1Wed. Apr 30, 2008 Phy208 Lecture 271Final Exam:Monday May 1212:25 - 2:25 pmIngraham B10Course evaluationsPlease evaluate Prof. Rzchowski today.Start lecture ~ 8:55 amThis week’s honors lecture: Prof. Ron Wakai, “Biomagnetic imaging”Wed. Apr 30, 2008 Phy208 Lecture 272Summary of quantum numbers• n : describes energy of orbit• ℓdescribes the magnitude of orbital angular momentum• m ℓ describes the angle of the orbital angular momentumFor hydrogen atom:Wed. Apr 30, 2008 Phy208 Lecture 273Modified Bohr model• Different orbit shapesBig angular momentumSmall angular momentumThese orbits have same energy,but different angular momenta:Rank the angular momentafrom largest to smallest:ABCa) A, B, Cb) C, B, Ac) B, C, Ad) B, A, Ce) C, A, B ! r L =r r "r p ( )Wed. Apr 30, 2008 Phy208 Lecture 274Orbital mag. quantum number mℓ• Directions of ‘orbital bar magnet’ quantized.• Orbital magnetic quantum number– m ℓ ranges from - ℓ, to ℓin integer steps (2ℓ+1) different values– Determines z-component of L:– This is also angle of LFor example: ℓ=1gives 3 states: ! Lz= mlhWed. Apr 30, 2008 Phy208 Lecture 275Electron spinNew electron property:Electron acts like abar magnet with N and S pole.Magnetic moment fixed……but 2 possible orientations of magnet: up and down• Spin downNS! ms= "1/2Described byspin quantum number msNS! ms= +1/2• Spin upz-component of spin angular momentum ! Sz= mshWed. Apr 30, 2008 Phy208 Lecture 276Include spin• Quantum state specified by four quantumnumbers:– Three spatial quantum numbers (3-dimensional)– One spin quantum number ! n, l, ml, ms( )2Wed. Apr 30, 2008 Phy208 Lecture 277Atomic Quantum number summary• Hydrogen atom states– n: principle quantum number• Determines energy• (n=1, 2, 3…)– ℓ: orbital quantum number• Magnitude of orbital angular momentum• ℓ=0, 1, 2, … n-1– mℓ: orbital magnetic quantum number• Orientation of• mℓ = - ℓ, - ℓ+ 1, … 0, … ℓ- 1, + ℓ– ms: spin quantum number• Orientation of• ms=-1/2, +1/2 ! n, l, ml, ms( ) ! L = h l l +1( ) ! r L ! Lz= mlh( ) ! r S Sz= msh( )Wed. Apr 30, 2008 Phy208 Lecture 278Quantum Number QuestionHow many different quantum states exist with n=2?A. 1B. 2C. 4D. 8ℓ = 0 :ml = 0 : ms = 1/2 , -1/2 2 statesℓ = 1 :ml = +1: ms = 1/2 , -1/2 2 statesml = 0: ms = 1/2 , -1/2 2 statesml = -1: ms = 1/2 , -1/2 2 states2s22p6There are a total of 8 states with n=2Wed. Apr 30, 2008 Phy208 Lecture 279QuestionHow many different quantum states are in a5g (n=5, ℓ =4) sub-shell of an atom?A. 22B. 20C. 18D. 16E. 14ℓ =4, so 2(2 ℓ +1)=18.In detail, ml = -4, -3, -2, -1, 0, 1, 2, 3, 4and ms=+1/2 or -1/2 for each.18 available quantum states for electronsWed. Apr 30, 2008 Phy208 Lecture 2710Putting electrons on atom• Electrons obey Pauli exclusion principle• Only one electron per quantum state (n, ℓ, mℓ, ms)Hydrogen: 1 electron one quantum state occupiedoccupiedunoccupiedn=1 statesHelium: 2 electronstwo quantum states occupiedn=1 states ! n = 1,l = 0,ml= 0, ms= +1/2( ) ! n = 1,l = 0, ml= 0,ms= +1/2( ) ! n = 1,l = 0, ml= 0,ms= "1/2( )Wed. Apr 30, 2008 Phy208 Lecture 2711Other elements: Li has 3 electronsn=1 states,2 total, 2 occupiedone spin up, one spin