# Quantum Mechanics

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Published on August 25, 2009

Author: ankush85

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Quantum Mechanics : 1 Quantum Mechanics Energy is the capacity to do work : 2 Energy is the capacity to do work Kinetic Energy is energy of motion Potential Energy is stored energy Heat is the energy of random motion Energy and Matter are related through Einstein’s famous equation:E=mc2 Matter is really just a very compact form of energy : FNI 1H Quantum Mechanics 3 Energy and Matter are related through Einstein’s famous equation:E=mc2 Matter is really just a very compact form of energy Work and Kinetic Energyw = f d KE = ½ mv2 : FNI 1H Quantum Mechanics 4 Work and Kinetic Energyw = f d KE = ½ mv2 Work is defined as applying a force through a distance. Energy is the capacity of a physical system to do work. The units of energy are the Joule, J which is the same as kg m2/s2 . http://hyperphysics.phy-astr.gsu.edu/hbase/work.html#wep Units of Energy : FNI 1H Quantum Mechanics 5 Units of Energy Energy of a photon : 6 Energy of a photon E=hf E is the energy of the photon f is the frequency of the photon h is Planck’s constant h = 6.626068 x 10-34 m2kg/s Calculate the frequency and energy of both a red (655 nm) and blue (350 nm) photon. Compare both the energy and frequency. : 7 Calculate the frequency and energy of both a red (655 nm) and blue (350 nm) photon. Compare both the energy and frequency. Quantum Mechanics : 8 Quantum Mechanics Photoelectric effect Wave particle duality Characteristic energy Quantum numbers Electron spin Electron tunneling Uncertainty principle Quantum entanglement Photoelectric Effect : 9 Photoelectric Effect It was found that when light shines on certain metals electrons are given off. Whether an electron is given off depends on the energy of the light. The energy of the electron given off depends on the energy of the light. This experiment was used to show that light behaves like particles. Solar cell demo Photovoltaic Photoresistor demo http://www.aip.org/history/einstein/essay-photoelectric.htm http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c2 http://www.solarserver.de/wissen/photovoltaik-e.html http://en.wikipedia.org/wiki/Photocell View DVD “Power of the Sun” 15 minutes Charge Q, Volts V, Electron volts eV, E = QV : 10 Charge Q, Volts V, Electron volts eV, E = QV Charge usually has the symbol Q and the units Coulombs, C. 6.242 x 1018 electrons together have a charge of 1 Coulomb. 1 e- = 1.602 x 10-19 C A volt is electric potential energy. It is measured in J/C. An electron volt is the energy an electron has when it is accelerated through one volt of electric potential. 1 eV = 1.602 x 10-19 J Slide 11: FNI 1H Quantum Mechanics 11 KE = Eγ-w Photoelectric effect Potassium = 2.0 eV needed to eject electron 700 nm 1.77 eV 550 nm 2.25 eV 400 nm 3.1 eV Vmax = 6.22 x 105 m/s Vmax = 2.96 x 105 m/s Eγ = hf e- e- No electron Slide 12: 12 KE = Ephoton-w KE = ½ mv2 h = 6.626x10-34 m2kg/s me = 9.11x10-31 kg c = 2.998x108 m/s 1 eV = 1.602x10-19 J Eγ = hf KE = Eγ – w c = λf Photoelectric Effect Example : 13 Photoelectric Effect Example Calcium work function 2.9 eV Green light 532 nm Will electrons be produced if a green laser is directed onto calcium metal? How fast will the electron be traveling? http://hyperphysics.phy-astr.gsu.edu/hbase/tables/photoelec.html#c1 h = 6.626x10-34 m2kg/s me = 9.11x10-31 kg c = 2.998x108 m/s 1 eV = 1.602x10-19 J Eγ = hf KE = Eγ – w c = λf Photoelectric Effect Practice : 14 Photoelectric Effect Practice Sodium work function 2.28 eV Red light 655 nm Will electrons be produced? How fast will the electrons be traveling? http://hyperphysics.phy-astr.gsu.edu/hbase/tables/photoelec.html#c1 Wave Particle Duality of Subatomic Particles : 15 Wave Particle Duality of Subatomic Particles It turns out that matter can sometimes be modeled best as waves and sometimes best as particles. For part 3 go to the following web site: http://www.colorado.edu/physics/2000/schroedinger/index.html Slide 16: 16 Slide 17: 17 Slide 18: 18 Slide 19: 19 DeBroglie Wavelength : 20 DeBroglie Wavelength Where: m is mass v is velocity h is 6.626 x 10-34 m2kg/s (Planck’s Constant) Characteristic Energy and Spectroscopy : 21 Characteristic Energy and Spectroscopy When gasses are excited by an electric field they give off discrete light. The spectrum of light given off is unique to each element. This means that electrons can only have certain energy levels. By treating electrons as standing waves theory can be made to match experimental results. As energy levels increase more nodes are introduced to the three dimensional waves. Electron Orbitals : 22 Electron Orbitals http://www.shef.ac.uk/chemistry/orbitron/ 1s 2s 2p Demos: Slinky, Flute and Gas Light, diffraction grating glasses Slide 23: 23 1s 2s 3s 2p 3p Spectroscopy : 24 How can we use light to find out about the nature of matter? Spectroscopy Applications of Spectroscopy : 25 Applications of Spectroscopy UV-spectroscopy is used to detect optical endpoints in plasma reactors. Since products in a chemical reaction give off a characteristic spectrum it can be used to determine when a reaction is complete. UV-Vis Spectroscopy is used in many biological applications such as detection of DNA or proteins. X-ray spectroscopy can be used with an electron microcope to determine which elements are present in a sample and in what proportions. Infrared spectroscopy is used to analyze materials and determine their chemical structure.

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