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Quantum Theory of Physics.
Max planck explained the black body problem in 1900 and set in motion a whole new branch of physics. Current thinking would have predicted that a hot object could produce much higher frequencies of radiation, at lower overall intensities than were actually found.
Planck imagined standing waves formed inside the black body. The longest wavelength possible would be one with only one half wavelength across the diameter, the next could have two half wavelengths, the next three and so on, all the way up to an infinite number of half wavelengths. The current thinking was that all such standing waves would be equally possible and the total amount of energy would be shared equally between them all. What Planck suggested was that only the part between each node should be thought of as an oscillator. So the simplest standing wave would have one oscillator, the next two oscillators, and so on. Now the energy of each standing wave would increase with frequency, as at high frequency there would be a shrter wavelength and more lobes in the standing wave. He produced the simple formula E = hf for each oscillator.
The result of this is that for any given amount of total energy, the oscillator could emit it as one huge high frequency or several smaller ones or lots of very small ones. The ideas of Maxwell when incorporated with this idea yields the kind of distribution detected in black body radiation. The constant h, which Planck called the quantum of minimum action, was called by everyone else Planck's constant. The units of h are J s, and the quantity energy x time is called action. In classical physics there had been for a long time a 'principle of least action' which showed that any path taken by light or a material body between A and B was the one for which action was a minimum. What Planck was saying in effect was that action had a minimum value of h = 6.6 x 10-34 J s. This was no more controversial than the idea of the atom as the minimum unit of matter. The number of lobes in the standing wave provied the discrete integral nature of the energy.
The distribution of energy in the black body spectrum turns out to be the solution to other quite different problems. For example, how do you divide up large amount of money for maximum effect? Do you go for one very large expensive project, spending all the money on one thing, or do you divide it up so as to produce huge numbers of cheap items, or a moderate number of mid priced ones. The answer turns out to be the Maxwellian distribution; a large number of moderate projects, with a few very expensive and a few very cheap ones.
It did not take long for Planck's ideas to be applied by others. Einstein explained the photoelectric effect by saying that light carried energy in packets of size E=hf and that these packets, which he called photons, collided with electrons in a metal plate and knocked them out as long as E exceeded the amount of energy needed to escape. He predicted that the emergent electrons would have energy proportional to the frequency of inciden light, not to its intensity.
Bohr applied Planck's idea to the energy levels within the atom. After Rutherford had discovered the necleus a new picture of the atom emerged in which electrons were pictured as in orbit around the nucleus in the same way that Planets orbit the Sun. The problem with this model was that the electrons would spiral down into the nucleus rather quickly, emitting radiation as they went, and the atom would cease to exist. Bohr suggested that if the energy was quantised there would only be certain energy levels allowed, including a lowest possible one.
Louis deBroglie took this idea further and imagined standing waves upon the orbits of the electrons themselves. The lowest orbit would have a one wave on it, the next two and so on. He further calculated that all particles would have a wave associated with them, which was later discovered experimentally by Davison and Germer. An electron in a high orbit corresponding to n lobes in its standing wave orbit could lose a fixed amount of energy and drop to the next level below with n-1 lobes, a quantum jump. The excess energy could be emitted as a photon of frequency hf. This was in perfect agreement with experiment and explained the line spectra of atoms.
Other physicists such as Schrödinger, (uncertainty) Heisenburg and Born have developed the ideas further and developed different mathematical methods for dealing with the wave mechanics.
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