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**Unformatted text preview: **Class 22 The Hydrogen Atom and the Periodic Table Physics 106 Fall 2011 Press CTRL-L 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 X-ray 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 Schrdinger Model (almost right) A Problem Uncertainty Principle I An electron moving in the z direction passes through a slit that has a width x = 1 m. I What is the uncertainty in the x component of its momentum? p x x h 4 p x h 4 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 x = 1 m. I What is the uncertainty in the x component of its velocity? p x h 4 x = 5 . 28 10- 29 kg m / s v x = 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 x = 1 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? v x = 57 . 9 m / s . 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 x = 1 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? = h p = h mv = 7 . 28 10- 8 m Uncertainty Principle I What is the first minimum in its single slit diffraction pattern? = 7 . 28 10- 7 m = a sin ( order = 1 ) a This is exactly 4 times the Uncertainty Principle result. Early Atomic Models Thompson Model of the Atom I J.J. Thomsons model of the atom I A volume of positive charge I Electrons embedded throughout the volume I A change from Newtons model of the atom as a tiny, hard, indestructible sphere Rutherford Model...

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