## Related questions with answers

The human body has a surface area of approximately $1.8 \mathrm{m}^{2}$, a surface temperature of approximately $30^{\circ} \mathrm{C}$, and a typical emissivity at infrared wavelengths of e = 0.97. If we make the approximation that all photons are emitted at the wavelength of peak intensity, how many photons per second does the body emit?

Solution

VerifiedTo get the number of photons emitted by a human body per second we need two variables, energy of a single photon and energy emitted in one second. First we get the latter by employing Stefan-Boltzman's law, $Q=e\sigma A T^4 \Delta t$ so we can write $Q=0.97\times 5.67 \times 10^{-8} \times 1.8 \times (303.15)^4$ $Q=836 \textrm{J}$ Now, we can get the $\lambda_{peak}$ $\lambda_{peak}=\frac{2.9 \times 10^{-3}}{303.15}$ $\lambda_{peak}=9570 \textrm{nm}$ From here the energy of single photon is $E_{ph}=\frac{hc}{\lambda_{peak}}$ $E_{ph}=\frac{6.63\times 10^{-34}\times 3\times 10^8}{9570 \times 10^{-9}}$ $E_{ph}=2\times 10^{-20} \textrm{J}.$ Finally, the number of photons is $N=\frac{Q}{E_{ph}}$ $N=417\times 10^{20}$

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