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by: Mrs. Peter Toy


Mrs. Peter Toy

GPA 3.96

Daniel Dessau

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Daniel Dessau
Class Notes
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This 3 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 2130 at University of Colorado at Boulder taught by Daniel Dessau in Fall. Since its upload, it has received 9 views. For similar materials see /class/232103/phys-2130-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.




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Date Created: 10/30/15
Announcements HW6 due today HW7 due Oct22 Course questionnaire posted on the web in the HWsection due Oct 20 This Friday Crashcourse on LASERS 9Welcome back Dr Evil Midterm 1 results Numberof Students A m a a an o m o Today39s class The Bohr model semiclassical description of the hydrogen atom FCQ Faculty Course Questionnaire Electron Nucleus I I Energy cl Higher levels quot Energy When an electron moves to location further away from the nucleus its ener increases because energy is required to separate positive and negative charges and there is an increase in the electrostatic otential ener of the electron Farm on electron is less but Potential Energyis higher I 9 Electrons at higher energy levels are further from the nucleus Potential energy of the electron in hydrogen D FCE r We de ne electron39s PE as 0 when far far away from the proton 9 Electron39s PE work done by electric field from rywr2D oulomb39s constant D D J39Fdr kqelectqut dr m m r2 D 2 dr 1 Ice PE kqgimqmiy kqelectqpyotm 3 399 9 for hydrogen k I I Coulomb force const Potential energy of a single electron in an atom PE of an electron 39 ance D from the proton is PE ke Ze D For Z protons ke2 1440eVnm distance from proton potential energy How can we calculatethe energy levels in hydrogen Sleol Make preclser ouanlrlalrye obseryalronsl leo 2 Be orealrye amp come up wrlh a model Howlo avold lhe KarBoom7 Bohr Model When Bohr saw Balmer s lormular he came up Wllh a new model lhal would predlcl ll and solve lhe problem ol eleolrons sprralrng rnlo l uoleus The Bohr model has some problems bul ll s slrll uselul Why doesn l lhe eleclron lall lnlo lhe nucleus7 7 Accoldlrlg lo olassroal physlcs 2 houldl a Accoldlrlg lo Bohr 2 uszdoesn 2 a Modern OM le glve a sallslylrlg answer oul you ll havel0 Wall llll nexl week Ollglnal paper Nrels aohr On the Common omloms and memos Phllosoumcal Magazlne Sales s VolumeZS p l 25rJuly1913 Bohr39s approach 1 Treal lhe meohamos olassroal eleolron sornmng around a orolon Newlon s laws assumed lo be yalrd Coulomb loroes provlde oenlnoelal aooeleralron 2 Bohr s hyoolhesrs Bohr had no orool lor lhlsr he lusl assume ll 7 lea s lo correcl resullsl The angular momenlum ol lhe eleolrons rs ouanlrzed rn mullroles om The lowesl angular momenlum rsrl a 142 Bohr Model a 1 Classical mechanics The oenlnpelal accelerallon 17quot W a yzrrs provlded by he coulomb loroe k ezyz V k 14220 Coulomb loroe oonsl Newlol l s second law gt var Inezr1 or The eleclron s Kll lellc energy ls KE I2m v2 The eleclrol l s polenlral enery rs PE r kezy gt E KE PE 12PE J2ke2r Therelore llwe Known We Know E and y elc 9E Bohr Model 2 uuamized angular momentum Bohr assumed lhal lhe angular kHzV2 momenlum ol lhe eleolron oou d only have he ouanlrzed yalues ol V L Andlherelore my mood WMquot Subslllullng lhrs no my leiHeads lo 2 Fun wwhr h 529pm rg Bohr radrus ke m 2 2 EM ERrfnyrrh ER 1 136ev r E Rydberg 2n Energy Bohr Model Results 7 mlzmzth 75 2 529pm rg Bohrradrus k 1m e 2 2 EM ERrlznyrrh ER quot ki 136ev EK Rydberg 2n Energy The Bohr model nol only oredrols a reasonable alomro radrus m bul rl also oredrols lhe energy levels rn hydrogen lo 4 drgrls aoouraoyl Possrble oholon energres E E E gt The Bohr model eXplall ls lhe Rydberg lormulall Only discrete energy levels possible Electrons hop down towards lowest level giving oll photons during the jumps Alums are stable in lowest level stancetrom proton potential energy Bohr couldn39t explain whythe angular momentum is quantized but his model lead to the FlydbergBalmer formula which matched to the e perimen a observations verywell He also predicted atomic radii reasonably well and was able to calculate the Rydberg constant 11 Successes of Bohr Model 39Explains39 source of Balmer formula and predicts empirical constantR Rydberg constant from fundamental constants R1912mmkze 47wh5 Explains why R is different for different single electron atoms called hydrogenlike ions Predicts approximate size of hydrogen atom Explains sort of why atoms emitdiscrete spectral lines Explains sort of why electron doesn39t spiral into nucleus Shortcomings of the Bohr model Why is angular momentum quantized yet Newton s laws still work Why don t electrons radiate when they are in fixed orbitals yet Coulomb s law still s No way to know a prioriwhich rules to keep and which to throw out Can39t explain shapes of molecular orbits and how bonds work Can t explain doublet spectral lines Questions Which of the following principles of classical physics is violated in the Bohr model gt Opposite charges attract with alorce inversely proportional to the square of the distance between them The lorce on an object is equal to its mass times its acceleration Accelerating charges radiate energy Particles always have a wellrdelined position and momentum moon All ol the above Note that both A amp B are used in derivation of Bohr model Ideas for how to resolve these problems 9 Matter waves TZD Chapter 6 Next class is on LASERS Welcome back Dr Evil


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