Topic 10 turns starlight into data. From a star's colour you get its temperature; from its brightness and distance you get its luminosity; from a galaxy's redshift you get the expansion of the Universe.
λmaxT = 2.898 × 10⁻³ m K · L = 4πr²σT⁴ · z = Δλ/λ = v/c · v = H₀dWien · Stefan–Boltzmann · redshift · Hubble
Luminosity vs intensity:luminosity L is the total power a star radiates (W). Intensity I is what we receive here, and it obeys an inverse-square law: I = L/(4πd²). Two stars can look equally bright and be wildly different objects.
Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
Topic 10 · black bodies
Wien's law and the Stefan–Boltzmann law
Stars are excellent black bodies: they absorb all incident radiation and emit a continuous spectrum whose shape depends only on temperature.
λmax T = 2.898 × 10⁻³ m KWien's displacement law — hotter stars peak at SHORTER wavelengths, so they look blue
L = 4π r² σ T⁴Stefan–Boltzmann law — σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; note the FOURTH power of T
Double a star's temperature and its luminosity goes up sixteenfold — temperature is by far the more brutal variable.
4πr² is simply the star's surface area: a red giant is cool but so vast that it is still hugely luminous.
Use the two laws together and you can find a star's radius from its colour and its brightness alone.
Worked example — a Sun-like star
λmax = 500 nm → T = 2.898 × 10⁻³ ÷ 500 × 10⁻⁹ = 5800 K
With r = 7.0 × 10⁸ m: L = 4π(7.0 × 10⁸)² × 5.67 × 10⁻⁸ × 5800⁴
4πr² = 6.16 × 10¹⁸ m² · T⁴ = 1.13 × 10¹⁵ K⁴ → L ≈ 3.95 × 10²⁶ W
Calculate
Your turn — Wien's law
1A star's spectrum peaks at a wavelength of 500 nm. Calculate its surface temperature. Give your answer in K to 2 significant figures. (Wien constant = 2.898 × 10⁻³ m K)
2That star has a radius of 7.0 × 10⁸ m and a surface temperature of 5800 K. Calculate its luminosity. Give your answer as a multiple of 10²⁶ W to 3 significant figures. (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴)
× 10²⁶ W
Hint: L = 4πr²σT⁴. 4πr² = 6.16 × 10¹⁸ m². T⁴ = 5800⁴ = 1.13 × 10¹⁵. Multiply all three together with σ.
Topic 10 · HR diagram
The Hertzsprung–Russell diagram
Plot luminosity (up) against temperature — with temperature increasing to the LEFT, a historical quirk you must not forget — and stars fall into distinct groups.
Hot and luminous stars sit top-left; cool dim stars bottom-right. White dwarfs are hot but tiny, so dim.
Main sequence — the diagonal band. Stars fusing hydrogen into helium in their cores. Our Sun spends about 90% of its life here.
Red giants / supergiants — top right: cool surfaces but enormous radii, so very luminous.
White dwarfs — bottom left: hot but Earth-sized, so faint. Supported by electron degeneracy pressure.
Topic 10 · stellar evolution
The life and death of a star
Every star begins the same way: a cloud of gas and dust collapses under gravity, heating up until the core is hot enough for hydrogen fusion to ignite. What happens next depends entirely on mass.
Low mass (like the Sun): main sequence → red giant → outer layers drift away as a planetary nebula → hot core remains as a white dwarf, which slowly cools.
High mass: main sequence → red supergiant → fuses successively heavier elements up to iron → core collapses → supernova → leaves a neutron star, or a black hole if massive enough.
The Chandrasekhar limit is about 1.4 solar masses: the maximum mass of a stellar core that electron degeneracy pressure can support. Above it, the core cannot stop collapsing and a white dwarf is impossible. Fusion cannot proceed beyond iron because iron has the highest binding energy per nucleon — fusing it would absorb energy, not release it.
Sort it
Low mass, high mass, or both?
Tap a stage or feature, then tap where it belongs.
🌞 Low-mass star only
💥 High-mass star only
🔁 Both
Topic 10 · distances
Measuring distance: parallax and standard candles
d (parsec) = 1 / p (arcseconds)p = the parallax angle; 1 parsec = 3.09 × 10¹⁶ m ≈ 3.26 light years
Stellar parallax: as the Earth orbits, a nearby star appears to shift against the distant background. The angle is tiny — even the nearest star has p < 1 arcsecond — so the method only works out to a few hundred parsecs.
Standard candles take over beyond that: objects whose luminosity is known, such as type Ia supernovae and Cepheid variables. Measure the intensity we receive and use I = L/(4πd²) to get d.
