h mc What about matter? Louis de Broglie ( ) French 8-5 Two ideas leading to a new quantum mechanics

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1 8-5 Two ideas eading to a new quantu echanics What about atter? Louis de Brogie ( ) French Louis de Brogie Werner Heisenberg Centra idea: Einstein s reativity E=c Matter & energy are reated Louis de Brogie de Brogie started with Einstein s eqn. Then he used Panck s reationship E = c E = hν c = hν Reca inear oentu: p = u p = c = hν c Next he used the eqn. c = λν p = c = p = c = hν c hν λν de Brogie arrived at the foowing eqn. h p = c = or λ = λ This is vaid for ight What about atter? h c Note: Photons have zero rest ass but wi have a reativistic ass and oentu

2 de Brogie equation predicts that atter shoud have waves h p = u = or λ = λ h u de Brogie s equation Einstein heped hi get his Ph.D. thesis accepted! λ = What is the waveength of an e - traveing at 1.00 x s -1 h u x10 J s λ = x10 kg 1.00x10 [Note: 1.0 J = 1.0 kg.. s - ] 7 s -1 = 7.7x10-11 or 7.7 p What is the waveength of a baseba traveing at 44 /s (ass = kg) λ = h u What is the waveength of a baseba traveing at 44 /s (ass = kg) h λ = [Note: 1.0 J = 1.0 kg.. s - ] u x10 J s -34 λ = = 1.04x kg 44.0 s The Uncertainty Principe The Uncertainty Principe: Ipications Δx Δp h 4π Δx Δp h 4π Uncertainty in position Uncertainty in oentu h = Panck s constant Uncertainties are standard deviations Liits to what we can know Causaity repaced with indeterinacy Einstein was deepy bothered by this as was Wien!!!!

3 Heisenberg s γ-ray Microscope Thought experient: Gedanken Heisenberg s γ-ray Microscope Thought experient: Gedanken Aoeba Microscope resoution is iited by λ of ight To easure position of an eectron Need very short waveength ight, i.e., γ-rays - Eectron position? Heisenberg s γ-ray Microscope Thought experient: Gedanken Heisenberg s γ-ray Microscope Thought experient: Gedanken γ-ray ν = 10 s -1 E γ = hν = 6.66 x J s. 10 s -1 E γ = 6.66 x 10-1 J But easiy ionize the e - E IE =.179 x J E γ = 6.66 x 10-1 J - Eectron position? - Eectron position? Heisenberg s γ-ray Microscope Thought experient: Gedanken Heisenberg s γ-ray Microscope Thought experient: Gedanken But easiy ionize the e - E IE =.179 x J E γ = 6.66 x 10-1 J Eectron takes off! - Excess energy goes into kinetic energy Changes the oentu -

4 Let s do an uncertainty cacuation What is the uncertainty in the position of a baseba ( = kg), if its veocity is easured with an uncertainty of s -1? 9.5 Two New Ideas Δx =? Δu = s -1 Δx Δp h 4π = kg h so Δx 4πΔp p = u so Δp = Δu = 0.145kg 0.11 s -1 Δp = kg s -34 h 6.66x10 Js Δx = 4πΔp 4π kg s -1 = 3.3x10-33 Very ow uncertainty -1 Heisenberg: Led Nazi effort to buid A-bob Uncertainty: The Life & Science of Werner Heisenberg by David C. Cassidy Werner Heisenberg and Nie Bohr Moe Berg

5 Copenhagen: A pay Bohr & Heisenberg Copenhagen by Michae Frayn Need Measureent to know position But act of easureent Changes Syste Need Measureent to know position But act of easureent Changes Syste Fundaenta quantu uncertainty Can no onger tak about defined orbits Fundaenta quantu uncertainty Can no onger tak about defined orbits Copenhagen Interpretation Quantu Mech. Probabiities and the act of easureent Bohr: Danish Founded Nies Bohr Institute University of Copenhagen Bohr Institute

