Problem 5.256

Transform Planck's formula for space spectral density $u_{\omega}$ of radiation from the variable $\omega$ to the variables $v$ (linear frequency) and $\lambda$ (wavelength).

Reveal Answer

u_{v}=\frac{16 \pi^{2} \hbar}{c^{3}} \frac{v^{3}}{e^{2 \pi \hbar v / k T}-1}, u_{\lambda}=\frac{16 \pi^{2} c \hbar \lambda^{-5}}{e^{2 \pi \hbar c / k T \lambda}-1}

Thermal Radiation. Quantum Nature of Light.