IB Physics HL E 5 7 Stellar Radii Questions

Calculate HL stellar radii from luminosity and temperature, using the Stefan–Boltzmann relationship and solar comparison data.

Exam points

apply L=4πR^2σT^4 to compare stellar luminosity, radius and surface temperature
calculate a star’s radius relative to the Sun from luminosity and temperature ratios, keeping squared and fourth-power terms correct
interpret constant-radius lines or stellar data to compare the sizes and luminosities of different stars

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Study E.5.7—Stellar radii conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Alpha Centauri A and B is a binary star system in the main sequence.

Table for Question IB Physics HL E 5 7 Stellar Radii Questions question 1 — IB Physics HL

(a)

The luminosity of the Sun is $3.8 \times 10^{26} \mathrm{~W}$ . Calculate the radius of Alpha Centauri A.

[ 2 ]

$r=\sqrt{\frac{1.5\times3.8\times10^{26}}{5.67\times10^{-8}\times4\pi\times5800^{4}}}=8.4\times10^{8}\ \mathrm m$

(b)

Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.

[ 2 ]

$A=\frac{L}{\sigma T^{4}}$ ;
B and A have similar temperatures.

Therefore, their areas are in the ratio of their luminosities, so the radius of B is less than that of A.

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IB Physics HL E 5 7 Stellar Radii Questions question 1

Question (a)

Question (b)