Wave-Particle Duality

The Photoelectric Effect

When the solution is simple, God is answering.

A. Einstein

Early in the eighteenth century, Newton published his assertion in a corpuscular theory of light. The experimental data available at the time led him to the conclusion that light consisted of small particles that: a) traveled in straight lines at great speeds; b) reflected from mirrors in a predictable way; and c) changed direction by speeding up when crossing from air to denser materials. While Newton's ideas were challenged by a rival wave theory set forth by Christian Huygens (1629-1695), the triumph of mechanics as laid out in the Principia afforded him the intellectual high ground in this battle of the theories. The wave theory was plausible. but most bet on corpuscles.

The supremacy of a particle theory lasted until 1801 when Thomas Young in England did a series of experiments passing light through narrow slits to show that light had a wave nature. (See Optics, Light as a wave) It became very cumbersome to manipulate the corpuscular theory to explain the pattern of bright and dark bars on a screen when such evidence is prima facie evidence of waves. Young's wave theory of light was therefore solidly ensconced in physics books in the nineteenth century until the discovery of the photoelectric effect in 1887.

Isaac Newton Christian Huygens Thomas Young
  Heinrich Hertz   Max Planck   Albert Einstein  Robert A. Millikan


Heinrich Hertz had been working with a cathode ray tube, using a high voltage power supply to energize the cathode. With this apparatus he got the same results as other experimenters. But he also discovered that cathode rays could be produced at a much lower voltage if the cathode were illuminated with ultraviolet light. Given that a cathode ray tube current was induced by light shining on the cathode, this phenomenon became known as the photoelectric effect..

A simple explanation could have been that the UV provides sufficient energy to help liberate cathode rays and therefore reducing the high voltage needed to do so. Not so fast. Hertz found that in order for cathode rays to be produced, the frequency of the incoming UV had to be above some threshold value. As long as this condition existed, even a dim UV ray produced a weak cathode ray. But if the frequency of incoming radiation was below a threshold value, no cathode rays were forthcoming, not even if the UV beam was very bright and not even if the exposure time was quite long.

German scientist Max Planck entered the arena in 1900 with a bold concept that light that normally exhibited a wave nature could also have a particle nature as well. An important feature of this scheme is that the two behaviors are not both evident at the same time. He suggested that the energy carried by a wave was delivered in lumps called photons or quanta Furthermore, the energy carried by a photon was directly proportional to the frequency (and therefore inversely promotional to wavelength). Thus, light had a wave-particle duality, a new phrase for the new century. Planck was awarded a Nobel prize for this work in 1918.

Now entering the picture is that soon-to-be rookie of the year, Albert Einstein. From nowhere. Yes, the same Albert who did not speak until he was three; Albert who failed in his first attempt to enter the polytechnic. The same Herr Einstein who graduated with a GPA of 4.6 (on a 6.0 scale). Married with two small children, he worked by day as a patent clerk (third class); at night, he wrote and thought about physics. The year 1905 is called his miracle year (the Latin appears below) during which he published no fewer than five ground-breaking papers. The titles are listed in the box. The papers represent refinement and advancement of work started by others. He, too, stood on the shoulders of giants.

1905 Annis Mirabilis

  On the Electrodynamics of Moving Bodies
This paper contains reference to special relativity and suggests that moving clocks run slow and moving meter sticks contract.
click here for a translation

Does the Inertia of a Body Depend on Its Energy Content?
It is in this paper that that which is tangible (has mass) is connected to that which is intangible (energy). The relationship is E = mc^2. Click here for a translation.

On a Heuristic Point of View Concerning the Production and Transformation of Light.
In this paper, Einstein gives an explanation for the photoelectric effect. For this work he was awarded the Nobel prize in physics in 1921. click here for a translation

On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat
This paper is Albert's attempt at explaining Brownian motion. click here for a translation

A New Determination of Molecular Dimensions
Einstein did his doctoral dissertation on a new way to calculate Avogadro's number. click here

Einstein suggested that, in order for an electron to be removed from the cathode, a given quantity of energy had to be delivered to the atom. He called this the work function, W. He adopted Planck's quantum theory of light for energy delivery. If an incoming photon cannot sastisfsy the work function, nothing happens. The electron cannot store the energy; two photons cannot gang up on an electron. But if the incoming photon has more energy than the work function, an electron is removed, the excess energy shows up as kinetic energy. As an equation


where h is called Planck's constant, a quantity that was first measured by Robert A. Millikan in 1921

It is for this work on the photoelectric effect that Einstein was awarded a Nobel prize in 1921.

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Last edited 12/26/05