Quantum Theory: Max Planck
The Wave Structure of Matter (WSM) & Standing
Wave Interactions (which occur at discrete Frequencies f) explains Quantum
Energy States of Matter & Light 'Quanta' (E=hf)
discovered by Max Planck (1900).

(Max Planck, 1919 Nobel Prize address, 'The Origin and Development of the Quantum Theory')
Max Planck (1858 - 1947)

Prior to then light had been considered as a continuous electromagnetic wave, thus the discrete nature of light was completely unexpected, as Albert Einstein explains;

Then Planck showed that in order to establish a law of heat
radiation (Infra red light waves) consonant with experience, it was necessary
to employ a method of calculation whose incompatibility with the principles
of classical physics became clearer and clearer. For with this method of
calculation, Planck introduced into physics the quantum hypothesis, which
has since received brilliant confirmation. (Albert Einstein,
on Quantum Theory, 1914)
In the year nineteen hundred, in the course of purely theoretical
(mathematical) investigation, Max Planck made a very remarkable discovery:
the law of radiation of bodies as a function of temperature could not be
derived solely from the Laws of Maxwellian electrodynamics. To arrive at
results consistent with the relevant experiments, radiation of a given frequency
f had to be treated as though it consisted of energy atoms (photons) of
the individual energy hf, where h is Planck's universal constant. During
the years following, it was shown that light was everywhere produced and
absorbed in such energy quanta. In particular, Niels Bohr was able to largely
understand the structure of the atom, on the assumption that the atoms can
only have discrete energy values, and that the discontinuous transitions
between them are connected with the emission or absorption of energy quantum.
This threw some light on the fact that in their gaseous state elements and
their compounds radiate and absorb only light of certain sharply defined
frequencies. (Albert Einstein, on Quantum Theory, 1940)

(Albert Einstein, on Quantum Theory, 1950)
We can now finally solve these problems by understanding the reason for these discrete energy states, which are due to the fact that standing waves only exist at discrete frequencies, like notes on the string of a guitar, thus while the correct Spherical Standing Wave Structure of Matter predicts that energy exchanges will be discrete, as observed, the continuous e-m wave does not anticipate this.
Thus the Spherical Standing Wave Structure of Matter explains Max Planck's (1900) discovery that there are only certain allowed discrete energy states for electrons in molecules and atoms, and further, that light is only ever emitted and absorbed by electrons in discrete or 'quantum' amounts, as the electrons move from one stable standing wave pattern to another.
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