Stellar radii
Cambridge A-Level Physics (9702) · Unit 25: Astronomy and cosmology · 9 flashcards
Stellar radii is topic 25.2 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 25 — Astronomy and cosmology , alongside Standard candles. In one line: Wien's displacement law states λmax ∝ 1/T, where λmax is the peak wavelength emitted by a black body and T is its temperature. This means hotter stars emit light at shorter (bluer) wavelengths, while cooler stars emit at longer (redder) wavelengths.
Marked as A2 Level: examined at A Level in Paper 4 (A Level Structured Questions) and Paper 5 (Planning, Analysis and Evaluation). It is not tested on the AS-only papers (Papers 1, 2 and 3).
The deck below contains 9 flashcards — 5 definitions, 3 key concepts and 1 calculation — covering the precise wording mark schemes reward. Use the 5 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Some cards in this deck are on other syllabus topics: 25.3 Hubble’s law and the Big Bang theory. Each card is labelled with its topic.
Wien's displacement law and how it relates to stellar temperature
Wien's displacement law states λmax ∝ 1/T, where λmax is the peak wavelength emitted by a black body and T is its temperature. This means hotter stars emit light at shorter (bluer) wavelengths, while cooler stars emit at longer (redder) wavelengths.
What the Cambridge 9702 syllabus says
2025-2027 syllabus, in our words · A2 LevelWhat the syllabus expects you to be able to do in this topic, in plain English. For the exact wording, see the official syllabus (PDF).
- Recall Wien's displacement law, λmax ∝ 1/T, and use it to estimate a star's peak surface temperature.
- Use L = 4πσr²T⁴, the Stefan-Boltzmann law, in calculations.
- Estimate a star's radius by combining Wien's displacement law with the Stefan-Boltzmann law.
Also in this deck: 25.3 Hubble’s law and the Big Bang theory
- Understand that spectral lines (emission and absorption) from distant objects are shifted to longer wavelengths than their known values.
- Use Δλ/λ ≈ Δf/f ≈ v/c to calculate redshift when a source of electromagnetic radiation moves relative to an observer.
- Explain why redshift suggests an expanding Universe.
- Recall Hubble's law, v ≈ H₀d, and use it (only SI units will be needed); explain how this law gives rise to the Big Bang theory.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in these topics
- › Ensure you specify that wavelength is inversely proportional to temperature only at the point of maximum intensity in the black-body spectrum.
- › Always link observations of distant galaxies to the redshift of electromagnetic radiation to explain universal expansion.
- › Check the relative motion; if an object moves toward the observer, the observed wavelength decreases (blueshift).
Topic 25.2 · Stellar radii
State Wien's displacement law and how it relates to stellar temperature.
Wien's displacement law states λmax ∝ 1/T, where λmax is the peak wavelength emitted by a black body and T is its temperature. This means hotter stars emit light at shorter (bluer) wavelengths, while cooler stars emit at longer (redder) wavelengths.
Topic 25.2 · Stellar radii
State Stefan-Boltzmann law, defining each term.
Stefan-Boltzmann law states L = 4πσr²T⁴, where L is the luminosity of a star, σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴), r is the radius of the star, and T is the surface temperature of the star.
Topic 25.2 · Stellar radii
How can Wien's displacement law and Stefan-Boltzmann law be used to estimate the radius of a star?
First, use Wien's law (λmax ∝ 1/T) to find the star's temperature (T) by measuring λmax. Then, use the Stefan-Boltzmann law (L = 4πσr²T⁴) and the star's luminosity (L) to calculate the radius (r).
Topic 25.3 · Hubble’s law and the Big Bang theory
Define redshift and its cause in the context of distant objects.
Redshift is the increase in wavelength (and decrease in frequency) of electromagnetic radiation from distant objects. This is caused by the Doppler effect as the source moves away from the observer. The further away an object is, the greater the redshift.
Topic 25.3 · Hubble’s law and the Big Bang theory
State the formula relating redshift (z) to wavelength change (Δλ), original wavelength (λ), velocity (v), and speed of light (c).
The redshift formula is: z ≈ Δλ/λ ≈ v/c. This approximation is valid for relatively small velocities compared to the speed of light.
Topic 25.3 · Hubble’s law and the Big Bang theory
Explain how redshift provides evidence for the expansion of the Universe.
The observation that most galaxies exhibit redshift indicates that they are moving away from us. Since the amount of redshift increases with distance, this implies that the Universe is expanding uniformly.
Topic 25.3 · Hubble’s law and the Big Bang theory
State Hubble's law and define each term.
Hubble's law states v = H₀d, where v is the recessional velocity of a galaxy, H₀ is the Hubble constant (about 2.3 × 10⁻¹⁸ s⁻¹ in SI units, or about 70 km s⁻¹ Mpc⁻¹), and d is the distance to the galaxy.
Topic 25.3 · Hubble’s law and the Big Bang theory
How does Hubble's law support the Big Bang theory?
Hubble's law implies that if we trace the expansion of the Universe backward in time, all matter would converge to a single point. This supports the Big Bang theory, which postulates that the Universe originated from an extremely hot, dense state and has been expanding ever since.
Topic 25.2 · Stellar radii
A star has a peak wavelength of 500 nm. Estimate its surface temperature using Wien's Law (Wien's displacement constant b = 2.90 x 10⁻³ m K).
Using Wien's Law, λmax = b/T. Therefore, T = b/λmax = (2.90 x 10⁻³ m K)/(500 x 10⁻⁹ m) = 5800 K. The star's surface temperature is approximately 5800 K.
Review the material
Read full revision notes on Stellar radii — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 25 — Astronomy and cosmology
Stellar radii sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Stellar radii deck
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