# Wave-Particle Duality

Is it a wave or is it a particle? We've seen from the interference patterns of Young's Double Slit Experiment and other experiments that light acts as a wave. At the same time, phenomenon such as Compton scattering tells us that photons have a particle nature. So which is it? Let's say both. Niels Bohr proposed the Principle of Complimentarity. This basically says, to understand any given experiment, use either the wave theory or the photon theory, but not both. We have to be aware of both - they compliment each other. Unfortunately, we can't visualize this. But wait - this gets harder.

In 1923, Louis de Broglie postulated that, if light behaved as a wave and a particle, then perhaps matter did as well. He said that the wavelength of a particle would be related to its momentum, similar to that of a photon. He gave the wavelength as

where *h* is Planck's Constant, *m* is the particle's mass, and *v* is the particle's velocity. This is called the *de
Broglie Wavelength*. We could figure out the wavelength, for example, of a baseball. Assume a ball with a mass of .15

kg. Suppose it is traveling with a velocity of 25 m/s, then from de Broglie's formula,

l = (6.63 x 10^{-34} J s)/ (.15 kg)(25 m/s) = 1.8 x
10^{-34} m.

This is a pretty small wavelength, and really doesn't fit the wave model of matter as de Broglie viewed it. He assumed atomic=sized particles
with speeds near that of light. So, how about the wavelength of an electron? Let's assume a velocity of 6 x 10^{6} m/s (we could obtain this by solving for kinetic energy of an electron
at a given frequency of light, by solving for the KE of an electron accelerated through a given potential difference, or through other methods) and a mass of 9.1 x 10^{-31} kg:

l = (6.63 x 10^{-34} J s)/ (9.1 x 10^{-31}
kg)(6 x 10^{6}m/s) = 1.2 x 10^{-10} m.

The wavelength of the electron is on the order of 10^{-10}m, or an Angstrom. This happens to be the same order of magnitude as the spacing
of the lattices of some crystal atoms. In 1927, C.J. Davisson and L.H. Germer performed an experiment
scattering electrons on a metal crystal, similar to using a diffraction grating to scatter light. They observed diffraction peaks which matched the de Broglie wavelengths and proved the wave nature
of particles. (Independently and at the same time, George Paget Thomson, son of J.J.
Thomson, performed a different set of experiments which also yielded the same results. Thomson and Davisson shared the Nobel Prize in Physics for the discovery of the wave nature of
matter. In one of the great ironies of Physics, J.J. Thomson receives a Nobel Prize for discovering the electron as a particle and his son wins it for discovering the electron as a
wave.) de Broglie's wavelength is not practical for large particles and should only be used to compute the wavelengths of atomic-sized
particles (neutrons, electrons, protons, positrons, etc.)

For more on the Davisson-Germer experiment, try

http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_DavissonGermer.xmlasp

For more on the wave nature of electrons and baseballs: http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html

http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html#c4

http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

http://www.colorado.edu/physics/2000/quantumzone/photoelectric2.html

For Practice Problems, Try: *Giancoli Multiple Choice Practice Questions* *(Don't worry if you can't solve all of
them just yet!)*