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The problem asks us to determine the power per unit area not from the peak wavelength ( ), but from arange of wavelengths, that is, from a small range. So Wien's Law doesn't suit us right now. And yes, Planck's Law given by the following relation:
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From this relation we will find the intensity related to any wavelength, not the wavelength at which the energy radiates most intensely, as Wien's Law shows us.
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