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# Section 5.1: Wave and Particle Properties

In the late 1800s, there was a clear division between objects: particles and waves. The resounding success of Maxwell's equations in explaining electricity and magnetism also included a description of light as an electromagnetic wave. In this formulation, light was considered a wave. Consider the following list and identify which of the following describes a wave and which describes a particle:

• Localized.
• More energy, it moves faster.
• One can cancel another one out.
• Collides with one thing at one time.
• Can bend around a corner.
• If two doors are open, part can pass through one and part can pass through the other.

Start the localization animation.  Where exactly is a wave located?  How can you describe its location at any one point in time?  For a traveling sinusoidal wave, it is located everywhere and asking for its location makes no sense. On the other hand, it is easy to identify where the ball is at a given instant of time.

Increasing the energy of particles means increasing its speed (KE = 1/2 mv2), but for a classical wave of fixed wavelength, an increase in energy (in terms of power delivered) means an increase in amplitude (peak height).

The third and fourth attributes on the list concern what happens when two objects collide.  When waves collide, they add or superimpose, while balls bounce off of each other. It is difficult to conceive of two balls colliding into each other and briefly canceling each other out so they disappear altogether. Notice what happens as the waves interact in the animation. There are times when the waves cancel each other out and times when they add to form a bigger wave.

Finally, the last two properties, diffraction and interference, are purely wave phenomena.  Diffraction, is simply the bending of light around a sharp edge: a spreading of the wave front (shown in the ripple tank animation). Interference occurs when waves collide and a good example of when this happens is when a wave passes through a double-slit (two doors).

Given these very distinct properties, it was quite surprising when experiments showed that light, although often described as a wave, could not be described solely as a wave. The photoelectric effect and the Compton effect were difficult to explain unless you described light as a particle (Section 5.2).   Similarly, although the electron could be described as a point particle, experiments showed that electrons do diffract and interfere (Sections 5.5, 5.6, and 5.7).  Thus, there was no clear dividing line between waves and particles. All matter, as it turns out, must be described as both a wave and a particle (complementarity).  This property is also called wave-particle duality. How we make a measurement determines whether we will be able to explain the outcome by applying wave or particle properties. If we perform an experiment designed to measure wave-like properties (such as the double-slit experiment), we see wave-like properties (an interference pattern).  If we perform an experiment designed to measure particle-like properties (such as the photoelectric effect), we see particle-like properties (light exciting an electron from a metal).