Problem 5.257

Using Planck's formula, find the power radiated by a unit area of a black body within a narrow wavelength interval \(\Delta \lambda\) \(=1.0\) nm close to the maximum of spectral radiation density at a temperature \(T=3000 \mathrm{~K}\) of the body.

Reveal Answer

\Delta P=4 \pi^{2} c^{2} \hbar T^{5} \Delta \lambda / b^{5}\left(e^{2 \pi \hbar c / k b}-1\right)=0.31 \quad \mathrm{~W} / \mathrm{cm}^{2}, \text { where b is the constant in Wien's displacement law.}

Thermal Radiation. Quantum Nature of Light.