# Quantum model for electromagnetic radiation

Maxwell's electromagnetic theory is very useful in explaining the phenomena related to the propagation of electromagnetic radiation. However, it does not explain some phenomena that occur in the interaction of these radiations with matter, nor some facts related to emission.

An example of this is the body's emission spectrum, which was studied by many scientists for half a century, since the ideas of the time were inconsistent between theoretical predictions and experimental results.

Subtitle:
- A: curve obtained from experimental results;
- B: curve predicted by classical theory.

The fact that the behavior of the blackbody radiation intensity graph as a function of Maxwell's predicted wavelength is very different from that obtained from experimental data became known in the nineteenth century as Violet catastrophe.

In 1900 Max Planck came up with a new theory, which conflicted with the classical theory hitherto accepted to solve the problem. Planck supposed that on the surface of a blackbody there were simple harmonic oscillators (OHS, represented by oscillating electric charges) capable of assuming certain energy values. Mathematically:

Where:

n = quantum number;
h = Planck constant (h = 6.63x10-34 J.s);
f = oscillator frequency.

Each value of n will represent one quantum state different from this oscillator and will always be a multiple of hf which means the energy of the oscillator is quantized, that is, it can only assume certain values.

According to classical physics, an OHS can have any energy value and is not dependent on the frequency but on the amplitude of the oscillations. This makes Planck's attitude of proposing a new theory contrary to these principles quite courageous. In addition, he proposed that OHSs on the body's surface emit or absorb energy only as they move from one quantum state to another.

Thus, if the oscillator goes from a higher energy level to a lower level, for example from n = 2 to n = 1, it emits a discrete amount of energy, which corresponds mathematically to the difference between the energies of the two levels. . If it goes from a lower energy level to a higher energy level, such as from n = 1 to n = 2, it absorbs a discrete amount of energy, similar to the previous case. This means that the emission and absorption of energy also occur in quantized quantities.

Each discrete portion of energy was called quantum, which comes from Latin, whose plural is how much. Because of this, Planck's theory gained popularity by the name of quantum theory.

Using the formulations made by Max Planck for energy quantization, it was possible to obtain a new graph of the radiation intensity emitted by the body as a function of wavelength in full agreement with the experimental results.

However, a new question troubled physicists of the day: If energy is emitted only in well-determined quantities, which implies certain well-established wavelengths and frequencies, how can the spectrum of thermal radiation be continuous? The answer is this: Because there are so many oscillators with different energies, the likelihood of radiating radiation of any frequency is also very high.

It is noteworthy that Planck never claimed that electromagnetic radiation propagated in discrete amounts of energy. In this view, he believed that Maxwell's theory was coherent. Therefore, for Planck, quantized were oscillators, not electromagnetic radiation.

It is important for us to know that the idea of ​​quantum, later called photon, was very useful in clarifying several other phenomena that classical physics could not properly explain.