The surface temperature of our sun is about 5800 K. a.) Using Wien’s law, what i

Question

The surface temperature of our sun is about 5800 K. a.) Using Wien’s law, what is lambda max (in nm) in the energy distribution curve of our sun? b.) The color of the wavelength from part a.) is cyan, a blue green. The energy distribution function u(lambda)=[8(pi)hc(lamba)^-5]/[exp(hc/(lambda)kT) – 1] gives the intensity vs wavelength of a blackbody. k=8.617 10-5 eV/K. Using this energy distribution function, what fraction of the sun’s emitted intensity at its peak wavelength (answer to a.) is emitted at the red color wavelength of 700 nm (i. e. how much dimmer is the red light emitted by the sun than the peak blue-green)?

Explanation / Answer

Wien's law relates surface temperature in kelvins (T) of stars to their peak wavelength emissions (Lambda max). Temperature and peak wavelength are inversely proportional. Specifically, using cm as a unit of length,
Lambda max = 0.29 cm / T
or, solving for T,
T = 0.29 cm / Lambda max
T1 = 0.29 cm / 7 x 10^-5 cm
T 1 = 4143 k

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