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Lecture 5sf

# Lecture 5sf - Wave-Particle Duality Is light a wave or a...

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Unformatted text preview: Wave-Particle 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 well-characterized and described in terms of wave equations. On the other hand, the photoelectric effect is successfully explained by viewing the light as consisting of particle-like 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 particle-like properties (photoelectric effect). This wave-particle duality also applies to matter normally considered to be particles. This was first suggested by Louis deBroglie in 1924. Combining quantum mechanics equations with Einstein’s E = mc 2 : E = h ν = = mc 2 Solving the last two terms for λ : λ = DeBroglie said that this can be generalized to: for any particle of mass m and velocity v. In this formula, λ 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 10-31 kg For this electron, v = 3.00 x 10 6 λ = = ) 10 x 00 . 3 )( 10 x 11 . 9 ( 10 x 626 . 6 6 31 34-- = 2.42 x 10-10 meter or 0.242 nm This is equivalent to an X-ray wavelength. X-rays undergo diffraction patterns by scattering off layers of crystals. Electron diffraction was observed by the Davisson-Germer experiment in 1927. Electrons, normally thought of as particles, exhibit wave-like behavior (diffraction). What is the wavelength of a 1.0 kg baseball traveling at 10.0 ? λ = = ) . 10 )( . 1 ( 10 x 626 . 6 34- = 6.6 x 10-35 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 wave-like properties, then how can we exactly specify its location? According to modern quantum mechanics, we can’t. 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 electron’s position) then ∆ p is high (more uncertainty in determining its momentum). Suppose we want to locate the electron. General principle of optics: we can’t 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: λ = or mv = A low λ thus means a high momentum for the photon, and the act of measuring the electron’s position will alter its momentum. If an electron has wave-like properties, and its position cannot be determined with complete...
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Lecture 5sf - Wave-Particle Duality Is light a wave or a...

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