where λ is the wavelength and T is the absolute temperature. This equation, derived in December 1900, is the first formula that contained Planck’s constant, h.
Often you can recover a classical (non-quantum) result by taking the limit as Planck’s constant goes to zero. Here’s a new homework problem to find the classical limit of the blackbody radiation formula.
Section 14.8
Problem 26 ½. Take the limit of Planck’s blackbody radiation formula, Eq. 14.33, when Planck’s constant goes to zero. Your result should should be the classical Rayleigh-Jeans formula. Discuss how it behaves as λ goes to zero. Small wavelengths correspond to the ultraviolet and x-ray part of the electromagnetic spectrum. Why do you think this behavior is known as the “ultraviolet catastrophe”?
Subtle is the Lord, by Abraham Pais. |
Einstein rederived Rayleigh’s formula from basic thermodynamics principles in, you guessed it, his annus mirabilis, 1905. Pais concludes “it follows from this chronology (not that it matters much) that the Rayleigh-Jeans law ought properly to be called the Rayleigh-Einstein-Jeans law.”
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