A star like the Sun behaves as a black body. Explain how the temperature of a star is related to the radiation it emits, and describe what this tells us about the colour of stars that are hotter than the Sun.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Stars emit electromagnetic radiation across a range of frequencies. The peak frequency of radiation emitted by a star depends on its surface temperature. The Sun appears yellow-white and has a surface temperature of approximately 5500 °C. Some stars are significantly hotter than the Sun.
Model answer (5 marks)
A black body absorbs all incident radiation and is an ideal emitter. The power emitted per unit area is given by the Stefan–Boltzmann law, (P=sigma T^{4}); therefore a hotter star emits more power. The spectral distribution follows Planck’s law, so the peak frequency is proportional to temperature (Wien’s law, (
u_{ ext{max}}propto T)). Consequently, stars hotter than the Sun have their peak radiation at higher frequencies, i.e. towards the blue/violet end of the visible spectrum. In contrast, cooler stars peak at lower frequencies, towards the red end, so the colour of a star indicates its temperature.
u_{ ext{max}}propto T)). Consequently, stars hotter than the Sun have their peak radiation at higher frequencies, i.e. towards the blue/violet end of the visible spectrum. In contrast, cooler stars peak at lower frequencies, towards the red end, so the colour of a star indicates its temperature.
Examiner tips
- State that a black body is an ideal emitter and absorber; link temperature to power via (T^{4}); mention Wien’s law for peak frequency; explain colour shift from red to blue as temperature rises.
Common mistakes
- Confusing temperature with luminosity alone; not mentioning the shift of peak frequency; describing colour change without linking it to temperature.
Mark scheme (5 marks)
- A black body absorbs all radiation incident on it (and is also an ideal emitter)
- The hotter the star, the greater the power / intensity of radiation emitted
- The hotter the star, the higher the peak frequency of radiation emitted
- Stars hotter than the Sun emit peak radiation at higher frequencies, towards the blue/violet end of the visible spectrum
- Cooler stars emit peak radiation at lower frequencies, towards the red end of the visible spectrum, so colour indicates temperature
Key terms in this question
Related
- All WJEC A-Level Physics (Wales) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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