6 Bohr entored any scientists Copenhagen interpretation of QM Einstein & Bohr debated QM Einstein: deterinistic. Bohr: probabiity Bohr Heisenberg Paui Bohr Institute "Not often in ife has a an given e so uch happiness by his ere presence as you have done," Einstein wrote to Bohr Phiosophica Batte Decades Long "God does not pay dice," Einstein "The Lord is subte but not aicious. Einstein At one point Bohr retorted "Einstein, stop teing God what to do!" Nice book on current state of affairs Taing the Ato by Han Christian von Baeyer 8-6 Wave Mechanics Cassica Waves Describe by wave equation: Ψ(r,t) Function of space & tie Soution to a type of differentia eqn. Standing waves in a string

7 1D Wave Equation Apitude ψ i( π t ) ( x, t) = A e kx - ν i = k = 1 π λ 1D Wave Equation Apitude ψ i = i( π t ) ( x, t) = A e kx - ν k = 1 π λ Spatia 1D Wave Equation Apitude ψ i = i( π t ) ( x, t) = A e kx - ν k = 1 π λ Spatia Wave vector Tepora 1D Wave Equation Apitude ψ i = i( π t ) ( x, t) = A e kx - ν k = 1 π λ Spatia Tepora Wave equation copetey specifies a cassica wave You don t have to eorize this equation! Standing Waves Standing Waves

8 Standing Waves Standing Waves For soe interesting video cips on standing waves take a ook at the foowing website: Standing%0waves&u=1&ie=UTF-8&sa =N&tab=wv# Standing Waves on a String L Standing Waves on a String L n = 1 n = n = 3 λ/ λ/ 3λ/ Osciating sections Constructive interference if L=nλ/ Standing Waves on a String L Standing Waves on a String L Nodes No osciations #Nodes=n+1 n = 3 Nodes #Nodes=n+1

9 Standing Waves: String Instruents Standing Waves on a String e - as a standing wave Vioin D standing waves on guitar body L=nλ/ constructive interference n=1,,3, n not integer destructive interference de Brogie equation: atter a wave Probe: Devise a wave equation for eectron Erwin Schrödinger soved it de Brogie equation: atter as a wave Probe: Devise a wave equation for eectron Erwin Schrödinger soved it: Muti-tasker! Erwin Schrödinger Austrian Nobe Prize Physics 1933 Erwin Schrödinger Austrian Nobe Prize Physics 1933 Schrödinger Wave Equation Schrödinger Wave Equation Wave function of e - HΨ = EΨ HΨ = EΨ Haitonian Energy Haitonian: Kinetic energy part & potentia energy part

10 It gets reay copicated HΨ = EΨ Ψ HΨ = ih Tie-dependent equation t Tie-independent equation It gets reay copicated Haitonian for H ato h H = - where e e - 4πε o r = + x y + z Are we responsibe for the Schrödinger Eqn.? No! Quotation fro Richard P. Feynan "Where did we get that [Schrödinger's equation] fro? It's not possibe to derive it fro anything you know. It cae out of the ind of Schrödinger." --Richard P. Feynan Wave functions are soutions to Eqn Wave functions: radia & anguar parts z radia variabe Ψ(r, θ, φ) anguar variabes y θ φ (x,y,z)=(r,θ,φ) r x Spherica poar coordinates The iportant point to reeber Wavefunction squared = probabiity Ψ(r, θ, φ) = e - Probabiity Max Born: Probabiity Concept Ψ(r, θ, φ) = e - Probabiity Probabiity of finding the eectron in space Deterines shapes of eectron orbitas Max Born: Physics Nobe

