Einstein explained the general observations for the photoelectric effect in 1905 using Planck's quantum hypothesis.  He proposed that the energy delivered by a single incident photon is defined by  E photon  =  hf  and that a certain amount of energy, called the  work function , is required to free an electron from a metal surface.  For example, it takes 4.70 eV of energy to eject an electron from copper, but only 2.30 eV of energy is required to free an electron from potassium.  The work function ( W ) is related to the threshold frequency by Planck's equation,  W = hf o .  
work function:  the minimum energy that a photon can have to cause photoemission from a metal
Each metal has a specific work function.

As illustrated in the graph, the threshold frequency for copper is greater than potassium because copper requires more energy to free an electron.  So, when a photon with energy greater than that of a metal's work function is incident on the surface of the metal, a photoelectron will be emitted.

Einstein's theory also predicted that if an incident photon has more energy than the metal's work function, the ejected photoelectron would leave with some kinetic energy, thus supporting the law of conservation of energy.

 


Lab Simulation:

Experiments performed by Robert Millikan in 1916 provided the evidence to support Einstein's photoelectric theory.  The simulation Photoelectric Effect will be used to explore a simplified version of this work. 


 

Directions:

Shoot a beam of light (flash the light) at the metal plate and observe the effect on surface electrons.  The type of metal as well as the wavelength and intensity of the light can be adjusted.  What does "intensity" mean in a quantum context?

In this simplification of Millikan's experiment, photons above the threshold frequency strike a metal plate in an evacuated tube.  A positive electrode connected to a power supply collects the emitted photoelectrons, thus establishing a photoelectric current. 

When the power supply polarity is reversed, it produces an electric force that effectively repels the photoelectrons and slows the current.  At sufficient voltage-called the  stopping voltage  or stopping potential difference-the photoelectric current observed in the ammeter drops to zero.


 

 

The voltage needed to "stop" the photoelectric current provides an indication of the kinetic energy of the photoelectrons.  Recall that the energy of a charged particle in a uniform electric field is defined by  E = Vq .  In this instance, the equation can be written as  E k  = qV stop , where  q  is the charge of an electron and  V stop  is the minimum voltage required to halt the current.  Therefore, measuring the voltage required to stop a photoelectric current gives the kinetic energy of the photoelectrons. 


Stopping Voltage:  the potential difference for which the kinetic energy of a photoelectron equals the work needed to move through a potential difference,  V.


Graphing the kinetic energy of the photoelectrons (as determined by the stopping voltage) versus the frequency of the incident radiation produces a graphical representation of the photoelectric effect like this one.

This graph is described mathematically by y = mx + b , where y is the kinetic energy of the photoelectrons, x is the frequency of the incident EMR, m is the slope of the line, and b is the y -intercept.  Comparing this equation with the conservation of energy gives a mathematical expression for the photoelectric effect.  According to the conservation of energy principle, the kinetic energy of the ejected photoelectron is equal to the difference between the energy of the incident photon and the work required to free it from the metal surface (the work function).

This can be stated mathematically (and compared to the graph equation) as follows:



According to this equation, the slope of the line for photoelectron energy versus incident light frequency is equal to Planck's constant.  Therefore, the photoelectric effect provides an experimental way to measure Planck's constant.




Physics  (Pearson Education Canada, 2007) p714, fig 14.12.  Reproduced with permission.