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Classical problem in physics that wasn't resolved until Max Planck introduced quantifed energy in the atom model.

The temperature of an object reflects the kinetic energy of the atoms or molecules flying/moving around (gases/liquids) or vibrating (solids). Some part of the heat energy is related to he motion/vibration of the atoms as a whole, some part of it is related to the motion of electrons in the atom. (See Thermos for more about this.) At a given temperature all these phenomena exist together. The thermal motion of electrons and the thermal motion of ions relative to each other lead, because of Maxwell equations, to electromagnetic radiation as mentioned above. This is called thermal radiation.

The electromagnetic radiation can occur at several frequencies depending on the frequency of the vibration of charges. Physicists tried to understand how the intensity of thermal radiation depends on frequency. Experimentally obtained results seemed to refuse to fit the calculations.

The theory predicted higher contribution from higher frequencies but the reality was that the intensity dropped drastically at higher frequencies.

Why is the spectral distribution of purely thermal radiation (black body radiation) not in accordance with classical radiation theory?

Planck realized that this was understandable if one made the assumption that atoms could absorb or emit electromagnetic radiation energy only in certain portions, where a portion of energy - a quantum - was proportional to the frequency. This proportionality factor is known as Planck's constant and noted by symbol h.

Black body radiation is sort of a reverse of what happens when you are sunbathing and you absorb heat energy from the rays of the sun. The hotter an object is, the more it will emit heat radiation of its own. You have probably noticed that black clothes absorb heat radiation better. Similarly, black objects emit more heat radiation, which is probably the origin of the term 'black body radiation'. Planck's explanation of the energy distribution of blackbody radiation was one of the first steps toward quantum mechanics .

Imagine two walls :

 
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Now how many vibrational modes can you fit between the two walls ? This is the question that was asked when people tried to calculate the energy spectrum that a heated object should emit. Back in the day before quantum mechanics the world was considered continuous. This means that you can divide the seperation between the walls into an infinite set of modes. Each mode contributes equally to the energy and as your number of modes diverges so does the energy that you expect to see coming out of the heated object. This is the ultraviolet catastrophe. Planck set a limit to the smallest size of the modes. He quantized the system. This was the first introduciton of quantization into physics. He did it in 1905

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