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Unformatted text preview: Class 22 The Hydrogen Atom and the Periodic Table Physics 106 Fall 2011 Press CTRLL to view as a slide show. Last Time Last time we discussed: I Quick Overview of Quantum Mechanics I Blackbody Radiation I Photoelectric Effect I Xray diffraction I Compton scattering I The Foundation of Quantum Mechanics Learning Outcomes Today we will discuss: I Uncertainty Principle Problems I Development of Atomic Models I The Bohr Model (some things are right) I The Schrödinger Model (almost right) A Problem Uncertainty Principle I An electron moving in the z direction passes through a slit that has a width Δ x = 1 μ m. I What is the uncertainty in the x component of its momentum? Δ p x Δ x ≈ h 4 π Δ p x ≈ h 4 π Δ x = 5 . 28 × 10 29 kg m / s Uncertainty Principle I An electron moving in the z direction passes through a slit that has a width Δ x = 1 μ m. I What is the uncertainty in the x component of its velocity? Δ p x ≈ h 4 π Δ x = 5 . 28 × 10 29 kg m / s Δ v x = Δ p x m = 57 . 9 m / s Uncertainty Principle I An electron moving in the z direction passes through a slit that has a width Δ x = 1 μ m. I If the electron velocity is 10000 m/s before it reaches the slit, it may likely be found at angles up to what value? Δ v x = 57 . 9 m / s θ ≈ . 332 ◦ Remember to convert radians to degrees! Uncertainty Principle I An electron moving in the z direction passes through a slit that has a width Δ x = 1 μ m. I If the electron velocity is 10000 m/s before it reaches the slit, it may likely be found at angles up to what value? I What is the electron wavelength? λ = h p = h mv = 7 . 28 × 10 8 m Uncertainty Principle I What is the first minimum in its single slit diffraction pattern? λ = 7 . 28 × 10 7 m λ = a sin θ ( order = 1 ) a θ ≈ λ This is exactly 4 π times the Uncertainty Principle result. Early Atomic Models Thompson Model of the Atom I J.J. Thomson’s model of the atom I A volume of positive charge I Electrons embedded throughout the volume I A change from Newton’s model of the atom as a tiny, hard, indestructible sphere Rutherford Model...
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 Fall '09
 mechanics, Electron, Angular Momentum, Diffraction, Radiation, Uncertainty Principle, Neils Bohr

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