Answer to Question #130926 in Physical Chemistry for bassant

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/m^2

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Answer 1

Using Stefan Boltzmann law, find the flux of photons j: 

j = σT⁴, where constant σ  = 5.67*10^-8 W/(m²*K⁴)

T is found from Wien displacement law: 

λ_max = σ_w /T, where constant σ_w = 0.002898 m*K

λ_max = 5*10^-7 m = 0.002898/T, hence, T = 5796 K

The flux of photons is:

j = 5.67*10^-8*(5796)⁴ = 6.4*10⁷ W/m²