The distance ladder: parallax calibrates Cepheids; Cepheids calibrate type Ia supernovae; supernovae reach the far Universe. Each rung depends on the one below it.
Calculate
Your turn — parallax
3A star has a parallax angle of 0.25 arcseconds. Calculate its distance in parsecs.
pc
Hint: d = 1 ÷ p = 1 ÷ 0.25.
Topic 10 · cosmology
Redshift, Hubble's law and the Big Bang
z = Δλ/λ = v/c · v = H₀ dz = redshift · H₀ = the Hubble constant ≈ 2.2 × 10⁻¹⁸ s⁻¹
Hubble found that almost every galaxy is redshifted, and that the recession speed is proportional to distance. The Universe is expanding.
It is not that galaxies are flying through space away from us — space itself is expanding, stretching the light waves in transit. There is no centre, and no privileged position.
Run the expansion backwards and everything converges: the Big Bang.
Age of the Universe ≈ 1/H₀, assuming a constant rate of expansion.
Evidence: the redshift–distance relation, the cosmic microwave background (a 2.7 K black-body glow filling all space), and the observed abundance of helium (about 25% by mass).
Fate of the Universe: it depends on the mean density. Above the critical density gravity wins and the Universe recollapses (closed); below it, expansion continues forever (open); exactly at it, expansion slows towards zero (flat). Observations of distant type Ia supernovae showed the expansion is actually accelerating — attributed to dark energy.
Calculate
Your turn — Hubble's law
4A galaxy lies 5.0 × 10²⁴ m away. Using H₀ = 2.2 × 10⁻¹⁸ s⁻¹, calculate its recession speed. Give your answer as a multiple of 10⁶ m s⁻¹ to 2 significant figures.
× 10⁶ m s⁻¹
Hint: v = H₀d = 2.2 × 10⁻¹⁸ × 5.0 × 10²⁴ = 1.1 × 10⁷ m s⁻¹. Express that as a multiple of 10⁶.
Calculate
Your turn — redshift
5A spectral line normally at 600 nm is observed at 612 nm in a distant galaxy. Calculate the galaxy's recession speed. Give your answer as a multiple of 10⁶ m s⁻¹ to 2 significant figures. (c = 3.00 × 10⁸ m s⁻¹)
× 10⁶ m s⁻¹
Hint: z = Δλ/λ = 12 ÷ 600 = 0.020. Then v = zc = 0.020 × 3.00 × 10⁸.
Calculate
Your turn — age of the Universe
6Estimate the age of the Universe from H₀ = 2.2 × 10⁻¹⁸ s⁻¹. Give your answer in billions of years to 3 significant figures. (Take 1 year = 3.15 × 10⁷ s)
billion years
Hint: Age ≈ 1/H₀ = 1 ÷ 2.2 × 10⁻¹⁸ = 4.55 × 10¹⁷ s. Divide by 3.15 × 10⁷ s per year to get 1.44 × 10¹⁰ years, then express in billions.
Quick check
Reading the HR diagram
?Where on a Hertzsprung–Russell diagram would you find a white dwarf?
Quick check
Wien's law
?Star A appears blue; star B appears red. What can you conclude?
Quick check
Why redshift?
?The light from distant galaxies is redshifted. What is the modern interpretation?
Quick check
The Chandrasekhar limit
?What is the significance of the Chandrasekhar limit (about 1.4 solar masses)?
Match it
Match the law to its equation
Tap an item on the left, then its partner on the right.
Law
Equation or value
Recap
The big ideas to know
Black bodies: Wien λ_max T = 2.898 × 10⁻³ m K (hotter = bluer) · Stefan L = 4πr²σT⁴ (fourth power of T)
Luminosity vs intensity: L is emitted power; I = L/(4πd²) is what we receive
HR diagram: temperature increases LEFTWARDS; main sequence diagonal; giants top-right; white dwarfs bottom-left
Evolution: low mass → red giant → planetary nebula → white dwarf · high mass → supergiant → supernova → neutron star or black hole
Chandrasekhar limit ≈ 1.4 M☉; fusion stops at iron (highest binding energy per nucleon)
Distances: parallax d(pc) = 1/p(arcsec), then standard candles (Cepheids, type Ia supernovae)
Cosmology: z = Δλ/λ = v/c · v = H₀d · age ≈ 1/H₀ · evidence: redshift, CMB at 2.7 K, helium abundance
That is Edexcel Topic 10 — from a star's colour to the age of the Universe. Press Finish to see your score.
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