IB Physics SL E 5 7 Stellar Radii Questions

Calculate SL 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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The graph shows an incomplete Hertzsprung-Russell (HR) diagram. The position of the Sun and three other stars, A, B and C , are shown.

Figure for Question IB Physics SL E 5 7 Stellar Radii Questions question 1 — IB Physics SL

$M_{\odot}, R_{\odot}$ and $L_{\odot}$ are the mass, radius and luminosity of the Sun.

Determine the radius of star B in terms of $R_{\odot}$ .

$L_B=L_A=10^6L_{\odot}$ .
$10^6=(R_B/R_{\odot})^2(3.0/6.0)^4$ .
$R_B/R_{\odot}=\sqrt{10^6\times16}=4\times10^3$ .

Award [3] for BCA. Do not allow ECF from MP2 to MP3.

\frac{R_B}{R_\odot}=\sqrt{10^6\times16}=4\times10^3

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IB Physics SL E 5 7 Stellar Radii Questions question 1