WOW
Frequency condition DE = hn, a form of Einstein's equation ½mv2 = hn - P
The frequency condition Ee - Ea = hn complements the equation ½mv² = hn - P, which regulates the light-electric effect (Einstein 1905), that is, the exit of electrons from metals, irradiated by short wave light. According to Einstein's concept, this process is: Energy quanta hn enter the surface layer of the body, their energy converts itself there (at least partially) into kinetic energy of electrons - the simplest concept is that one quantum of light passes its entire energy to a single electron as kinetic energy. As such an electron reaches from inside the body the surface, it has lost a part of its kinetic energy. In addition, during the passage through the surface, every electron performs work which is characteristic for the body (exit work). Those electrons will have the largest velocity, which have been excited immediately below the surface and exit perpendicularly to the surface. Their kinetic energy is ½mv² = hn - P, where v is the exit velocity, m the electron mass and P the work performed during the exit. This is the energy which can be measured outside the surface. Measurements have shown that this law is strictly realized for the entire spectral range. For most metals, the exit work lies between 1 and 3 Volt. Bohr's theory of the nuclear atom allots to the exit work P a frequency np by setting P = hnp; the term hnp corresponds to the tension Vp, which is just sufficient to remove the electron from the atom - to ionize it, whence np is also the frequency of the border of the absorption series.
If the absorbed radiation energy is insufficient to liberate an electron from an atom, nevertheless the atom's interior changes itself by raising the electron to a higher quantum orbit. It returns again the potential energy, which the atom has gained in this manner, according to the equation DE = hn as it reverts. Then no exit work is performed, whence ½mv² = hn. The energy ½mv² can also be given to the electron by the work eV, whence eV = ½mv² = hn. This equation regulates - reading from the right hand side to the left hand side - the electron release by light of the frequency n, and - reading from the left hand side to the right hand side - the generation of radiation of light (ultraviolet, X-rays) by electrons at the Volt velocity V.
