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Unformatted text preview: WaveParticle Duality Is light a wave or a particle? In many respects it acts like a wave. It undergoes refraction (bending through a different medium), diffraction (scattering through a small opening), interference patterns (positive and negative reinforcement). All of these are wellcharacterized and described in terms of wave equations. On the other hand, the photoelectric effect is successfully explained by viewing the light as consisting of particlelike photons, each photon having a particular energy proportional to its frequency. We say that light has a dual nature and cannot be completely characterized as wave or particle. Sometimes it demonstrates its wavelike properties (refraction, diffraction, interference); sometimes it demonstrates its particlelike properties (photoelectric effect). This waveparticle duality also applies to matter normally considered to be particles. This was first suggested by Louis deBroglie in 1924. Combining quantum mechanics equations with Einsteins E = mc 2 : E = h = = mc 2 Solving the last two terms for : = DeBroglie said that this can be generalized to: for any particle of mass m and velocity v. In this formula, is called the deBroglie wavelength. What is the wavelength of an electron which moves at of the speed of light? For an electron, m = 9.11 x 1031 kg For this electron, v = 3.00 x 10 6 = = ) 10 x 00 . 3 )( 10 x 11 . 9 ( 10 x 626 . 6 6 31 34 = 2.42 x 1010 meter or 0.242 nm This is equivalent to an Xray wavelength. Xrays undergo diffraction patterns by scattering off layers of crystals. Electron diffraction was observed by the DavissonGermer experiment in 1927. Electrons, normally thought of as particles, exhibit wavelike behavior (diffraction). What is the wavelength of a 1.0 kg baseball traveling at 10.0 ? = = ) . 10 )( . 1 ( 10 x 626 . 6 34 = 6.6 x 1035 meter Such a small wavelength is undetectable. A baseball may have wavelike properties, but it has no practical significance. It is not useful to use quantum mechanics to deal with macroscopic objects like baseballs. Heisenberg Uncertainty Principle If an electron has wavelike properties, then how can we exactly specify its location? According to modern quantum mechanics, we cant. There is a limitation to our knowledge of both position and momentum of the electron. The Heisenberg Uncertainty Principle states this mathematically: x p where p = momentum = mv x = uncertainty in position p = uncertainty in momentum If x is low (less uncertainty in locating the electrons position) then p is high (more uncertainty in determining its momentum). Suppose we want to locate the electron. General principle of optics: we cant resolve (locate) an object to any less than the wavelength of the light used. So to locate the electron accurately, we use electromagnetic radiation of a small wavelength. But: = or mv = A low thus means a high momentum for the photon, and the act of measuring the electrons position will alter its momentum. If an electron has wavelike properties, and its position cannot be determined with complete...
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This note was uploaded on 02/20/2012 for the course 160 161 taught by Professor Kim during the Fall '08 term at Rutgers.
 Fall '08
 kim

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