"I am convinced that He [God] does not play dice"
Albert Einstein

•  Perhaps the most famous demonstration of the particle properties of electromagnetic waves is the photo-electric effect . The surface of a metal is illuminated with UV light leading to the emission of electrons.  In 1905 Einstein explained this phenomenon by assigning particle properties to the incident UV light.  It was this explanation which, in 1921, earned Einstein the Nobel Prize - not his theory of Relativity !


• UV light is incident on the metal.  The metallic surface is included as part of a circuit, so that the emitted electrons will create a current, measured by the ammeter.


• Einstein assumed that the incident UV light was comprised of a " stream" of  photons (particles of light).  Each photon carries an energy,
  E = hf
  where f is the frequency of the UV light and h = 6.63 x 10 ^-34 J.s, known as Planck's constant   (Planck had previously proposed this expression for the energy of a photon, when attempting to explain black-body radiation ). Upon interaction with the metallic surface, the photon is absorbed by an atom (of the metal) and an electron is emitted.  Energy conservation for this single photon process leads to
  
  hf =  KE of emitted electron  +  energy necessary to release electron from metallic surface,
  or
  hf = (KE)_e^-  +  
  where  is called the "work function" of the metal. Each metal has a characteristic work function.


• Note that the photoelectric effect is not observed for insulators.  In metals each atom has at least one electron which is "loosely" bound to the atom; an UV photon provides enough energy to release these electrons.  In an insulator all electrons are "tightly" bound;  the energy of an UV photon is insufficient to release the electron from the atom.

•  What makes the photoelectric effect so important in the development of quantum mechanics is the fact that it could not be explained by the existing classical laws of  physics.  In fact classical physics lead to contrary predictions.  There are three critical properties in which the classical predictions could not be reconciled with the quantum results.
  
  
  
  
  
  1. Cut-off frequency:  Experimentally it is observed that if the frequency of the incident light is less than a particular (cut-off) frequency, f_c, then no electrons are emitted, independent of the intensity of  the source.
     
     Quantum explanation: If the energy of each incident photons is less than   then electrons cannot be released from the surface of the metal; the cut-off frequency is given by,
     
     hf_c =
     Classical prediction:  There should be no cut-off frequency.  The energy of a wave depends on the intensity (not the frequency). Sooner or later, even a very low intensity light source will deposit enough energy to release an electron.
  
  
  
  
  
  2. Time delay:  Experimentally it is observed that for f > f_c electrons appear immediately upon illumination of the surface, no matter how low the intensity of the source.
     
     Quantum explanation:  The process of electron emission is a  particle process.  Even a single photon can emit an electron.
     
     Classical prediction:  There should be a "time delay" between the source being illuminated and the emission of the first electron. The energy of a wave is "spread out" meaning that, for a weak source, it could take some significant time to accumulate enough energy at the location of a single atom to release an electron.
  
  
  
  
  
  3. Electron kinetic energy:  Experimentally it is observed that for a given source frequency (f > f _c ) the kinetic energy of the emitted electrons is independent of source intensity.
     
     Quantum explanation:  The kinetic energy of the electrons depends on the frequency of the source.  Increasing the intensity of the source increases the number of photons which in turn will increase the number of emitted electrons, but each electron will have the same kinetic energy.
     
     Classical prediction:  Electron kinetic energy should increase with source intensity.  Greater wave intensity implies more energy deposited at the location of each atom.  This additioinal energy appears as increased kinetic energy. 

• Wave properties dominate at low energy (E = hf), equivalent to long wavelength and small frequency, e.g. radio waves.


• Particle properties dominate at high energy, equivalent to short wavelength and high frequency, e.g.X-rays.


• However, at any wavelength (frequency) it is possible to observe both aspects - but not simultaneously .

• The energies involved in atomic processes such as the photo-electric effect are extremely small by everyday standards.  In order to avoid having to keep track of large negative powers of ten when dealing with energy (mass and momentum) a new unit of energy is introduced - the electron volt (eV).

• Definition:
  
   The electron-volt is the energy given to an electron when accelerated through a potential difference of 1 volt
  

   Supplementary Problems 

Why did the chicken cross the road?
Aristotle: "It is the nature of chickens to cross roads."


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu