## Definition

A material particle, emitting the electromagnetic radiation, extracts a portion of its own beam, respectively losing own energy and own momentum. Since the vortex has a shape of a wave (solition), the wavelength of the emitted beams depends on its energy.

The quantization occurs only with the quantum effects in the atoms. The radiation with any combination of power and wavelength is always completely absorbed by the material particles, but it can be immediately emitted back because of the quantum effects.

## Bremsstrahlung

Bremsstrahlung occurs when the particles reduce their momentum (brake) in an electric field. This effect is a consequence of the law of conservation of momentum, and it is not associated with the electromagnetism. Bremsstrahlung is a cause of the electron shells radiation (see Atom), and some cases of the nuclear radiation. Bremsstrahlung, which arises at the high energy center of a vortex of mass $$m$$, which loses a momentum $$p$$, has an initial velocity: $v=\frac{p}{m}\tag{1}$ The initial wavelength of the beam is $$\lambda_0$$ ("Mass and momentum", 2), but while moving away from the center and reaching the speed of light, the wavelength becomes increased up to: $\lambda=\lambda_0\frac{c}{v}=\frac{h}{p}\tag{2}$

## Photons

Bremsstrahlung pulse, which is produced in a quantum effect, is called the quantum or the photon. The photon or the quantum is an abstract particle with a momentum ("Mass and momentum", 8), where the virtual mass has a physical meaning of the quantum energy: $p=\frac{h}{\lambda}=\frac{E}{c}=mc\tag{3}$ $E=\frac{hc}{\lambda}=h\nu\tag{4}$ The Compton effect is a mechanical interaction of the photons with the electrons, which is accompanied by a change in the photon wavelengths.

The dimensions of a photon i.e. the volume, which contains most of the energy, is proportional to the wavelength. The quantum effects are observed at the shorter wavelengths, when the photons almost do not overlap each other.

The photoelectric effect is explained by the low concentration of the small photons. The electrons absorb the rare single photons, so their energy is proportional to the wave frequency, similarly to the absorbed photons.

The quantum theory of the photoelectric effect, which was founded by Einstein, is violated during the multi-photon ionization by a concentrated beam of the photons, or by an irradiation with high energy density, when the electrons rapidly accumulate energy of several weak photons, and don't give it away. For example, in one experiment [1], a radiation of power about 1015 W/cm2 had caused the ionization of a rarefied gas at a wavelength greater than it is required on the quantum theory of the photoelectric effect.