Einstein's Theory of the Photoelectric Effect
Model of Discrete Energy Revolutionizes our View of Light
Aug 28, 2008
The photoelectric effect is an observed phenomenon of the quantization of light energy. Emission of electrons out of a clean metal surface due to incident light is only possible for frequencies greater than a certain lower limit, specific to the metal.
Einstein theorized an explanation of this effect, changing the way light was viewed and how light interactions are modelled.
Lenard's Original Experiment
In 1902 Philipp Lenard used cleaned metal surfaces to ensure any measured effect would be that of the metal alone. The metal sample was housed in a tube called a photocell, connected to a circuit and its surface was illuminated with light of different frequencies and intensities.
The power supply had its negative end connected to the non-illuminated plate. This set up a potential difference opposing photoelectrons from reaching the collector:
- A low applied voltage repelled only the least energetic electrons, with the current observed to decrease.
- Increasing voltage prevented more and more electrons from reaching the collector until no electrons were able to leave the emitter surface. The ammeter reading dropped to zero.
The value of voltage at which this occurs is called the Stopping Potential, or Work Function, and is a measure of the maximum kinetic energy of the electrons emitted as a result of the photoelectric effect.
Effect of Light Intensity and Frequency
Intensity of incident light was found to have no effect on the maximum kinetic energy of the photoelectrons. Electrons ejected due to exposure to a very bright light had the same energy as exposure to very dim lighting of the same frequency. Robert Millikan found that light with frequencies below a certain cut-off value, called the threshold frequency, would not eject any photoelectrons from the metal surface, no matter how bright the source (Fig 1) and this threshold was also specific to the material.
Einstein's Explanation
The photoelectric effect was explained by Einstein in 1905 using his new particle-like model for light. He viewed light as a stream of discrete packets of energy called photons, each carrying energy Ep = hf, where h is Planck's constant and f is the frequency of incident light. Work function W for the metal is given by:
Work Function: W = hfo
If the light frequency is greater than a threshold frequency, fo, then a photoelectron will be ejected with kinetic energy up to a maximum value, Ek , according to the linear formula (Fig. 2):
Photoelectric Equation: Ek = hf - W
The energy of the fastest photoelectrons may be expressed in terms of the electron volt (1eV = 1.6 x 10^-19J). We may then write as Ek = eVo = 1/2 mv², where Vo is the stopping potential and m, the mass of the electron. Rearranging, for maximum speed yields:
Max Speed: v = sqrt(2eVo/m)
Worked Examples
Yellow - green light of wavelength 500 nm shines on a metal surface whose stopping voltage is found to be 0.80 V. Find the fastest speed of the photoelectrons. Substituting in values for max speed we get, v = sqrt(2 x 1.6.10^-19 x 0.80)/9.1 x 10^-31) = 5.3 x 10^5 m/s.
What is the work function of this metal? Using the photoelectric equation and f = c/λ and making W the subject, we get: W = hc/λ - Ek = (6.63 x 10^-34 x 3 x 10^8)/5x10^-7 - 0.8 x 1.6 x 10^-19 = 2.69 x 10^-19 J (or 1.68 eV)
Conclusion
As a consequence of the explanation of the photoelectric effect, it is understood that light has a dual wave-like and particle-like nature. The particle model as expounded by Einstein, suggests that light energy is quantized rather than continuous.
The reader may be interested in more details about this topic or learn about light interference.
