In 1900, Max Planck proposed the first truly workable solution to the problem of black-body radiation, as defined in the latter half of the nineteenth century.
His solution required the creation of a new mathematical constant, Planck’s Constant (denoted by an “h”), and the breaking up of light waves into discrete little chuncks which became known as photons (or “quanta.”
The second problem that had been proposed during these years was that concerning the “photoelectric effect,” wherein light waves fired toward certain metals at differing energies caused the production of free electrons to jump off the material.
The problem lay in the fact that as the light’s intensity changed, it was expected that the energy of the resulting electrons would change accordingly. This was not the case, however. As the intensity changed, only the number of electrons changed, rather than their energy. The only way to get the energy of the electrons to change was by changing the color (or “wavelength”) of the light.
This was one of the key problems to which Einstein successfully applied Planck's equation in his 1905 paper – On a Heuristic Viewpoint Concerning the Production and Transformation of Light. He found that there is absolutely no problem at all in the photoelectric effect, if one assumes that Planck is correct after all, and that light is firmly quantized.
If so, in the case of the photoelectric effect, as the light intensity increases, only the number of quanta (photons) of light being emitted from the source will increase, not the intensity. So from a brighter light a greater number of photons strike the metal and more electrons are freed.
If the color is changed, however, say to one with a shorter wavelength, the same number of electrons will be released, because the same number of photons will strike the surface, though with a higher intensity, as the wavelength of the light is shorter. This explanation fit perfectly with experimental results.
The photoelectric effect, like black-body radiation, is rather easily solved by the acceptance of this new quantum theory. And indeed, with such great successes, it seemed that after Einstein’s 1905 paper had finally gained acceptance, the quantum revolution had begun in earnest.
Even after Einstein's paper (remember that Einstein was unknown in the scientific world at that point), it took a while for quantum physics gain steam. In fact, it took until 1918 for Planck to finally receive a Nobel prize for his work, and until 1921 for Einstein to receive his.
Still, at least they got the snowball rolling down the hill. They got people thinking.
The key to the work of both Planck and Einstein in this regard was not the answer these specific questions – it was that this answer led to the idea of light as being quantized, which had implications much more far-reaching than these simple problems.
This became a springboard for more questions than can possible imagine, and so began an avalanche of physicists (as soon as they began to catch on) attempting to understand the world through brand new glasses in which everything was quantized.
For the question was now set on the table: Is light a particle after all? Or is it a wave? Is it both? Is it neither? Is it sometimes one and sometimes another? What else might obey such quantum rules?
These became some of the essential questions which led to the popularization of quantum physics. And it quickly became apparent that quantization doesn't apply only to light. Over the course of the next few decades following Einstein's paper, it soon became clear that all atomic and sub-atomic processes were governed by the laws of quanta.
And from here on, things began looking very small to physicists.
References:
Einstein, A. (1905). On a Heuristic Point of View about the Creation and Conversion of Light. Annalen der Physik .
Gribbin, J. (1994). In Search of Schrodinger's Cat: Quantum Physics and Reality. New York, NY: Bantam Books.
Herbert, N. (1985). Quantum Reality. Garden City, NY: Anchor Press/Doubleday.