Photoelectric Effect.

The Black Body radiation spectrum forced upon us the idea of quantized oscillators
radiating EMW and a departure from the concepts of Classical Physics. Another phenomena was soon discovered which seemed to defy a classical explanation in terms of EMW. This was the photoelectric effect which demonstrated that incident radiation on the (metal) surface are able to eject electrons. The electrons are called photo electrons and may constitute a current called a photo current

In 1886 Hertz did his famous experiment on this effect



http://physics.info/photoelectric/circuit.html

* Image from Flickr "Robbo Coach's" photostream

Several interesting features may be noted

1. The current I is NOT ZERO till a "reverse voltage is applied". This shows that
the electrons are ejected with some kinetic energy. The current saturates at some value of the forward voltage and this is dependent on the intensity of the incident radiation.

2. The cut off voltage is independent of Intensity of the radiation but depends on the frequency.

3. Millikan showed that the stopping potential varied linearly with the frequency and there was a "cut off frequency" ν₀ beyond which no electrons are emitted.

*Graph

An explanation of this phenomena based on the Classical Wave picture of EMW fails
due to the following reasons

1. Kinetic energy of photo electrons in particular the maximum kinetic energy K_max
=e V₀ where V₀ is the stopping potential should depend on the intensity as Intensity is proportional to the Electric Field amplitude squared in an EMW and this is the field that energizes the electron in the wave picture. But experiment shows otherwise.

2.The effect should occur for any frequency provide the incident radiation is intense enough to energize the electron. Experiment shows a cut off frequency specific to the material below which no photo electrons are ejected.

3. Effect should show a time lag as the wave energy is diffused over a spatial extent. Experiment shows that the effect is instantaneous.


These discrepancies inspired Einstein to apply the idea of Quantization due to Planck to EM radiation. Einstein postulated that EM radiation is composed of a large number of discrete packets of localized energy which behave like particles. The particles were called photons and their energy was quantized as E=hν where ν was the frequency of the radiation.

Einstein postulated that in the photoelectric effect 1 photon was absorbed by 1 electron to be energized and ejected provided the energy was adequate for the electron to overcome the surface atomic attractions.

So the kinetic energy of the ejected electrons would be K=hν-W where W is the energy for overcoming the surface barriers.

The maximum kinetic energy K_max=hν -W₀ where the second term was called the work function of the material and referred to the minimum energy for electrons to overcome the surface atomic attractions.

The photon picture was able to explain the experimental results

1. Intensity of radiation was proportional to the number of photons or their density. However each electron could absorb only 1 single photon. Hence the maximum kinetic energy was independent of the intensity.

2. At threshold when an electron is Just ejected with zero kinetic energy ( corresponding to the stopping potential K_max=0 and hν₀=W₀ where ν₀ is the cut off frequency
and no emission was possible below this.

3. As the energy of radiation was highly localized in the photon picture the absorption is instantaneous and hence there was no time lag as observed experimentally but was predicted by the classical wave picture.


From the equation K_max=eV₀=hν -W₀
its is seen that the stopping potential V₀ varies linearly with the frequency and from the slope of the graph of the stopping potential vs frequency
we can fix the Planck's constant h knowing e and m for the electron, which comes out to be close to the measured value.