By: Conor Donohue and Jen Davis

Waves are everywhere. But what makes a wave a wave? What characteristics, properties, or behaviors are shared by all the phenomenon which we typically characterize as being a wave? How can waves be described in a manner that allows us to understand their basic nature and qualities?

 A wave can be described as a disturbance that travels through a medium from one location to another location.

 The repeating and periodic disturbance which moves through a medium from one location to another is referred to as a wave.  A slinky would be an example of a wave.

 Introduced the theory of electron waves, including wave –particle duality and the theory of matter.  According to de Broglie, a particle is a wave.  He proposed that the relationship of wavelength lambda to momentum p would determine the wavelength of any matter, in the relationship: l  lambda = h / p.

 Performed a classic experiment in which a beam of electrons of known momentum (p) was directed at an angle onto a nickel surface. The angles of reflected electrons were measured and the results matched up with de Broglie's hypothesis for electron wavelength.

 A wave-particle dual has been found to be characterized by electrons  The Davisson and Germer model established the evidence of wave nature with electrons  The evidence for the description of light as waves is proven by the photoelectric effect which shows evidence of particle nature.

 The photoelectric effect refers to the emission, or ejection, of electrons from the surface of, generally, a metal in response to incident light.  Energy contained within the incident light is absorbed by electrons within the metal, giving the electrons sufficient energy to be 'knocked' out of, that is, emitted from, the surface of the metal.

 Particle duality exhibits both wave-like and particle-like properties  The central concept of "particle" and "wave" fully describes the behavior of quantum mechanics  Quantum mechanics are a set of scientific principles describing the known behavior of energy and matter.  The uncertainty principle states that certain pairs of physical properties, like position and momentum.

- Δ here indicates standard deviation, a measure of spread or uncertainty; - - x and p are a particle's position and linear momentum respectively. - - is the reduced Planck's constant (Planck's constant divided by 2π).

 The baseball displays wave-particle duality: the path of the baseball could not be precisely determined. The map shows where a "pitched" electron will cross home plate.  The probability of finding the electrons at various locations outside the nucleus and on the field is shown on the map.  The probability map is called an orbital.

1) A wave can be described as a) disturbance that travels through a medium from one location to another b) distance from one location to another c) an ocean current d) a hand gesture used to say hello/goodbye 2) True/false A slinky could be used as an example of a wave.

3) According to de Broglie, a __________is a wave. a) Particle b) Nucleus c) Scientist 4) A wave-particle dual has been found to be characterized by a) Protons b) Neutrons c) Electrons d) The Nucleus 5) True/False Quantum mechanics are a set of scientific principles describing the known behavior of energy and matter.

6) The photoelectric effect refers to the emission, or ejection, of from the surface of, generally, a metal in response to incident light. a) Protons b) Electrons c) Neutrons d) Photo-electricons 7) What is the formula of uncertainty principle? a) b) E=mc^2 c) F=ma d) A=b*h

8) Which picture shows particle duality a) c) b) d)

 1) A  2) True  3) A  4) C  5) True  6) B  7) A  8) C

Energy + Matter

 Publicized early in the debate about whether light was composed of particles or waves, a wave-particle dual nature soon was found to be characteristic of electrons as well.  The evidence for the description of light as waves was well established at the turn of the century when the photoelectric effect introduced firm evidence of a particle nature as well.

 The particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer established the wave nature of the electron.

 The details of the photoelectric effect were in direct contradiction to the expectations of very well developed classical physics.  The explanation marked one of the major steps toward quantum theory.

 The remarkable aspects of the photoelectric effect when it was first observed were:  1. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

 Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light.  Whatever was knocking the electrons out had an energy proportional to light frequency.

 hp?sim=Photoelectric_Effect hp?sim=Photoelectric_Effect

 Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea.  Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.  Similarly, neutron diffraction uses neutrons with a wavelength of about one ångström, the typical spacing of atoms in a solid, to determine the structure of solids.

1. Bill and Ted’s experiments established the wave nature of the electron. T/F 2. The details of the photoelectric effect were NOT in direct contradiction to the expectations of very well developed classical physics. T/F 3. Wave-particle duality is exploited in electron microscopy. T/F 4. The explanation of the photoelectric effect marked one of the major steps toward quantum theory. T/F 5. Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. T/F