Black Body Radiation & Quantum Mechanics

The Problem

A black body is an idealized object that should be a perfect absorber of electromagnetic waves (light for example), meaning it would absorb all electromagnetic waves of all frequencies, in contrast to say a red object that absorbs only wavelengths that don’t correspond to red light, thereby only emitting light from the red spectrum. A box (or any cavity at all) will serve as a good example of a black body since the radiation won’t get out of the box, you can say that the box has absorbed it:

You have a box, and the box is filled with electromagnetic waves, which constitute the temperature inside the box. Now, let’s try to divide up the total energy inside the box between the various numbers of electromagnetic waves that would be inside such a box:
First, the frequency of the waves can’t have any number at all, the waves have to fit between both sides of the box and have a whole number wavelength. Then we first have one large wave stretching from one side of the box to the next with one peak, then we can have a wave with two peaks in the same space, three and so on. You can cram whatever amount of peaks between the walls you want, there’s no end to it, so there is an infinite number of possible waves, with the frequency becoming larger and larger. Now we have an infinite amount of possible waves, and since the black body should treat all waves equal, not favoring any of them, the energy has to be divided up equally between all the possible waves. The dilemma is that no matter how small portion of the total energy you give to each wave, because of the total wave number being infinite the energy will also be infinite.

The Solution

In the wave model of the black body radiation, each electromagnetic wave could carry and arbitrary small amount of the total energy. Which then would lead to an infinite total energy. The man who resolved this, and is considered a founder of quantum mechanics, was Max Planck. He proposed that energy couldn’t take on an arbitrary value, but had to come in quanta’s or packages which had a specific whole number value and that value depended on the frequency of the wave in question. So now the energy was in packages, which had a minimum energy value. And as we move up to waves with higher and higher frequencies, the quanta also gets a higher energy. But here’s the point; when the waves frequency become so high that its quanta’s energy exceeds the energy which the energy field they belong to have (e.g. the energy in the box), then it gets counted out. Meaning that quanta’s which has to high energies isn’t allowed and therefore doesn’t come into existence.

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