# The Photoelectric Effect

The photoelectric effect posed a significant challenge to the study of optics in the latter portion of the 1800s. It challenged the classical wave theory of light, which was the prevailing theory of the time. It was the solution to this physics dilemma that catapulted Einstein into prominence in the physics community, ultimately earning him the 1921 Nobel Prize.

## What Is the Photoelectric Effect?

Annalen der Physik

When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right.

## Setting Up the Photoelectric Effect

By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation:

Kmax = eVs

## The Classical Wave Explanation

Iwork function phiPhi

Three main predictions come from this classical explanation:

1. The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.
2. The photoelectric effect should occur for any light, regardless of frequency or wavelength.
3. There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.

## The Experimental Result

1. The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons.
2. Below a certain frequency, the photoelectric effect does not occur at all.
3. There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.

As you can tell, these three results are the exact opposite of the wave theory predictions. Not only that, but they are all three completely counter-intuitive. Why would low-frequency light not trigger the photoelectric effect, since it still carries energy? How do the photoelectrons release so quickly? And, perhaps most curiously, why does adding more intensity not result in more energetic electron releases? Why does the wave theory fail so utterly in this case when it works so well in so many other situation

## Einstein's Wonderful Year

Albert Einstein Annalen der Physik

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 (ν), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (λ) and the speed of light (c):

E = = hc / λ
or the momentum equation: p = h / λ

νφ

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

Kmax = - φ

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 (νc), we get:

νc = φ / h
or the cutoff wavelength: λc = hc / φ

## After Einstein

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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