Einstein on the Photoelectric Effect

The final part in this series of understanding the dual nature of light ends here with Einstein’s theory on the nature of the photoelectric effect. The photoelectric effect is a phenomenon first documented in 1887 by Heinrich Hertz and later by Lenard in 1902 in which light shone upon a material causes electrons in the material to be ejected, this material usually being some metal. This experiment revealed several issues with the wave theory of light proposed by Huygens and Young. For one, according to the wave theory of light, energy is uniformly distributed across the wavefront and is dependent only on the intensity of the beam, basically saying brighter light means faster electrons due to those electrons having more kinetic energy from brighter light. Experimentally, however, it was shown that the kinetic energy of electrons was independent of light intensity. The second issue this experiment revealed was the fact that not just any frequency of light would be able to eject electrons as wave theory had suggested. There was a threshold frequency (v0) where frequencies of light above it were able to eject electrons. Thirdly and finally, energy is dependent on intensity according to wave theory, implying that if you were to shine low intensity light long enough on a sheet of metal, an electron would come out. This, however, was proven experimentally to not be the case, it was shown instead that electrons seem to spontaneously eject from the metal, even at low intensities of light.

Einstein showed that using Plank’s idea of light being a particle with some discrete/specific energy proportional to the frequency of the light, represented by the formula.

E = hv

Where E is the energy, h is Plank’s constant, 6.6261 x 10-34 Js and v being the frequency of the light. Einstein theorized that when a photon strikes the surface of a metal, all of the quanta of light’s energy is transferred to the electron. Some of the quanta of light’s energy is used to break the electron free from the binding forces which hold it in the metal and the rest of it is used to give the electron its kinetic energy. Those electrons beneath the metal’s surface will not have as much kinetic energy as those electrons on the surface of the metal when struck by a quanta of light due to the inner electron using more of the photon’s energy on breaking free of the binding energy rather than on its own kinetic energy.

We can write this mathematically as 

E = W + KE

hv = W + KE

KE = hv - W

V0 = Threshold frequency  V0  ElectronEmission Frequencies (Y) 

 W =  hV0

KE = 2-1mv2max = hv - hV0

       = 2-1mv2max = h(v - V0)

So light is a particle but, as shown by the information in previous articles aside from the one mostly about Newton and Huygens, light is a wave. How fun and how strange no?