Einstein's photon model of the photoelectric effect suggested that a photon behaves as a particle.  Other experimental observations also supported the idea that a photon behaves as a particle.  While experimenting with X-rays directed at graphite blocks, Arthur Compton observed what is now known as the  Compton effect .  He noticed that when X-rays are scattered by a graphite block, there is a subtle change in their wavelength and that this change is related to the angle at which the X-rays are scattered.  The scattering of an X-ray when it collides with an electron is now known as  Compton scattering.

Compton effect:  an increase in wavelength of an X-ray as a result of its interaction with matter

 

Compton scattering:  the scattering of an X-ray when it interacts with an electron

 

Compton observed the energy and momentum of the incident X-ray, the scattered X-ray, and the electron and discovered that the collision demonstrated the conservation of momentum and energy-just as it would for an elastic collision between two particles.  The experimental design is similar to that of a photoelectric effect, except using X-rays rather than lower energy EMR.

 

 

 

In terms of energy, Compton found that the total energy of the incident X-ray and the electron before the collision were equal to the total energy of the scattered X-ray and the ejected electron after the collision.  This shows that the collision that occurred is perfectly elastic.

 

In terms of momentum, it is possible to generate an expression for the momentum of a wave using Einstein's equation .  Accordingly, mass and energy are just different forms of the same thing.

 

Manipulating the equation in terms of mass gives .

 

The familiar momentum equation can also be expressed in terms of mass: .

 

Putting the two equations together gives , since v = c for a photon travelling at the speed of light.

 

Substituting produces the following two equations that describe the momentum of a photon: .

 

By measuring the wavelengths of the incident and scattered X-rays as well as the velocity of the ejected electron, Compton was able to analyze the momentum involved in the collision between a photon and an electron.  He determined that the total momentum of the incident X-ray photon was equal to the total momentum of the scattered X-ray photon and the ejected electron.  Indeed, the collision appears to behave as a perfectly elastic collision between two particles.

 

 
Self-Check

Answer the following self-check (SC) questions then click the "Check your work" bar to assess your responses.

 

SC 1.  

Complete the "Concept Check" on page 721 of your physics textbook.

 

SC 2.

Draw a vector addition diagram to show the conservation of momentum applied to the Compton effect shown in the diagram above.

 

   Self-Check Answer

SC 1.

The photon with a wavelength of 2 nm will have the larger momentum because momentum is inversely proportional to wavelength.

 

SC 2.