Explain why the intensity of radiation emitted by the Earth's surface is predominantly in the infrared region of the electromagnetic spectrum, whilst the radiation received from the Sun is predominantly in the visible region.

IB DP Physics Standard Level (2023 syllabus) — B.2 Greenhouse effect · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

The Sun has a surface temperature of approximately 5800 K. The Earth's surface has an average temperature of approximately 288 K.

Model answer (4 marks)

The intensity of radiation emitted by any body depends on its temperature – a hotter body emits a spectrum that peaks at a shorter wavelength, while a cooler body peaks at a longer wavelength (Wien’s displacement law). The Sun, with a surface temperature of about 5800 K, has a peak wavelength of roughly 0.5 µm, which lies in the visible part of the spectrum. In contrast, the Earth’s surface temperature is only about 288 K; applying Wien’s law gives a peak wavelength of around 10 µm, which is in the infrared region. Thus the Sun’s high temperature places its peak in the visible, whereas the Earth’s much lower temperature shifts its peak into the infrared.

Examiner tips

  • Mention Wien’s law and the inverse relationship between temperature and peak wavelength
  • Give the approximate temperatures and peak wavelengths for Sun and Earth
  • Explain the shift from visible to infrared due to the temperature difference

Common mistakes

  • Confusing the direction of the temperature–wavelength relationship (higher T → longer λ)
  • Using the wrong units or forgetting to state that the Earth’s radiation is in the infrared

Mark scheme (4 marks)

  1. All bodies emit radiation with a peak wavelength that depends on their temperature (Wien's displacement law / blackbody radiation principle).
  2. The Sun's high temperature (~5800 K) means its peak emission wavelength falls in the visible region of the spectrum.
  3. The Earth's much lower surface temperature (~288 K) means its peak emission wavelength is much longer, falling in the infrared region.
  4. Peak wavelength and temperature are inversely proportional, so the much lower Earth temperature produces a peak wavelength roughly 20 times longer than the Sun's peak wavelength.

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