11 Eectron Charge Density Probabiity - Ψ(r, θ, φ) + - = e Probabiity Bohr: Eectron Orbits Cassica Trajectories Eectron orbita 3D space in which you wi find the eectron with a defined probabiity Can ony sove Schrödinger eqn. for specia cases Partice in a box Hydrogen ato: H Hydrogen oecue: H Can ony sove Schrödinger eqn. for specia cases Partice in a box Hydrogen ato: H Hydrogen oecue: H Hydrogen-ike species, e.g., He Quantu Nubers 8-7 Quantu Nubers & Eectron Orbitas Quantu Nubers n s principa quantu nuber anguar oentu quantu nuber agnetic quantu nuber spin quantu nuber 8.7 Quantu Nubers Goa: Deterine Eectronic Configurations Need to Assign quantu nubers Specific rues for quantu nubers 8.7 Quantu Nubers Principa Quantu Nuber: n n can be a non-zero positive integer n = Principa Quantu Nuber n = 1,, 3, 4,...

12 8.7 Quantu Nubers n is reated to the energy eve: principa she orbita Higher n=5 n=4 Energy n=3 n= 8.7 Quantu Nubers Orbita Anguar Moentu Quantu No. is zero or positive integer up to n-1 = Anguar Moentu Quantu No. = 0,1,, 3,..., n -1 Lower Energy n=1 E 8.7 Quantu Nubers is reated to the subeve or subshe ( orbita ) 8.7 Quantu Nubers is reated to the subeve or subshe = 0 =1 = = 3 s subshe p subshe d subshe f subshe 8.7 Quantu Nubers Magnetic Quantu Nuber is an integer fro - to Quantu Nubers deterines the no. of eectronic orbitas = Magnetic Quantu Nuber = -, - + 1, - +,..., + 1 vaues of 0,1,,..., -1, = 0 = 0 s orbita One s orbita

13 8.7 Quantu Nubers deterines the no. of eectronic orbitas 8.7 Quantu Nubers deterines the no. of eectronic orbitas = 1 = -1, 0, + 1 p orbita Three p orbitas = d orbita = -,-1, 0, + 1, Quantu Nubers deterines the no. of eectronic orbitas 8.7 Quantu Nubers deterines the no. of eectronic orbitas = d orbita = 3 f orbita = -,-1, 0, + 1, + Five d orbitas = -3,-,-1, 0, + 1, +, + 3 Seven f orbitas 8.7 Quantu Nubers Orbitas have we defined shapes 8.7 Quantu Nubers s Spin Quantu Nuber for an eectron Shapes of the probabiity couds for the eectrons s = + 1 or 1 - Spin Up or Spin Down

14 8.7 Quantu Nubers H ato: orbitas of the sae n have sae E Degenerate orbitas (have identica energy) Degenerate Orbitas for Hydrogen 8.7 Quantu Nubers Can an orbita have the foowing quantu nubers: n=3, =0, =0? Fig 8.3 Sae energy Note! This is ony true for H ato Not true for uti e - atos n = 3 Positive integer...ok = 0 can range fro 0 to n -1...OK = 0 can range fro - to...ok These are vaid quantu nos. for an orbita 8.7 Quantu Nubers What type of orbita corresponds to the quantu nubers n=3, =1, =1? n 3p orbita n and Deterine the Orbita type =1 p orbita Orbita type 8.9 Eectron Spin: 4 th Quantu Nuber s Spin Quantu Nuber for an eectron Iportant point This eans two e - in one orbita ust have different s vaues s = + 1 or 1 - Spin Up or Spin Down Maxiu of two eectrons per orbita Their spins ust be opposite: paired 8.9 Paui Excusion Principe No two eectrons can have exacty the sae set of four quantu nubers (Paui) If n,, and are the sae, then s ust differ s can be +1/ or -1/ so axiu two eectrons per orbita Note: If n,, and are the sae, then the eectrons are in the sae orbita and ust differ in s vaue 8.9 Eectron Spin: 4 th Quantu Nuber Spinning eectron generates agnetic fied Spin Up Spin Down

