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blackbody_radiation [2021/01/29 23:02] – [1.ii.2 The Blackbody Spectrum] adminblackbody_radiation [2021/01/29 23:06] (current) – [1.ii.4 The Quantum Postulate] admin
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   \[\boxed{\lambda_{\max} \propto \frac{1}{T}.}\]   \[\boxed{\lambda_{\max} \propto \frac{1}{T}.}\]
   * **Stefan-Boltzmann Law**: In 1879, Stefan found experimentally that the total intensity (power per unit surface area obeys)   * **Stefan-Boltzmann Law**: In 1879, Stefan found experimentally that the total intensity (power per unit surface area obeys)
-  \[\boxed{P = a\sigma T^4,}\]+  \[\boxed{I = a\sigma T^4,}\]
   where   where
     * $a$ is a constant that depends on the material     * $a$ is a constant that depends on the material
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   * Rayleigh considered the statistical mechanics of radiation and derived   * Rayleigh considered the statistical mechanics of radiation and derived
-  \[\boxed{u(\nu,T) = \frac{8\pi \nu^2}{c^3} k T}.\]+  \[\boxed{u(\nu,T) = \frac{8\pi \nu^2}{c^3} k T.}\]
   * This only works for small $\nu$.   * This only works for small $\nu$.
   * Ultraviolet catastrophe: Total intensity $\int_{-\infty}^{\infty} u(\nu,T)\,\mathrm{d}\nu$ diverges for high frequency.  Implies that the cavity contains infinite energy   * Ultraviolet catastrophe: Total intensity $\int_{-\infty}^{\infty} u(\nu,T)\,\mathrm{d}\nu$ diverges for high frequency.  Implies that the cavity contains infinite energy
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 This is the //**quantum postulate**//. This is the //**quantum postulate**//.
  
-Since not everyone taking this class has studied statistical mechanics yet, the derivation of this is beyond the scope of this course, but see [[http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf|this link]] for a derivation.+Since not everyone taking this class has studied statistical mechanics yet, the derivation of the Planck distribution from the quantum postulate is beyond the scope of this course, but see [[http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf|this link]] for a derivation.
  
 ====== 1.ii.5 Wien's Displacement Law ====== ====== 1.ii.5 Wien's Displacement Law ======