Cambridge International AS & A Level · 25 · structured
Distinguish luminosity, then infer radius
From stellar luminosity and spectral peak to radius · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 7
- Topics
- 2
- Answer
- Complete
Define luminosity and distinguish it from the radiant flux intensity at Earth. A star's total luminosity is 2.85 × 10²⁷ W and its wavelength-spectrum peak is 725 nm. Estimate its radius using b = 2.90 × 10⁻³ m K and σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Show how you combine the two radiation laws and state the physical approximation.
- (a)
Define luminosity and distinguish it from received flux intensity.
2 marks - (b)
Combine Wien's and Stefan–Boltzmann laws to estimate radius.
4 marks - (c)
State the physical approximation.
1 mark
Ready to self-mark?Reveal the detailed answer guide
(a)
Define luminosity and distinguish it from received flux intensity.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Total emitted power in W versus received power per area in W m⁻².
(b)
Combine Wien's and Stefan–Boltzmann laws to estimate radius.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
T = 4000 K; r = √[L/(4πσT⁴)] = 3.95 × 10⁹ m.
(c)
State the physical approximation.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Approximately black-body stellar surface with total luminosity.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Define L as the total radiation power emitted by the star; F is received power per unit area and has units W m⁻².
- λ_max = 7.25 × 10⁻⁷ m; T = 2.90 × 10⁻³/(7.25 × 10⁻⁷) = 4000 K.
- Use L = 4πr²σT⁴ and rearrange to r = √[L/(4πσT⁴)].
- Insert the calculated T to get r = 3.95 × 10⁹ m.
- The estimate assumes the stellar surface behaves approximately as a black body and L is total over wavelengths.
Private on this device