15 8.9 Eectron Spin: 4 th Quantu Nuber Spinning eectron generates agnetic fied Spin Up 8.9 Eectron Spin: 4 th Quantu Nuber Spinning Eectron generates Magnetic Fied Spin Up Spin Down Spin Down For paired eectrons in an orbita agnetic fieds cance For unpaired singe eectron In an orbita Net ag. fied or 8.9 Eectron Spin: 4 th Quantu Nuber Can detect agnetic fied fro unpaired eectron spins Stern-Gerach Expt., Univ. of Frankfurt, 19 Siver (Ag) atos with unpaired e - of different spin state were defected in opposite directions by agnetic fied N S Stern-Gerach Experient ore ore detais Bea of neutra (not charged) Ag atos fro a vaporized Ag source is directed through an externa agnetic fied (not an eectrica fied) The effect is observed due to the agnetic fied of the one unpaired eectron spin in the neutra siver atos as they pass through the externa agnetic fied The one unpaired eectron in each individua siver ato can be either spin up or spin down which accounts for the observation of two spots defected either up or down where the siver atos strike the detector Partice Detector Note this is not a charge effect it is due entirey to the eectron spin and the presence of the externa agnetic fied Ag Ag ato with unpaired N Ag e - Ag Ag Ag Ag Ag Ag Ag Ag Ag Ag Bea of Ag atos (neutra charge) S Otto Stern Wather Gerach 8.9 Eectron Spin: 4 Quantu Nuber Eectronic structure: ust specify a four quantu nubers

16 8.9 Eectron Spin: 4 th Quantu Nuber Eectronic structure: ust specify a four quantu nubers e.g. n=3, =1, =0, s =1/ 8.9 Eectron Spin: 4 th Quantu Nuber Eectronic structure: ust specify a four quantu nubers e.g. n=3, =1, =0, s =1/ The Cheist s notation 1 3p =1 p orbita 8.9 Eectron Spin: 4 th Quantu Nuber Eectronic structure: ust specify a four quantu nubers e.g. n=4, =, =-1, s =1/ And n=4, =, =-, s =1/ = d orbita The Cheist s Two eectrons 4d notation n Orbita type Note: This notation gives the eectron configuration for the orbita 8.8 Orbitas of the Hydrogen Ato 8-8 Orbitas of the Hydrogen Ato 8.8 Orbitas of the Hydrogen Ato You don t need to know Orbita Functions Lectures wi cover what you need to know 1 R(s) = Y(p ) = x 3 4π Z a o 1/ 3/ - ( - σ) e σ sin θcos φ 8.8 Orbitas of the Hydrogen Ato : Anguar Moentu Quantu No. & Orbita Type (e.g. s, p, d, f orbita) Orbitas have different shapes of e - probabiity couds Probabiity couds: Where a I ikey to find the eectron within the ato?

17 8.8 Orbitas of the Hydrogen Ato s orbita = 0 Ψ(r, θ, φ) = 0 = e - s orbita One s orbita Probabiity Ψ(r) e - probabiity at distance r fro the nuceus 8.8 Orbitas of the Hydrogen Ato s Oobita Ψ(r) e - probabiity at distance r fro the nuceus Ψ 1s orbita Ψ s orbita r r Distance fro nuceus Nodes Zero probabiity of finding e - Nodes Ψ 3s orbita r 8.8 Orbitas of the Hydrogen Ato s orbitas are spherica in shape n>1, s orbita wi have nodes (e.g. 3s orbita) Note: Orbita Size is proportiona to n More ikey to find 1s e - cose to nuceus 8.8 Orbitas of the Hydrogen Ato s orbitas are spherica in shape n>1, s orbita wi have nodes (e.g. 3s orbita) Note: Orbita Size is proportiona to n More ikey to find 1s e - cose to nuceus 1s s 3s Nodes 1s s 3s Node: Ψ changes sign n-1 nodes for s orbita 8.8 Orbitas of the Hydrogen Ato (End) p orbitas = 1 = -1, 0, + 1 Ψ(r) p orbita p orbita Three p orbitas 8.8 Orbitas of the Hydrogen Ato p orbitas = 1 = -1, 0, + 1 p orbita Noda panes Three p orbitas r Distance fro nuceus Dubbe shape for p orbitas p x orbita p y orbita p z orbita p orbita shape depends on radia & anguar Nuber of noda panes =

