IIT JEE , AIEEE Forum - Physics , Modern Physics - Atomic Physics [admin]: De-Brooglie's Duality principle

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De Broglie's hypothesis

In 1924, Louis-Victor de Broglie formulated the hypothesis, claiming that all matter, not just light, has a wave-like nature; he related wavelength, ? (lambda), and momentum, p:

$lambda = rac{h}{p}$

This is a generalization of Einstein's equation above since the momentum of a photon is given by p = E / c where c is the speed of light in vacuum, and

=c/

.

de Broglie's formula was confirmed three years later for electrons (which have a rest-mass) with the observation of electron diffraction in two independent experiments.

de Broglie was awarded the Nobel Prize for Physics in 1929 for his hypothesis. Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work.

Einstein's photoelectric effect

In 1905, Albert Einstein provided an explanation of the photoelectric effect, a hitherto troubling experiment which the wave theory of light seemed incapable of explaining. He did so by postulating the existence of photons, quanta of light energy with particulate qualities.

In the photoelectric effect, it was observed that shining a light on certain metals would lead to an electric current in a circuit. Presumably, the light was knocking electrons out of the metal, causing them to flow. However, it was also observed that while a dim blue light was enough to cause a current, even the strongest, brightest red light caused no current at all. According to wave theory, the strength or amplitude of a light wave was in proportion to its brightness: a bright light should have been easily strong enough to create a large current. Yet, oddly, this was not so.

Einstein explained this conundrum by postulating that the electrons were knocked free of the metal by incident photons, with each photon carrying an amount of energy E that was related to the frequency, ? of the light by

$E = h \nu\,$

Only photons of a high-enough frequency, (above a certain threshold value) could knock an electron free. For example, photons of blue light had sufficient energy to free an electron from the metal, but photons of red light did not. More intense light above the threshold frequency could release more electrons, but no amount of light below the threshold frequency could release an electron.

Einstein was awarded the Nobel Prize in Physics in 1921 for his theory of the photoelectric effect.

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De Broglie's hypothesis