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what is ultraviolet catastrophe???
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In the 19th century a major problem for physicists was to predict the intensity of radiation emitted by a black body at a specific wavelength. Wilhelm Wien made a theory that predicted the overall form of the curve by treating the radiation as gas molecules. However, at long wavelengths his theory disagreed with experimental data. Rayleigh and Jeans then produced a formula by considering the radiation within the black body cavity to be made up of a series of standing waves. They thought that electromagnetic radiation was emitted by oscillating atoms in the walls of the black body and this radiation set up a standing wave between the walls. Their formula stated:
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However, this formula also had a problem. For large wavelengths it fitted the experimental data but it had major problems at shorter wavelengths. The problem was the l term in the denominator. It meant that as the wavelength tended to zero, the curve would tend to infinity. However we know that there is a peak wavelength for each temperature, and the energy emitted at either side of this peak dropped. The Rayleigh-Jeans Law predicted no peak wavelength.
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Therefore the wave theory of the time could be used to explain behaviour on either side of the peak, but the peak would be infinitely high. The failure of these formulae to account for the decrease in energy emitted at short wavelengths (the ultraviolet wavelengths) became known as the ultraviolet catastrophe. A major breakthrough was made by Max Planck who made a formula that agreed with experimental data, which is showed above. However, he had major problems proving this law. His idea was that the oscillating electrons of the surface atoms of the black body emitted radiation according to Maxwell's laws of electromagnetism. Before Planck it was assumed that these could have any value of energy but Planck decided that the energy must go up in discrete amounts (quantised) because the frequencies of the oscillating electrons could only take certain values. As energy is proportional to frequency (E = hf) , where h is the Planck constant 6.626 x 10-34 Js) if frequency can only take discrete values, this means that energy is also quantised. The electrons have a fundamental frequency (like standing waves on a string) and the frequency can only go up in whole multiples of this frequency, called the quantum number. This assumption led Planck to correctly derive his formula. If he ignored the quantised energy, he obtained the Rayleigh-Jeans formula. Einstein took the next step by working out that all radiation is quantised. He argued that an oscillating charge can accept or lose energy in small values of DE = hDf. This energy is lost as electromagnetic radiation. Therefore this radiation must be emitted in small packets, each containing DE. He then suggested that each energy of radiation will have its own frequency. Therefore he no longer thought of radiation from an object as continuous. He said it consisted of a series of "packets" of energy. This meant that radiation was being thought of as a "packet of energy" but also as a wave because it had a frequency. These became known as photons.
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Acc to Rayleigh Jeans law, Energy density is proportional to 1/λ4.
It implies that even at room temp, we are bombarded with large amounts of short-wavelenght radiation which is an absurd result, called UV catastrophe.
PS: AFAIK, its not in the JEE syllabus.