18 8.8 Orbitas of the Hydrogen Ato d orbitas = d orbita = -,-1, 0, + 1, + Five d orbitas d xy d xz d yz d x -y d z 8.8 Orbitas of the Hydrogen Ato Nodes : ψ = 0 so ψ changes sign Radia nodes = n 1 Noda panes or anguar nodes = 3p orbita: n=3 and = = 1 Radia node 1 Noda pane r Noda panes Nuber of noda panes= 3p orbita 3p orbita e - density 8.8 Orbitas of the Hydrogen Ato Different eectron orbitas can overap Each eectron obeys its own ψ 8.8 Orbitas of the Hydrogen Ato f orbitas f orbita = 3 = -3,-,-1, 0, + 1, +, + 3 Seven f orbitas 3s orbita & 3p orbita Orbitas of the Hydrogen Ato s orbitas, shape fro radia ony p, d, & f orbitas, shape fro radia & anguar 8.10 Mutieectron Atos 8-10 Mutieectron Atos Ψ(r, θ, φ) = e - Probabiity radia variabe anguar Orbita shape variabes pays an iportant roe in bonding between atos covered ater in the course

19 8.10 Mutieectron Atos Hydrogen Ato: Singe Eectron 8.10 Mutieectron Atos Hydrogen Ato: Singe Eectron 1 H Z=1 Z=p p=e - H has one eectron 8.10 Mutieectron Atos A other atos have ore than one eectron 8.10 Mutieectron Atos Must consider severa new effects for utieectron atos Greater nucear charge Z>1 ore protons Repusion between negativey charged eectrons in orbitas Screening of outer she e - fro the fu attraction of the nuceus by inner she e Mutieectron Atos H ato orbitas sae n sae Energy Degenerate Orbitas for Hydrogen Sae energy Note! This is ony true for H ato 8.10 Mutieectron Atos Muti e - sae n different energies Due to charge attraction & repusion e - e - Repusion between eectrons e - p + Attraction between eectrons & protons

20 8.10 Mutieectron Atos We ust consider the ocation of e - reative to the nuceus and nucear charge (Z) Reca that eectron orbitas differ in size (n) 1s s 90% probabiity coud 3s 8.10 Mutieectron Atos We ust consider the ocation of e - reative to the nuceus and nucear charge (Z) Reca that eectron orbitas differ in shape (s,p,d,f orbitas) Orbita size & shape wi affect screening abiities of its eectrons Screening how we inner e - bock outer e - fro attractive force of nuceus 8.10 Mutieectron Atos Eectron screening Inner she (orbita) eectrons screen outer e - fro fu attraction of the nuceus Outer e - experience a ower effective nucear charge Z eff < Z 8.10 Mutieectron Atos Wave Function: Radia & Anguar Functions Ψ(r, θ,φ) = R(r) Y(θ, φ) Wave function Radia function Anguar function 8.10 Mutieectron Atos Ψ is the probabiity of finding e - at a singe point in space Ψ(r,θ, φ) (r,θ,φ) = e - Probabiity at (r,θ, φ) Ψ = probabiity at one point 8.10 Mutieectron Atos P(r) the radia distribution function P(r) is the tota integrated probabiity for a spherica she at distance r fro the nuceus r P(r) = 4πr R () r Radia wave function Note: P(r) = 0 for r = 0

