IB Physics SL E.5.7 Stellar Radii

Practise determining stellar radius from luminosity and surface temperature using Stefan-Boltzmann scaling and comparing stars through ratios that cancel shared constants.

Exam points

rearrange L = 4πR²σT⁴ to calculate radius from luminosity and absolute temperature
form L/L☉ = (R/R☉)²(T/T☉)⁴ to compare stellar radius with the Sun from luminosity and temperature ratios
check HR-diagram radius trends: cool luminous giants are large and hot faint white dwarfs are small

[Maximum number: 3]

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 E.5.7—Stellar radii 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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E.5.7—Stellar radii question 1