# Electromagnetic radiation from sun and human body

What is the difference between infrared radiation produced in sun and thermal radiation, in infra red range, by human body in terms of its energy or are they the same?

Thermal radiation of the sun and human body could be approximated by black body radiation.

The spectrum of the black body radiation is a function of its temperature. As the temperature increases, the spectrum is shifted toward short wavelengths, as shown on the diagram below (copied from this site). The peak wavelength of the spectrum (dots on the diagram) could be determined using Wien's displacement law:

$$\lambda_{max}=\frac b T$$

where $$b=2.9\times10^{-3}Km$$ is Wien's displacement constant.

Using this formula, we can find that the peak wavelength for the sun radiation, assuming $$T=5778K$$, is about $$0.5\mu m$$ micron, which is in the middle of visible light spectrum, while the peak wavelength of a human body radiation, assuming $$T=310K$$, is about $$9.4\mu m$$, well into the infrared spectrum, which spreads from $$0.7\mu m$$ to $$1mm$$.

The diagram below (copied from this site) shows the radiation spectrum of the sun and the Earth, the latter, assuming $$T=300K$$, is close to the spectrum of a human body. Energy of electromagnetic radiation is only dependent on its frequency, so for a given frequency, or equivalently, for a given wavelength, the energy of a photon is $$E=hf$$, where $$h$$ is just Plank’s constant.

Of course, depending on the temperature and the size of the body, the total power emmited at a certain wavelength, i.e. the number of photons emmited per time with a certain energy, will be different. So the total power emmited by the sun at a certain wavelength is greater than that of a human body, even though each photon of that wavelength carry the same energy.