21 8.10 Mutieectron Atos Pots of P(r) vs. r/a o Most probabe radius a o = 5.9 p Bohr Radius 1s s p 3s 3p 3d s orbitas have greater penetration Note: e - in s orbitas can get coser to nuceus 8.10 Mutieectron Atos s orbitas are better at screening than p & d Screening s orbitas > p orbitas > d orbitas Strength s Z eff > p Z eff > d Z eff (for sae n) Orbita energy depends on n and Z eff Zeff En - In genera, for the sae vaue of n s orbitas ie at ore negative E than p, than d n 8.10 Mutieectron Atos Note: for utieectron atos, orbitas with the sae n are not degenerate 8-11 Eectron Configurations Less negative higher energy E 3p 3s More negative ower energy 3d Cheica Properties: Eectron Configurations Vaence (outer) Eectrons are ost Iportant Goa: Deterine e - configurations for atos Iportant to understanding cheica bonding Rues: Buiding up e - configurations for Z>1 1. Eectrons occupy orbitas in a way that iniizes the energy of the ato. No two e - in an ato can have the sae set of four quantu nubers (Paui Excusion Principe)

22 Rues: Buiding up e - configurations for Z>1 3. Eectrons wi occupy orbitas of the sae energy singy (i.e., unpaired). The singe e - in these degenerate orbitas wi have the sae spin state (Hund s Rue) Rues: Buiding up e - configurations for Z>1 3. Eectrons wi occupy orbitas of the sae energy singy (i.e. unpaired). The singe e - in these degenerate orbitas wi have the sae spin state (Hund s Rue). 4. Once orbitas of the sae energy are fied singy, additiona eectrons can be added with the opposite spin. Notations for Eectron Configurations: e.g., C C Z=6 so 6e - to fi spdf notation (condensed) spdf notation (expanded) Orbita diagra C C n Orbita type C 1s 1s s s p 1s s p No. of eectrons 1 1 px py Rue 1. Miniize the overa Energy Fi ower Energy orbitas first Order for fiing e - orbitas n =0 =1 = =3 Arrows indicate fiing order You ust know this tabe Rue. Paui Excusion Principe Ipication: Orbita can contain a axiu of two eectrons (they ust be paired i.e. have opposite spins) Rue 3. Fi degenerate orbitas singy first This iniizes eectron-eectron repusion Austrian Physics Nobe 1945 Wofgang Paui Paui was a waking ab disaster! E s p

23 Rue 3. Fi degenerate orbitas singy first This iniizes eectron-eectron repusion Rue 3. Fi degenerate orbitas singy first This iniizes eectron-eectron repusion E s p E s p Rue 3. Fi degenerate orbitas singy first This iniizes eectron-eectron repusion Rue 4. Once degenerate orbitas are fied singy, we can then begin to add a second e - to each orbita (this fis the orbita) E s p E s p Rue 4. Once degenerate orbitas are fied singy, we can then begin to add a second e - to each orbita (this fis the orbita) In Nature, we woud actuay have a distribution of a spin up & a spin down E p p s s Cheists typicay ony use the up arrows! Rue 4. Once degenerate orbitas are fied singy, we can then begin to add a second e - to each orbita (this fis the orbita) E s p

24 Rue 4. Once degenerate orbitas are fied singy, we can then begin to add a second e - to each orbita (this fis the orbita) Rue 4. Once degenerate orbitas are fied singy, we can then begin to add a second e - to each orbita (this fis the orbita) E s p E s p Buiding up e - : Aufbau process (Geran) Ato: Deterine Z then fi equa no. of e - Ground state eectron configurations (owest energy) Deterine Z fro Periodic Tabe e. g. K Z=? Deterine Z fro Periodic Tabe e. g. K Z=? 19 K Z=19 Need to fi 19 e -

