Tuesday, October 15, 2013

Planck's Theory

The wave theory of light helped explain each and every aspect of optics up to the last decimal point. Interference, Diffraction, Refraction, Reflection and many more phenomenons except one thing, and that was the black body radiation.


The Classical Theory predicted that the total energy radiated by a body at higher frequencies tends to infinity(black curve in the pic). But we all know that is not possible when it comes to radiating energy. This problem was due to the fact that light was considered as a wave. Considering it as a wave, the average degrees of freedom is equal to kT where k is called Boltzmann's constant and T is the absolute temperature.
This was explained by Rayleigh in his law where it was given that the radiance is inversely proportional to the 4th power of wavelength.

where c is the speed of light and B is the spectral Radiance.            

 This equation agreed with the experimental results for longer wavelengths. But for shorter wavelengths like UV region, it became a catastrophe, thus known as the ultra violet catastrophe.

To deal with this problem, Planck proposed his theory. In his theory he said that the radiance was not just proportional to the frequency, but also inversely proportional to frequency in exponential form.




This new idea agreed very well with the experimental results in the longer and shorter wavelength regions as well. Thus this theory came to be known as Planck's Black body radiation.

The other form of this theory was that λT=k where k is a constant. Thus plotting the curves, there were maximas for a particular wavelength only at a particular temperature only(red, green and blues curves)

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