I have read some books and references about quantum mechanics and black body radiation but still I didn't understand that what is the black body in fact and how did Planck solve the problem of black body? in the chart of the Planck for the black body radiation, we see that after a frequency, our line comes down and energy decreases. but it is not logical. where does this energy go and what happens to that high frequency?
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2 Answers
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Planck calculated the radiation spectrum not according to classical electrodynamics (where a mode of the electromagnetic field) could be continuously excited, but under the assumption that a mode of the the field with frequency $\nu$ could only be excited in discrete units. The energy of the mode had to be $nh\nu$ for some nonnegative integer $n$. This required the introduction of a new constant of nature, $h$, which was naturally named after Planck. However, it gave correct descriptions of the observed spectra of black bodies.
The reason that the spectral density Planck calculated falls off at large frequencies is fairly simple. Classically, the energy of every mode of the electromagnetic field is proportional to $kT$, and this is accurate when $kT\gg h\nu$, so that the classical expectation value of the energy corresponds to a large value of $n$. (In other words, many photons of frequency $\nu$ are present.) However, in the opposite limit, $kT\ll h\nu$, there is generally not enough energy to excite even one photon of energy $\nu$. There are occasional excitations of the mode, due to quantum fluctuations, but as $\nu$ increases, it becomes increasingly likely that the mode will have no energy in it at all. This "energy gap" behavior is characteristic of discrete quantum systems at low temperature. If there is not enough energy to consistently excite a mode, then the mode will almost always be in its ground state, carrying no energy. As the size of the energy gap between the ground state and the first excited state grows (e.g., with increasing $\nu$ for photon modes), the probability of being in the excited state become exponentially small.
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$\begingroup$ I am sure that your answer is enough and correct but if it is possible,say it in more simple words. $\endgroup$ Commented May 1, 2020 at 18:23
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$\begingroup$ @AmirhosseinTaebi I am not sure exactly how to be more clear, since I do not have a good idea of what elements of the problem are confusing you. If you edit your question to be clearer about what you understand and what you don't, I can probably provide a more useful answer. $\endgroup$– Buzz ♦Commented May 2, 2020 at 1:36
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A blackbody is an idealized system that perfectly absorbs all incoming electromagnetic radiation, and can also emit radiation. Making this assumption simplifies our model of how matter emits radiation.
Planck's background was in thermodynamics, which gave him the idea to model these systems as a collection of classical oscillators which were in equilibrium with the electromagnetic field. (This model was chosen out of convenience and not because he believed it accurately represented matter, since earlier work by Kirchhoff showed that the spectral distribution of radiation was independent of the mechanism of radiation.) Planck then hypothesized a relationship between the entropy of an oscillator and its energy, as a function of frequency and temperature. Since the entropy of a configuration is statistically related to its probability, this function determines the distribution of radiation over different frequencies/wavelengths.
In order to explain this distribution, Planck assumed that the energy of the system was discrete so that he could "count" all of the possible configurations and compute their probabilities. He therefore proposed that the energy in each mode/frequency of vibration could only be increased in amounts $nh\nu$, where $n$ is an integer and $\nu$ is the frequency of vibration.