25 Start fiing up e - as we increase Z Increasing Z Ato: Deterine Z then fi equa no. of e - H (Z=1): 1s 1 Ato: Deterine Z then fi equa no. of e - H (Z=1): 1s 1 He (Z=): 1s Ato: Deterine Z then fi equa no. of e - H (Z=1): 1s 1 He (Z=): 1s Li (Z=3): 1s s 1 Ato: Deterine Z then fi equa no. of e - H (Z=1): 1s 1 He (Z=): 1s Li (Z=3): 1s s 1 Be (Z=4): 1s s Ato: Deterine Z then fi equa no. of e - H (Z=1): 1s 1 He (Z=): 1s Li (Z=3): 1s s 1 Be (Z=4): 1s s B (Z=5): 1s s p 1

26 Ato: Deterine Z then fi equa no. of e - B (Z=5): 1s s p 1 C (Z=6) 1s s p Ato: Deterine Z then fi equa no. of e - B (Z=5): 1s s p 1 C (Z=6) N (Z=7) 1s s p Ato: Deterine Z then fi equa no. of e - B (Z=5): 1s s p 1 C (Z=6) N (Z=7) O (Z=8) 1s s p Ato: Deterine Z then fi equa no. of e - B (Z=5): 1s s p 1 C (Z=6) N (Z=7) O (Z=8) F (Z=9) 1s s p Ato: Deterine Z then fi equa no. of e - B (Z=5): 1s s p 1 C (Z=6) N (Z=7) O (Z=8) F (Z=9) We have fied across the Tabe to Ne Ne Nobe gas Nobe gases Ne (Z=10) 1s s p

27 We have fied across the Tabe to Ne Ne Nobe gas Nobe gases Stabe eectron configs. Nobe Gas Eectron Configuration Fied octet: 8e - Ne (Z=10) 1s s p Inner she e - Vaence eectrons (orbitas with highest n) Nobe gases are unusuay stabe because they have copetey fied orbitas They don t want to gain or ose e - Nobe Gas Eectron Configuration Ne (Z=10) 1s s p To sipify the notation, cheists use the foowing notation to represent fied inner shes: [Nobe Gas Cheica Sybo] Ato: Deterine Z then fi equa no. of e - Ne (Z=10) 1s s p Na (Z=11) [Ne] 3s 3p [Ne] stands for 1s s p 6 Ato: Deterine Z then fi equa no. of e - Ne (Z=10) 1s s p Na (Z=11) [Ne] Ato: Deterine Z then fi equa no. of e - Ne (Z=10) 1s s p Na (Z=11) [Ne] Mg (Z=1)[Ne] 3s 3p Mg (Z=1)[Ne] A (Z=13) [Ne] 3s 3p

28 Ato: Deterine Z then fi equa no. of e - Ne (Z=10) 1s s p Na (Z=11) [Ne] Mg (Z=1)[Ne] Ato: Deterine Z then fi equa no. of e - Ne (Z=10) 1s s p Na (Z=11) [Ne] Mg (Z=1)[Ne] A (Z=13) [Ne] 3s 3p A (Z=13) [Ne] 3s 3p Copete inner shes Copete Inner shes Vaence e - Configuration Notation Convention Note: 4s fis before 3d e.g. Sc + [Ar] 3d 1 4s 1 But we choose to write: ower n to the eft Sc (Z=1) [Ar] 3d 1 4s Instead of fiing order: [Ar] 4s 3d 1 Why? Because ionized e - are usuay pued fro the orbita with the higher n (which ay not be the ast one fied as in this case) Fi d orbitas in Sae way Cr & Cu exceptions* 3d 4s The exceptions We expect: 3d 4s Cr (Z=4) [Ar] [Ar] 3d 4 4s Actua: Cr (Z=4) [Ar] [Ar] 3d 5 4s 1 We expect: Cu (Z=9) [Ar] [Ar] 3d 9 4s Actua: Cu (Z=9) [Ar] [Ar] 3d 10 4s 1 Reason: Extra stabiity for fied and haf-fied d orbitas