downn=2 states,8 total, 1 occupied ! n = 1l = 0ml= 0ms= +1/2" # $ $ $ $ % & ' ' ' ' ! n = 1l = 0ml= 0ms= "1/2# $ % % % % & ' ( ( ( ( ! n = 2l = 0ml= 0ms= +12" # $ $ $ $ $ % & ' ' ' ' ' ! n = 2l = 0ml= 0ms= "12# $ % % % % % & ' ( ( ( ( ( ! n = 2l = 1ml= 0ms= +12" # $ $ $ $ $ % & ' ' ' ' ' ! n = 2l = 1ml= 0ms= "12# $ % % % % % & ' ( ( ( ( ( ! n = 2l = 1ml= 1ms= +12" # $ $ $ $ $ % & ' ' ' ' ' ! n = 2l = 1ml= 1ms= "12# $ % % % % % & ' ( ( ( ( ( ! n = 2l = 1ml= "1ms= +12# $ % % % % % & ' ( ( ( ( ( ! n = 2l = 1ml= "1ms= "12# $ % % % % % & ' ( ( ( ( ( Wed. Apr 30, 2008 Phy208 Lecture 2712Atom ConfigurationH 1s1He 1s2Li 1s22s1Be 1s22s2B 1s22s22p1Ne 1s22s22p61s shell filled2s shell filled2p shell filledetc(n=1 shell filled -noble gas)(n=2 shell filled -noble gas)Electron Configurations3Wed. Apr 30, 2008 Phy208 Lecture 2713The periodic table• Atoms in same columnhave ‘similar’ chemical properties.• Quantum mechanical explanation:similar ‘outer’ electron configurations.Be2s2Li2s1N2p3C2p2B2p1Ne2p6F2p5O2p4Mg3s2Na3s1P3p3Si3p2Al3p1Ar3p6Cl3p5S3p4H1s1He1s2CaK As4p3Ge4p2Ga4p1Kr4p6Br4p5Se4p4Sc3d1Y3d28 moretransition metalsCa4s2K4s1Na3s1Wed. Apr 30, 2008 Phy208 Lecture 2714Atoms with more than one electron• Electrons interact withnucleus (like hydrogen)• Also with other electrons• Causes energy to dependon ℓ in addition to n1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4dStates fill in order of energy:Wed. Apr 30, 2008 Phy208 Lecture 2715Hydrogenwavefunctions• Radial probability• Angular not shown• For given n, probabilitypeaks at ~ same place• Idea of “atomic shell”• Notation:– s: ℓ=0– p: ℓ=1– d: ℓ=2– f: ℓ=3– g: ℓ=4Wed. Apr 30, 2008 Phy208 Lecture 2716Na Optical spectrumNa589 nm, 3p -> 3s• 11 electrons– Ne core = 1s2 2s2 2p6(closed shell)– 1 electron outsideclosed shellNa = [Ne]3s1• Outside (11th) electroneasily excited to otherstates.Wed. Apr 30, 2008 Phy208 Lecture 2717How do atomic transitions occur?• How does electron in excitedstate decide to make atransition?• One possibility: spontaneousemission• Electron ‘spontaneously’drops from excited state– Photon is emitted‘lifetime’ characterizes averagetime for emitting photon.Wed. Apr 30, 2008 Phy208 Lecture 2718Another possibility:Stimulated emission• Atom in excited state.• Photon of energy hf=ΔE ‘stimulates’ electron to drop.Additional photon is emitted,Same frequency,in-phase with stimulating photonOne photon in,two photons out:light has been amplifiedΔEBefore Afterhf=ΔEIf excited state is ‘metastable’ (long lifetime for spontaneousemission) stimulated emission dominates4Wed. Apr 30, 2008 Phy208 Lecture 2719LASER: Light Amplification byStimulated Emission of RadiationAtoms ‘prepared’ in metastable excited states…waiting for stimulated emissionCalled ‘population inversion’(atoms normally in ground state)Excited states stimulated to emit photon from a spontaneousemission.Two photons out, these stimulate other atoms to emit.Wed. Apr 30, 2008 Phy208 Lecture 2720Ruby Laser• Ruby crystal has the atoms which will emit photons• Flashtube provides energy to put atoms in excited state.• Spontaneous emission
View Full Document
Unlocking...