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.
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
Official 2025-2027 spec · A2 LevelThese are the exact learning outcomes Cambridge sets for this topic. The candidate is expected to be able to do each of these on the relevant paper.
- recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the peak surface temperature of a star
- use the Stefan–Boltzmann law L = 4πσr 2 T 4
- use Wien’s displacement law and the Stefan–Boltzmann law to estimate the radius of a star
- understand that the lines in the emission and absorption spectra from distant objects show an increase in wavelength from their known values
- use ∆λ / λ . ∆f / f . v / c for the redshift of electromagnetic radiation from a source moving relative to an observer
- explain why redshift leads to the idea that the Universe is expanding
- recall and use Hubble’s law v . H0d and explain how this leads to the Big Bang theory (candidates will only be required to use SI units)
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 Stellar radii
- › 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).
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.
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.
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).
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.
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.
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.
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 Hubble's constant (approximately 70 km s⁻¹ Mpc⁻¹), and d is the distance to the galaxy.
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.
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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