If you drill a hole in a block of metal and heat it to a uniform temperature of, say, 4000 K, you will see an image like this (Halliday&Resnick):
A tungsten tube heated to high temperature emits light. The bright spot at the center is light emitted from a hole drilled into the tube.The emitted radiation intensity from the hole or cavity is given by the Stefan-Boltzmann Law:
Let us now turn to the question of the distribution of the emitted radiation as a function of wavelength. According to classical physics, this distribution is given by the Rayleigh-Jeans law:
However, this formula has a great defect: it grows quadratically with frequency leading to the so-called ultra-violet catastrophe. The Rayleigh-Jeans law (at 6000 K) is given by the dashed line while experimental measurements of this distribution do not diverge at high frequency as shown by the solid lines (for 6000, 5000, and 4000 K):
The solid curves are in fact predicted by Planck’s reformulation of the radiation intensity problem for a black box, the Planck radiation law:
The maxima of these curves follow the Wien displacement law:
Note: Many books, including McQuarrie, give the following formulas for the Rayleigh-Jeans law and the Planck distribution law:
These expressions are for the radiation energy density (J/m3) inside the cavity rather than the emitted intensity per unit area. There is a factor of c/4 between the two expressions. The shape of the curves is clearly the same, however.
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