Quantum Mechanics and Electron Configurations with Periodic Properties PDF

A Cursory Guide to Quantum Mechanics and Electron Configurations with a Slight Lead-in to Periodic Properties tronconfiguration 32 Part I: Waves and Light Creating a transverse pulse Shake it continuously with the...

A Cursory Guide to Quantum Mechanics and Electron Configurations with a Slight Lead-in to Periodic Properties tronconfiguration 32 Part I: Waves and Light Creating a transverse pulse Shake it continuously with the wall very, very far away (so no reflection occurs) 459 vibration pulse vibration is perpendicular to directionof propagation Anatomy of a transverse wave Crest topof thewave equilibrium line trough of bottom thewave Kwangth Let’s look at this differently…… of direction propagation O Ibkthxaxisisti.n t M time I Period and Frequency…… time Period: __________ that it takes for a wave to repeat itself (or for any cycle to repeat). Units: 5 seconds Frequency: How many _____________ cycles you have in a given period of time. Units: Hertz Hz Relation between period and frequency….. period t L assec period T t Yos 10 Holtz s sCEF SH frequency try f 2s 44 IHz  f f f 0 F f if frequency Constructive interference A β A B They hitcombine andthen their AB separate g antinode ways AB B A B A Destructive interference A B theymeet cancelout and movealong A B Boundary Conditions pulse incident theendcanmove free boundary ref reflectedpulse fixed boundary Standing Waves Standing waves are formed by alternate spatial constructive and destructive interference as two identical waves travel in opposite directions. antinode node node antinode node antide node we For a standing wave, as the frequency increases, the energy ____________. increases Light as a transverse wave… Brightness of light (very closely related to the intensity of light)….. All electromagnetic waves travel at the same speed in safe a vacuum (c = 3 x 108 m/s) I p in istn spted oflight c=f Energy of light oscillatingelectron oscilatingelectricfield  f 3H invite what does he see after I sec tithe he's looking at a Diffraction: _______________ bending of a wave around a barrier, or through an opening in a barrier Only waves diffract……particles do not diffract!! this doesnt happen The marble stays the Wood same size 0000 wood Diffraction and interference crest there t constructiveinterference waterwaves crests crestwith trough destructiveinterference Classical physics……… light demonstrates diffraction and interference, so light is definitively a wave But…maybe quantum mechanics says differently…… Max Planck’s Interpretation of blackbody radiation (1900) Blackbody radiation: the spectral (electromagnetic – EM) distribution given off by an object by virtue of its temperature Equivalent way of thinking about blackbody radiation ftp resonator Cavity Me o0 ooanode n What distribution of EM waves would be produced by a cavity at a certain temperature  oflight brishtness Eight is proportional to f.az A MT Classicallythere isno limitto light howsmalltheentry oflight canbe  According to classical physics, the EM waves allowed must form standing waves. All of these waves have the same energy. That energy is greater if the cavity has a higher temperature. The problem is that an infinite number of standing waves satisfy the boundary so, in principle the total energy of a black body is infinite. f classical physics eachstandingwavehas someenergy Emin Planck’s resolution Light of a certain frequency, has a minimum energy E Emin = hf frequency E where h is Planck’s constant E (a really small number, h = 6.6 x 10-34 J-s ) E If Emin > E (the energy the standing wave is supposed to it vii it have) then the standing wave Doesn’t exist in the black body. wave Foes the sonowthenumberofwavesisfiniteandnot infinite  light I 111 if I screen light f IEEE S s diffraction gradient  Einstein’s interpretation of the Photoelectric Effect (1905) Simplest set-up A little more of what’s going on…. p light This is pretty much a solar cell. photoemissive surface The AP version of this is Photoelectron (outermost (valence) Spectroscopy (PES). It is tuned to specifically electrons pop off) cause emission of inner or outer electrons  I photocurrent pop off Ammeter electrons measures current photocurrent Remember, according to classical physics, to profial Elight.  fA2 where f is the frequency and A2 is proportional to the brightness (intensity) of the light. Series of experiments………….  