9702 · 25.2
Stellar radii flashcards
Revision flashcards for Cambridge 9702 Stellar radii (syllabus 25.2). Flip, recall, then mark a real past-paper question.
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What is stellar luminosity (L)?
The total power of electromagnetic radiation emitted by a star, measured in Watts (W).
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What is radiant flux (F)?
The power of radiation received per unit area at a specific distance from an astronomical object, measured in W m⁻².
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State the inverse square law for radiant flux.
$F = \frac{L}{4\pi d^2}$, where L is luminosity, d is distance, and F is flux.
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What are 'standard candles' in astronomy?
Celestial objects with a known intrinsic luminosity, used to determine distances to other objects by measuring their apparent flux.
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What does Wien's Displacement Law describe?
The relationship between a star's peak emission wavelength (λ_max) and its absolute surface temperature (T).
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State Wien's Displacement Law formula.
$λ_{max} T = \text{constant}$ (approximately $2.9 \times 10^{-3} \text{ m K}$).
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What is a blackbody radiation curve?
A graph showing the intensity of radiation emitted by a blackbody at different wavelengths for a given temperature. The peak of the curve shifts to shorter wavelengths as temperature increases.
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How does a star's temperature relate to its colour?
Hotter stars have shorter peak wavelengths, appearing bluer; cooler stars have longer peak wavelengths, appearing redder.
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What does the Stefan-Boltzmann Law relate?
A star's total luminosity (L) to its radius (r), absolute surface temperature (T), and the Stefan-Boltzmann constant (σ).
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State the Stefan-Boltzmann Law formula.
$L = 4\pi r^2 \sigma T^4$.
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Why is temperature raised to the fourth power in the Stefan-Boltzmann law?
This T⁴ dependence is a fundamental result from thermodynamics and statistical mechanics for blackbody radiation. It means a star's energy output is extremely sensitive to its surface temperature.
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What is the value of the Stefan-Boltzmann constant (σ)?
$5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$.
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Why are stars often modelled as 'blackbodies'?
This theoretical ideal allows us to use laws like Wien's and Stefan-Boltzmann's, as blackbodies perfectly absorb and emit all wavelengths of electromagnetic radiation.
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How can a star's radius be calculated from its observable properties?
First, find luminosity from flux and distance, and temperature from peak wavelength. Then, use the Stefan-Boltzmann Law, rearranged as $r = \sqrt{\frac{L}{4\pi \sigma T^4}}$, to solve for radius.
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How can you compare the radii of two stars if you know their luminosities and temperatures?
Use the ratio method with the Stefan-Boltzmann law: $(r_1/r_2)^2 = (L_1/L_2) \times (T_2/T_1)^4$. This allows you to find the ratio of their radii.
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What is the relationship between a star's properties on the Hertzsprung-Russell (H-R) diagram?
The H-R diagram plots luminosity against temperature. Stars are not randomly scattered but fall into groups like the main sequence, giants, and dwarfs. A star's position is determined by its mass, age, and composition, which in turn dictate its radius and temperature.