Bohr Atom, Quantum Mechanics, Wave-Particle Properties
Bohr Atom, Quantum Mechanics, Wave-Particle Properties CHEM-1070-30
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This 3 page Class Notes was uploaded by Nina Kalkus on Sunday November 1, 2015. The Class Notes belongs to CHEM-1070-30 at Tulane University taught by Schmehl, Russell in Fall 2015. Since its upload, it has received 24 views. For similar materials see General Chemistry I in Chemistry at Tulane University.
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Date Created: 11/01/15
Chemistry Notes 102715 Atomic Emissions For hydrogenlike atoms lllllllllll l IgtW8Velength lt frequency energy Understanding of Blackbody Radiation 1900 Max Planck Light eXists as quantized packets of energy E hv h 66quot 103934 Js Photoelectric Effect ionization of metal by light 1905 Einstein Energy of light ionization energy kinetic energy of electron energy required to free the electron energy left over hv eVo 12mu2 e charge on the electron u velocity 1913 Niels Bohr Ehv C V E hCk mu2 for an electron u is approaching C hk mu gt linear momentum of the electron 639 F1 centripedal force Ze2r2 F2 centrifugal force mV2r When F1F2gt stable orbit Orbit 11 2Hr mV2r Ze2r2 gt r mV2r2Ze2mm Zcharge on nucleus mvr2Ze2m Angular momentum mvr hrk nh2H r n2h24H2Ze2m n2a0Z gt if you increase the charge you39re going to decrease the radius gt if you increase the mass you39re going to decrease the radius m mass of e approximately 9 103931 kg Bohr radius 53 pm picometers gt for hydrogen smallest possible Bohr Atom Energies Energy of e KE Potential Energy 12 mu2 Ze2r Since forces are equal mu2r Ze2r2gt mu2 Ze2r E 12 Ze2r Ze2r 12 Ze2r En 2H2mZ2e4n2h2 Z2e22n2a0 Proportionality constant ke 899 109 Nm2C2 Bohr Atom Transitions between Energy levels 9a 0 A hv2 Enz E111 Ze22n22a0 Ze22n12a0 Zkee22a01n221n12 4a 0 V 0 Wave Particle Duality Double Slit Experiment Particles create 2 clumps Waves create another wave pattern of frequency Electrons more likely to end up in some spots but not exactly particle or wave pattern random chance as to What position the electron is on the wave function DeBroglie 1924 E mu2 hv mu hvugt momentum p p approximately hv C hk certain momentum will have a certain wavelength But only works for one electron hv 102915 Continuing Quantum Mechanics Isotropic system force applied in any direction system has same effect Anisotropic system forces applied in different directions yield different effects 1913 Bohr Atom 1924 DeBroglie waveparticle duality Einstein Emc2 m relativistic mass of a photon traveling at the speed of light E hv hCk mc2 hck mc h9t p momentum 1926 Bohr and Heisenberg uncertainty in our ability to measure the position and the momentum of an electron ApAX Z h27t X position of object Ap uncertainty in momentum mAv electrons in atoms behave as particlewaves 11 standing wave L mm L M2 De ne wavefunction IX sqrt2Lsinn7tXL xOgtsin0 O xLgtsin7t O xl2Lgtsin7t2l x32Lgtsin37t2 l l2X proportional to the probability of electron being at position X For the electron KE 12mu2 m2u22m p22m From DeBroglie L hp pht KE h2k22mgt 9 now must fit the standing wave 9 2Ln KE n2h28mL2 3l 2 IX gt2X n3gt 2 nodes n2gt 1 node nodes nl In 3 dimensions Enxanyanf h28mnx2Lx2ny2Ly2nb2Lb2 dXdx O gt peaks and troughs of waves Cl12XdX Ogt in ection points nodesendpoints For a standing wave Cl12XClX 27t21X JX sin function Spherical Polar Coordinates z e Kay z Exp proportional to h28pi2mr2 r IrthetaphiRr Ytheta phi Radial wave function Angular wave function
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