The
Photoelectric Effect
By: Alana Bradley, Joshua Griffin, Greg Huff, and Ryan Macomber
Introduction
Investigations began on the photoelectric effect in 1887, however, this phenomena wasn’t able to be explained until 1905 when Albert Einstein discovered the photon. In a metal, if an electron can gain enough energy from a photon; the electron can then be ejected from the metal. The photoelectric effect can be described using Einstein’s equation for the energy of a photon,
Eph = hν
This equation simply states that the energy of a photon is proportional to the frequency of light; where E is the energy of a photon, h is Planck’s constant, and ν is the frequency of light.
The Classical Approach to the Photoelectric Effect
Heinrich Hertz was the first to make observations on the photoelectric effect in 1887. His observations were on the production and reception of electromagnetic waves that were run through a coil to produce a spark. He observed the spark in different conditions, but did not make any attempt to explain this effect. Then, in 1899, Joseph John Thompson found that cathode rays consisted of negatively charged particles which he called “corpuscles”. We would later call them electrons. He found that in an oscillating magnetic field, a “corpuscle”, could be emitted after reaching a certain amplitude, and a current could then be detected. Thompson saw that larger frequency would produce more current. In 1902, Philipp von Lenard made observations on the change in electron energy with the change in light frequency. In Lenard’s experiment, he measured potential electron energy and found that the maximum electron kinetic energy is proportional to the frequency of light. Although all of these observations helped Einstein in explaining the photoelectric effect; these observations were labeled the classical approach due to the fact that they were missing a major factor in describing the photoelectric effect.
Problems with the Classical Approach
The problems found with von Lenard’s classical approach were due to the fact that they were not quantitative. His experiments had to be done on freshly cut metal, but metal will oxidize in a matter of minutes. Although he found that the electrons emitted by the surface were determined by the intensity of light, he did not know of photons.
The Quantum Explanation
Developed by Albert Einstein in 1905, the quantum explanation of the photoelectric effect helped give insight into the existence of the photon. Einstein said that for a given metal, at a certain frequency, photons interact with the electrons of the metal as if they were discrete particles. Through this interaction, the photons transfer energy, hf, to the electron causing the electron to be ejected from the metal with a velocity, v.
Evidence of the Superiority of the Quantum Approach
The classical approach to the photoelectric effect was based on the fact that the average energy of the emitted electrons could be increased by increasing the intensity, or amplitude, of the light. Einstein proved that the intensity increased the number of photons in the light, and had nothing to do with the average energy of the electrons. Instead, Einstein showed that if the frequency was increased, the average energy of the electrons could be increased. According to equation 11.12 from Atkins, 0.5mv2 = hν – Φ, the energy supplied by the photon, hf, has a direct correlation to the amount of average energy the ejected electrons have. If the frequency were increased, the photon would be able to supply more energy, thus allowing for a greater energy for the electron.
Significance of the Quantum Approach to Advancement of Quantum Theory
By proving the existence of the photon, Einstein allowed for a correlation between particles and waves, with respect to light, to be examined. With these new ideas, light could now be measured as either a particle or a wave, which helped lead the way for De Broglie’s wave-particle dualty experiments. He also showed that it was possible for the electromagnetic field to be quantized.
Discussion of Reduction of Quantum to Classical
For the energy of a photon the correspondence principle states that the energy of a photon at a macroscopic level must be equal to the energy found using the classical approach. If you have a very large number of photons the two theories do agree.
Biography of the Scientist who proposed the quantum approach to the Photoelectric effect
The scientist that proposed the quantum approach to the Photoelectric effect was Albert Einstein. Einstein was born in Ulm, Württemberg, Germany, on March 14, 1879. His family was Jewish. His father was Hermann Einstein, who was a salesman. His mother was a Pauline Koch. During World War I, Einstein worked as a professor at the University of Berlin.
A small bump that Einstein encountered was not being accepted to Federal Polytechnic Institute in Zurich in 1895. This was because he dropped out of secondary school, and had to take an exam, which he did not pass. He eventually got accepted to the school and earned a teaching degree. But even with this teaching degree he could not find a job straight out of school.
In 1905, at the age of 26, Einstein published a series of papers known as “Annus Mirabilis Papers” in the German journal Annalen der Physik. His first paper proposed that photons were real, and showed how they could be used to explain the photoelectric effect. To write this paper Einstein worked on Max Planck’s assumption that energy was quantized.
At first Einstein’s quantum ideas were not embraced by fellow physicists. This was because many just refused to believe in quantized energy. Because Einstein was Jewish living in Germany, many people discredited his ideas, just for that. Finally in 1919 Arthur Eddington was working on Einstein’s theory of general relativity (theory of gravity) and made measurements during a solar eclipse. These measurements grabbed the physics community and physicists finally began to say that his ideas were “substantiated.” In 1921, two years after these measurements, he was given the Nobel Prize for his work on the photoelectric effect.
Problems
Number 1
Number 2 Number 2 using Maple
Number 3
References