itlight kE violet bright off More electronspop Same asdim violetlight  afewelectronsp.p.gg fit Kinetic greenislessthan energyd im the KEofviolet bright i bc Violethas moreelectronspopoff ELEY saggy ingreenbutstillless Flight fA Nothing happens photocurrent 0 T sonothinghappens A guy is collecting shells, a tsunami waves comes over her but nothing happened to her ÉÉi happens 100ft high land Nothing happens totheblindingredlight similar A little, tiny wave hits the guy but he goes ying TIE 1mmhigh  Energy In leftover Absorbed Energy Energy ripoff anelectronyou acatan need amount ofenergy Ephoton W KE electrons W workfunction is bythesurface energyabsorbed KE different w different surfaces electrons Ephoton W hf. E KEewns photon hf I photon hf This isfor monochromatic 1 lightismadeupofphotons minimmers photon samecolor more photons brighterlightsmoreenergy samewavelength min Iphoton fx f f re L KEatrons  ex brightvioletlighthadsame KEasdimvioletlight Basic Energy Balance KE electron photocurrent Intensity of monochromatic light Intensity monochromatic light brightness hecolor KEe hf W At what is I KE y mxb jsi.peh If onephoton doesnt worknone ofthemwar electrons KE hf w muffidly O hfo W Ephoton hf é barelypopoff W_ qq.mg g So here is what we are left with…… Diffraction and interference of light: wave light is a ______________. Photoelectric Effect light is made up of particles (photons) lightsometimesacts like sometimes particle a waveand a This is an example of the Wave/Particle duality. poly 1C one  Momentum lighthasnomass but wasthoughttohavemomentum p mv DeBroglie (1924) After Einstein Plight So since light which was classically considered a wave si has a particulate aspect to it……… maybe ………………. particles canhave a wave aspect small very particle to have a measurable wavelength I in the ______________ momentum in practice will need a really, really small mass Protons/neutrons……..too heavy where m is mass and v is velocity electrons………..smallenough measurable wavelength  diffractionand interference 3 Sowavenature wasproven a a firedelectronsintonickelcrystal theholesmakethenickelcrystal actlike a diffraction grating  What is the wave nature of a particle? Max Born (1926) The wave aspect of a particle relates to the probability of finding the particle in a given region of space. How to calculate the wave function function, in 1 dimension ……………Schrodinger Wave Equation…..don’t worry you won’t have to use this 2 = probability of finding particle in given region of space Why we really can’t even talk about circular orbits for electrons in atoms…. Heisenberg uncertainty principle: The better you know the position of an electron, the less you know about how it is moving (and vice versa) ftp.tmfee ee ftp.m positi on Let’s imagine that you were trying to show that an electron has a circular orbit in hydrogen…. To find the position of the electron, you’d have to strike with something, like a photon. But then the photon would disturb whatever path it was on, so you wouldn’t know how it was/is moving So it’s impossible to know the trajectory (path) of an electron. If that is true, then it becomes meaningless to even talk about electrons having a path at all. So electrons (particles) have a wave nature to them. That wave aspect can be calculated through the Schrodinger Wave Equation, which is in terms of , the wave function.  is the probability of finding the electron (particle) in a given region of space. It’s meaningless to talk of electrons having trajectories (paths) since you can never know what they are. The particle in a box ( a thought experiment)….. Imagine a particle exists in a 1 dimensional box. The walls of the box are infinitely strong and would take an infinite amount of energy to breach. Describe and  for each of the energy levels the particle might occupy Y boxbc it wouldneedinfinite energy  Lowest Energy Level Next Energy Level    probability  M n allof these solutions have electron intheboxCantonnew discrete energy energy So the wave equation solutions for an atom are more complicated: 1) varying potential energy part of equation 2) 3 dimensional (spherical coordinates) 3) more complicated boundary conditions But, in their heart and soul, these solutions are really just the ‘particle in the box’  1 type of s orbital 3 types of p orbitals 8 5 types of d orbitals Shapes of orbitals are really just a map, diagram, of where electron is most likely to be 7 types of found. f orbitals Each orbital can hold up to 2 electrons. Difference between 1s, 2s, 3s orbitals Difference between 2p, 3p and 4p orbitals Maximum number of electrons in each principal energy level How orbitals get filled in…. A way to remember the order….. Zé 8é A t A 18e x 325 secondary fe different spins 2e Pauliexclusion principle electroninthesame orbital have  s Periodic Table and 49 2s 2p3pYpSpGp Electron Configuration Period (rows) = Energy Level Groups (columns) have same ending electron configuration (thus similar chemical properties)