All Problems

Thermal Radiation. Quantum Nature of Light.

Problem 5.255

Using Planck's formula, derive the approximate expressions for the space spectral density uωu_{\omega} of radiation (a) in the range where ℏω≪kT\hbar \omega \ll k T (Rayleigh-Jeans formula); (b) in the range where ℏω≫kT\hbar \omega \gg k T (Wien's formula).

Reveal Answer
(a) uω=(kT/π2c3)ω2u_{\omega}=\left(k T / \pi^{2} c^{3}\right) \omega^{2} (b) uω=(ℏ/π2c3)ω3e−ℏω/kTu_{\omega}=\left(\hbar / \pi^{2} c^{3}\right) \omega^{3} \mathrm{e}^{-\hbar \omega / k T}
Prev
Next