A level Physics · Edexcel 9PH0 · Topic 10A

Luminosity and black body radiation

Key points

Luminosity $L$ is the total power radiated by a star (W). The intensity (radiation flux) received at distance $d$ is $I = \frac{L}{4\pi d^2}$ , an inverse square law.
A black body absorbs all radiation that falls on it and emits a continuous spectrum that depends only on its temperature.
Stefan–Boltzmann law: $L = \sigma AT^4$ , with $A = 4\pi r^2$ for a star and $\sigma = 5.67 \times 10^{-8}$ W m $^{-2}$ K $^{-4}$ .
Wien's displacement law: $\lambda_{max}T = 2.898 \times 10^{-3}$ m K, so hotter stars peak at shorter wavelengths and look bluer.
Black-body curves get taller and their peak moves to shorter wavelength as temperature increases.
Combine Wien's law (to find $T$ ) with Stefan–Boltzmann (to find radius or luminosity) in multi-step questions.

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A star's brightness in our sky depends on how much power it emits and how far away it is. Treating stars as black bodies lets us find their temperatures and sizes from their light alone.

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