Question

The intensity distribution of solar radiation peaks at a wavelength of approximately 500 nm. Assuming the Sun radiates like a black body, calculate the flux of photons leaving the sun in W/m2.

Answer 1

According to the Stefan-Boltzmann law, the black body radiant emittance can be predicted using the following expression:

$j*=\sigma T^4$ ,

where $\sigma$ is the Stefan-Boltzmann constant 5.67x10^-8 W m^-2 K^-4. The temperature of the black body is related to the spectrum of its radiation through the Wien’s displacement law:

$\lambda_{peak} =\frac{b}{T}$ ,

where $b$ is the Wien’s displacement constant, 2.898x10^-3 m K. Making use of these two laws, the flux of photons leaving the Sun is:

$j* = \sigma\frac{b^4}{\lambda_{peak}^4}$

$j*=5.67\cdot10^{-8}\frac{2.898^4\cdot10^{-12}}{500^4\cdot10^{-36}}$

$j* = 6.40\cdot10^7$ W m^-2.

Answer: The flux of photons leaving the Sun is 6.40x10⁷ W m^-2.