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Photoelectric Effect Explained

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Einstein's Wonderful Year

In 1905, Albert Einstein published four papers in the Annalen der Physik journal, each of which was significant enough to warrant a Nobel Prize in its own right. The first paper (and the only one to actually be recognized with a Nobel) was his explanation of the photoelectric effect.

Building on Max Planck's blackbody radiation theory, Einstein proposed that radiation energy is not continuously distributed over the wavefront, but is instead localized in small bundles (later called photons). The photon's energy would be associated with its frequency (nu), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (lambda) and the speed of light (c):

E = h nu = hc / lambda

or the momentum equation: p = h / lambda

In Einstein's theory, a photoelectron releases as a result of an interaction with a single photon, rather than an interaction with the wave as a whole. The energy from that photon transfers instantaneously to a single electron, knocking it free from the metal if the energy (which is, recall, proportional to the frequency nu) is high enough to overcome the work function (phi) of the metal. If the energy (or frequency) is too low, no electrons are knocked free.

If, however, there is excess energy, beyond phi, in the photon, the excess energy is converted into the kinetic energy of the electron:

Kmax = h nu - phi
Therefore, Einstein's theory predicts that the maximum kinetic energy is completely independent of the intensity of the light (because it doesn't show up in the equation anywhere). Shining twice as much light results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons won't change unless the energy, not the intensity, of the light changes.

The maximum kinetic energy results when the least-tightly-bound electrons break free, but what about the most-tightly-bound ones; The ones in which there is just enough energy in the photon to knock it loose, but the kinetic energy that results in zero? Setting Kmax equal to zero for this cutoff frequency (nuc), we get:

nuc = phi / h

or the cutoff wavelength: lambdac = hc / phi

These equations indicate why a low-frequency light source would be unable to free electrons from the metal, and thus would produce no photoelectrons.

After Einstein

Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, and his work confirmed Einstein's theory. Einstein won a Nobel Prize for his photon theory (as applied to the photoelectric effect) in 1921, and Millikan won a Nobel in 1923 (in part due to his photoelectric experiments).

Most significantly, the photoelectric effect, and the photon theory it inspired, crushed the classical wave theory of light. Though no one could deny that light behaved as a wave, after Einstein's first paper, it was undeniable that it was also a particle.

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