Rayleigh Jean’s Law

Illustration of vibrations of a drum.
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Lord Rayleigh made an attempt to explain the energy distribution in black body radiation, which was completed by Jeans in 1900. The results obtained by then are known as Rayleigh-Jean’s Rules on Black Body Radiation. The law covering these rules is called Rayleigh Jean’s Law.

The black body emits radiation of continuously variable wavelengths right from zero to infinite. This radiation can be imagined as broken up into monochromatic waves. These monochromatic waves originate as a result of a different modes of vibration of the medium, which at that time was supposed to be an electromagnetic sensitive medium called ‘ETHER’ According to well-known result of statistical mechanics, the number of such modes of vibration lying between the wavelength range $ \lambda $ and $ \lambda+d\lambda $ is equal to $ 8\pi{\lambda}^{-4}d\lambda $ per unit volume. And also according to the theorem of equipartition of energy, the total energy of a system for each mode of vibration (or degree of freedom) is equal to $ kT $ , where $ k $ is the Boltzmann constant and $ T $ is the temperature of the system in Kelvin. Hence, the total energy of the radiation lying between the wavelength range $ \lambda$ and $ \lambda + d\lambda $ per unit volume is
$ u_{\lambda}d\lambda$ =number of mode of vibration $ \times kT $
or, $ u_{\lambda}d\lambda=8\pi kT{\lambda}^{-4}d\lambda $

This is Rayleigh Jean Law.

Gaurav Tiwari

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