which region of the electromagnetic spectrum it now lies in.
  3. Define the redshift $z$ for the CMB photon above and verify it is consistent with the expansion factor calculated in part (1).
  4. A student claims: "Because the universe has expanded by a factor of 1100, a galaxy that was 1 Mpc away at recombination is now 1100 Mpc away." Evaluate this claim.
Synthesis, connect the ideas

In this lesson, three ideas lock together:

  • The hot Big Bang model: not an explosion into empty space, but expansion from an extremely hot, dense early state about 13.8 billion years ago; it does not provide a tested account of an initial singularity.
  • Cosmic evolution: as space expanded, temperature fell ($T \propto 1/a$), allowing matter to cool into particles, then atoms, then stars.
  • The CMB: the observable remnant of recombination, photons released when the universe first became transparent, now stretched to microwave wavelengths by the same expansion.
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Independent practice

Show what you can do without prompts

Complete a shuffled question-bank set, then write full Big Bang and redshift responses in HSC style.

Quick recall, the Big Bang theory
+5 XP

A fresh five-question set drawn from this lesson's bank, feedback shown immediately. +5 XP per correct · +25 XP all correct

Pick your answer, then rate your confidence, that tells the system what to drill next.

Short Answer
+5 XP

ApplyBand 4(4 marks) 1. (a) Distinguish between the Big Bang as an "explosion" and the Big Bang as an "expansion of space." (b) Describe the cosmic microwave background and explain what physical process produced it. (c) The CMB was emitted at ~3000 K and is now observed at 2.725 K. Calculate the redshift $z$ of the CMB. (d) Outline two key events in the evolution of the universe between the Big Bang and the formation of the first stars.

1 mark each: (a) distinction, (b) description + process, (c) correct z, (d) two events

AnalyseBand 6(5 marks) 2. (a) Explain why, from any galaxy in the universe, all other galaxies appear to be receding. Does this imply that the observing galaxy is at the centre of the universe? (b) Distinguish between cosmological redshift, Doppler redshift, and gravitational redshift. (c) A galaxy's calcium absorption line (rest wavelength 393 nm) is observed at 432 nm. Calculate its redshift $z$ and estimate its distance using Hubble's law ($H_0 = 70$ km/s/Mpc, $c = 3.0 \times 10^5$ km/s). (d) Explain why the formula $v = cz$ may give an overestimate of the recession velocity for high-redshift galaxies.

1 mark each: (a) no centre + explanation, (b) three types distinguished, (c) correct z and d, (d) limitation explained

Show all answers

Multiple choice

MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set drawn from the lesson bank.

Short Answer, Model Answers

Q1 (4 marks): (a) An "explosion" implies matter expanding into pre-existing empty space from a centre; the hot Big Bang model instead describes the expansion of spatial distances everywhere, with no observed centre or edge, and does not establish what preceded the early state (1 mark). (b) The CMB is thermal (black-body) radiation at 2.725 K filling all of space uniformly. It was released at photon decoupling around recombination (~380,000 years after the Big Bang), when the universe cooled sufficiently for electrons to bind to nuclei; the universe became transparent and these photons have been travelling and redshifting ever since (1 mark). (c) Using $T \propto 1/a$: expansion factor $= 3000/2.725 \approx 1100$; therefore $z = (a_{\mathrm{now}}/a_{\mathrm{then}}) - 1 \approx 1099 \approx 1100$. Alternatively, using $\lambda_{\mathrm{obs}}/\lambda_{\mathrm{emit}} = 1+z$: $z = 3000/2.725 - 1 \approx 1099$ (1 mark). (d) Any two of: nucleosynthesis (~3 min, protons and neutrons form light nuclei); quarks combine to form protons and neutrons (~$10^{-6}$ s); inflation in the standard cosmological model (~$10^{-35}$ s); recombination and photon decoupling (~380,000 yr) (1 mark).

Q2 (5 marks): (a) Space expands uniformly in all directions. From any galaxy, every other galaxy appears to recede because the distance between all pairs of galaxies increases. This does NOT imply a centre, the expansion is homogeneous; every observer sees the same pattern (1 mark). (b) Cosmological redshift: space itself expanding stretches photon wavelengths, dominant for distant galaxies. Doppler redshift: caused by relative motion through space, applies to nearby galaxies with peculiar velocities. Gravitational redshift: photons climbing out of a gravitational potential lose energy and shift to longer wavelengths (1 mark). (c) $z = (432 - 393)/393 = 39/393 \approx 0.099$; $v = cz = 3.0\times10^5 \times 0.099 \approx 2.97\times10^4$ km/s; $d = v/H_0 = 2.97\times10^4/70 \approx 424$ Mpc (1 mark). (d) The formula $v = cz$ is a low-$z$ approximation derived from the linear term of the cosmological redshift relation. For high-$z$ galaxies, the expansion rate has changed over time (the universe was decelerating then accelerating), so the simple proportionality breaks down and $v$ could exceed $c$ in the calculation, which is not physically meaningful. The full treatment requires integrating the Friedmann equations (1 mark).

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Final step

Retrieve, reflect and finish

Check what stuck, revisit your opening predictions about reversing the expansion, and record what you will reuse.

Check what actually stuck
How did your thinking change?

At the start you were asked about the 2.725 K microwave hiss that Penzias and Wilson measured at Bell Labs in 1965 using a 6 m horn antenna, the signal that turned out to be the Cosmic Microwave Background, the relic radiation of the Big Bang.

  • Did you predict that the uniform 2.725 K signal meant the universe was once extremely hot and dense, and the microwave hiss is the cooled afterglow of that early state? Correct, the CMB is direct evidence of the hot Big Bang, stretched from visible-light wavelengths to 1.9 mm microwave wavelengths by 13.8 billion years of cosmic expansion.
  • Did you predict that reversing the expansion would lead back to an extremely small, hot state? Correct, this is the essence of the Big Bang model: $T \propto 1/a$, so a smaller scale factor means higher temperature.
  • Did you predict that Earth is not at the centre of the expansion? Correct, from any galaxy, all others appear to be receding. The expansion has no centre; every point sees the same pattern.
← Module overview Next: Evidence for the Big Bang →

Module overview · Physics