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Q.1 Describe the distribution of energy in the spectrum of black body radiation.

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Q.1 Describe the distribution of energy in the spectrum of black body radiation.

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Solution

The distribution of energy in the spectrum of black body radiation can be described by Planck's law of black body radiation. Here are the steps to describe it:

  1. Black body radiation is the theoretical radiation emitted by a perfect black body, which is an object that absorbs all incident radiation, regardless of frequency or angle of incidence.

  2. The energy distribution of this radiation across different frequencies is not uniform and depends on the temperature of the black body. This distribution is described by Planck's law.

  3. According to Planck's law, the energy of each quantum of radiation is proportional to its frequency, specifically, E = hv, where E is energy, h is Planck's constant, and v is frequency.

  4. The distribution curve of energy versus frequency (or wavelength) has a specific shape with a peak at a certain frequency. This peak shifts to higher frequencies (or shorter wavelengths) as the temperature of the black body increases. This is known as Wien's Displacement Law.

  5. The total energy emitted by the black body also increases with temperature, following the Stefan-Boltzmann Law.

  6. At low frequencies (long wavelengths), the energy distribution follows Rayleigh-Jeans Law, which predicts that the energy should increase with frequency, but this is not observed experimentally. This discrepancy is known as the Ultraviolet Catastrophe.

  7. At high frequencies (short wavelengths), the energy distribution follows Wien's Law, which predicts that the energy should decrease exponentially with frequency, which is observed experimentally.

  8. The correct distribution, which matches experimental observations at all frequencies, was given by Planck's law, which combines the features of both Rayleigh-Jeans Law and Wien's Law. This was one of the first indications of the quantum nature of light.

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