The shape of the lesson
By the end of the lesson, learners can
- Farther means faster: Set a galaxy's distance and watch its spectral line slide into the red while the point climbs the straight v = H₀d line.
- Redshift, Hubble, Big Bang: A short chain of ideas takes you from a shifted line to the age of the Universe.
- Standard candles: luminosity L (W); flux F = L / (4πd²); known L gives d = √(L / 4πF).
- Stellar radii: Wien λₘₐₓT = 2.90×10⁻³ m K; Stefan-Boltzmann L = 4πσr²T⁴.
- Cosmology: Δλ/λ ≈ v/c; Hubble v = H₀d; age ≈ 1/H₀.
One picture every idea returns to
Spectral lines from a receding galaxy are redshifted: their wavelength is stretched. For speeds well below c, the fractional shift gives the speed, Δλ/λ ≈ Δf/f ≈ v/c. Hubble found recession speed is proportional to distance, v = H₀d, evidence that the whole Universe is expanding from a Big Bang. Running it backwards gives an age of about 1/H₀.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The Universe is expanding.. Light from distant galaxies arrives stretched toward the red, and the further away a galaxy is, the faster it is fleeing. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Farther means faster | Set a galaxy's distance and watch its spectral line slide into the red while the point climbs the straight v = H₀d line. Project tab 3 of the lab (Hubble's law) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Redshift, Hubble, Big Bang | A short chain of ideas takes you from a shifted line to the age of the Universe. | Cooperative Concept Mapping |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 32 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Redshift, Hubble, Big Bang, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Cooperative Concept Mapping
Teams receive the key terms on cards and arrange them on a large sheet, drawing and labelling the links. Compare maps between teams before showing the model map.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| A redshift is a shift to longer wavelength and lower frequency. | The relation Δλ/λ ≈ v/c holds only for speeds much smaller than c. To use 1/H₀ for an age you must convert H₀ into base SI units (s⁻¹) first, since 1 Mpc = 3.09 × 10²² m; the result is a time in seconds. |
Hubble's law and the Big Bang: topic worksheet
4 questions, 32 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
A spectral line that has a laboratory wavelength of 434 nm is observed at 442 nm in the light from a galaxy.
(a) State what is meant by redshift. [1]
(b) Calculate the fractional shift Δλ/λ. [2]
(c) Calculate the speed of recession of the galaxy. [2]
(d) State the direction of motion of the galaxy and how the spectrum shows it. [2]
The galaxy in question 7 recedes at 5.5 × 10⁶ m s⁻¹. Take H₀ = 2.3 × 10⁻¹⁸ s⁻¹.
(a) State Hubble's law. [1]
(b) Calculate the distance to the galaxy, in metres. [2]
(c) Convert this distance to megaparsecs. [2]
(d) Describe the graph of recession speed against distance for many galaxies, and state what its gradient represents. [3]
Observations show that almost all galaxies are receding, with v = H₀d. Take H₀ = 2.3 × 10⁻¹⁸ s⁻¹.
(a) Explain how Hubble's law supports the idea of an expanding Universe and the Big Bang. [2]
(b) Estimate the age of the Universe, in seconds. [2]
(c) Convert this age into years. (1 year ≈ 3.16 × 10⁷ s) [2]
(d) State one assumption made when using 1/H₀ as the age. [2]
Astronomers build a "distance ladder" using several methods together.
(a) State how each of standard candles, Wien's law and redshift contributes to studying a distant galaxy. [3]
(b) A Cepheid variable places a galaxy at 15 Mpc. Using H₀ = 70 km s⁻¹ Mpc⁻¹, calculate the expected recession speed. [2]
(c) A type Ia supernova in the same galaxy has a known luminosity and a measured flux. Explain how this independently confirms the distance. [2]
(d) Suggest why redshift, rather than standard candles, is used for the most distant galaxies. [2]
Answer key and marking notes
- (a)An increase in the observed wavelength of spectral lines, caused by a source moving away ✓
- (b)Δλ/λ = (442 − 434) / 434 ✓ = 8 / 434 = 0.018 ✓
- (c)v ≈ c × Δλ/λ = 3.00 × 10⁸ × 0.018 ✓ = 5.5 × 10⁶ m s⁻¹ ✓
- (d)Moving away from us (receding) ✓; the lines are shifted to longer wavelengths (toward the red) ✓
- (a)The recession speed of a galaxy is proportional to its distance: v = H₀d ✓
- (b)d = v / H₀ = 5.5 × 10⁶ / 2.3 × 10⁻¹⁸ ✓ = 2.4 × 10²⁴ m ✓
- (c)2.4 × 10²⁴ / 3.09 × 10²² ✓ ≈ 78 Mpc ✓
- (d)A straight line through the origin ✓; speed increases in direct proportion to distance ✓; the gradient is the Hubble constant H₀ ✓
- (a)If every galaxy is receding, they were all closer together in the past ✓; running the expansion back gives a hot, dense origin (the Big Bang) ✓
- (b)t ≈ 1 / H₀ = 1 / 2.3 × 10⁻¹⁸ ✓ = 4.3 × 10¹⁷ s ✓
- (c)4.3 × 10¹⁷ / 3.16 × 10⁷ ✓ ≈ 1.4 × 10¹⁰ years (about 14 billion years) ✓
- (d)The expansion rate (H₀) has stayed constant throughout the history of the Universe ✓✓
- (a)Standard candles give the distance from known L and measured F ✓; Wien's law gives the surface temperature from the peak wavelength ✓; redshift gives the recession speed (and, via Hubble, distance) ✓
- (b)v = H₀d = 70 × 15 ✓ = 1.05 × 10³ km s⁻¹ (1050 km s⁻¹) ✓
- (c)With L known and F measured, d = √(L / 4πF) ✓; this is a second, independent estimate that should agree with the Cepheid distance ✓
- (d)The most distant galaxies are too faint to resolve individual standard candles ✓; their redshift is still measurable, so Hubble's law gives the distance ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
Light from a distant galaxy is redshifted. This tells us the galaxy is:
- Amoving away from us
- Bmoving toward us
- Cstationary
- Dgetting hotter
A galaxy shows a fractional shift Δλ/λ = 0.02 in its spectral lines. Its recession speed is about:
- A6 × 10⁶ m s⁻¹
- B3 × 10⁸ m s⁻¹
- C1.5 × 10⁶ m s⁻¹
- D0.02 m s⁻¹
A graph of recession speed v against distance d for many galaxies is a straight line through the origin. Its gradient is:
- Athe Hubble constant H₀
- Bthe speed of light c
- Cthe age of the Universe
- Dthe redshift z
The expansion of the Universe described by Hubble's law is evidence for:
- Athe Big Bang, with an age of roughly 1/H₀
- Ba Universe that is contracting
- Ca Universe with no beginning or change
- Dthe Earth being at the centre of the Universe
Quiz key
A redshift stretches the wavelengths, which happens when the source recedes. An approaching source would give a blueshift (shorter wavelengths).
v ≈ c × Δλ/λ = 3 × 10⁸ × 0.02 = 6 × 10⁶ m s⁻¹ (2% of the speed of light).
Hubble's law v = H₀d is the equation of that line, so the gradient is H₀. The age is then estimated as roughly 1/H₀.
If everything is receding and was once closer together, the Universe began hot and dense (the Big Bang). Reversing a constant expansion gives an age of about 1/H₀.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.