Modern Electron Structure

Presentation Objectives Describe the modern atomic electron structure Learn the first 3 quantum numbers and their significance Know the shapes and quantum number designations for each the s, p, d and f orbitals Write electron configurations and orbital diagrams for elements and ions

Electrons as Matter and Wave From De Broglie’s work derived that e-s have both matter and wave-like properties Have mass like matter Show a diffraction pattern like light when passed through 2 closely located slits

Schroedinger’s Wave Function - Y 1926 - Erwin Schroedinger described wave and particle dual nature of e-s in an atom Developed a wave function equation Much math but most important are the solutions Solutions to equation are called orbitals Orbitals represent probabilities of e-s locations Each orbital is distinguished with a set of 3 quantum #s

Heisenberg Uncertainty Principle 1927 – Werner Heisenberg Can determine either momentum (speed) of an e- or its position but not both at the same time Therefore Can only determine probability of finding a particle in a given region of space Supported probability concept of Wave Equation

Quantum Numbers A set of 3 numbers used to distinguish orbitals Principal Secondary Magnetic Numbers progressively more specific about the e- location Lead us to describing electron configurations of elements and ions

Principal Quantum Number, n Energy Level/Level/Size/Distance from Nucleus/Shell Has integer values 1 to ¥ n = 3 n = 4 n = 2 n = 1 Contain subshells

Principal Quantum Number, n Where 90% of the e- density is found for the 1s orbital e- density (1s orbital) falls off rapidly as distance from nucleus increases

Secondary Quantum Number, l Angular Momentum or Azimuthal Quantum Number Within an energy level, divides Shells into Subshells/Sublevels Specifies shape/general e- distribution of Subshell Integer values from 0 to n-1 For n =1 l = 0 1 Subshell For n =2 l = 0,1 2 Subshells For n =3 l = 0, 1, 2 3 Subshells For n =4 l = 0, 1, 2, 3 4 Subshells l values have a corresponding letter (older system) 0 = s 1= p 2 = d 3 = f

l = 0 S Subshell

l = 1 p subshell

Magnetic Quantum Number, ml Divides Subshells into Individual Orbitals Gives # of orbitals and their orientation in space Integer values between -l and +l (including 0) For l = 0 ml = 0 1 orbital For l = 1 ml = -1, 0, +1 3 orbitals For l = 2 ml = –2,-1,0,+1,+2 5 orbitals For l = 3 ml = –3,-2,-1,0,+1,+2,+3 7 orbitals

Quantum #s Letter System S Subshell and Orbital ml = 0 Example Quantum #s Letter System 1, 1, 0 1s

P Orbitals ml = -1 ml = 0 ml = +1 No relationship exists between ml values and orientation in space Example Quantum #s Letter system 2, 1, -1 or 0 or +1 2px or 2py or 2pz

3dx^2 –y^2 or 3dz^2 or 3dxy or 3dxz or 3dyz D Orbitals ml = -2 ml = -1 ml = 0 ml = +1 ml = +2 Example Quantum #s 3, 2, -2 or -1 or 0 or +1 or +2 Letter System 3dx^2 –y^2 or 3dz^2 or 3dxy or 3dxz or 3dyz

F Orbitals ml = -3 ml = -2 ml = -1

4f in different orientations F Orbitals - More ml = 0 ml = +1 ml = +2 ml = +3 Example Quantum #s 4, 3, -3 or -2 or -1 or 0 or +1 or +2 or +3 Letter System 4f in different orientations

Quantum Number Calculations Relation between Quantum Numbers and Atomic Orbitals

Learning Check How many 2p orbitals are there in an atom? n=2 If l = 1, then ml = -1, 0, or +1 2p 3 orbitals l = 1 How many electrons can be placed in the 3d subshell? n=3 If l = 2, then ml = -2, -1, 0, +1, or +2 3d 5 orbitals which can hold a total of 10 e- l = 2

Calculations Shortcuts -1 Number of subshells in a shell = n # For n = 1: # of subshells/n = 1; i.e 0 or s For n = 3: # of subshells = 3; i.e 0, 1, 2 or s, p, d Number of orbitals in a shell = n2 For n = 4: # of orbitals/n = (4)2 = 16 Corresponds to 1 of s, 3 of p, 5 of d, 7 of f Number of e- in a shell = 2n2 For n = 4: # of e-/n = 2n2 = 32

Calculations Shortcuts -2 Number of orbitals in a subshell = 2 l + 1 For l = 2 # orbitals/ l = 2(2) + 1 = 5 Corresponds to ml = -2, -1, 0, +1, +2 Number of e- in a subshell = 2(2 l + 1) For l = 2 # e-/ l = 2(2*2 + 1) = 10

Learning Check How many subshells when n = 4? # subshells/n = n # = 4 s, p,d,f or 0,1,2,3 How many subshells when n = 7? Theoretically 7 s, p,d,f,a,b,c How many orbitals at energy level 3? # of orbitals/n = n2 = (3)2 = 9 How many e- at shell 5? Theoretically # of e-/n = 2n2 = 2(5)2 = 50 How many orbitals for sublevel 3? # orbitals/ l = 2 l + 1 = 2(3) + 1 = 7 How many orbitals for sublevel 7? Theoretically # orbitals/ l = 2 l + 1 = 2(7) + 1 = 15

e- Configurations Describe how the e are arranged around the nucleus of the elements e- configurations explain chemical behavior of elements Periodic table constructed on the basis of e- configurations

e- configurations - Aufbau Principle Aufbau Principle used to construct e- configurations Aufbau is German for “building up” As protons are added one by one, e-s fill up orbitals e-s occupy lowest energy available orbital

Aufbau Order Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d Aufbau Order represents respective energy level of the subshells in a multi-electron atom where e-s repel one another

Aufbau Order – Simplified Form 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p

Writing e- Configurations 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Na 1s2 2s2 2p6 3s1 Fill orbitals sequentially with e-s by following diagonal arrows Use superscripts to indicate # of e-s in subshell

Aufbau Order of e- Configurations

PT Filling Order of e- Configurations Alternate and easier method Think of PT as set of boxes each holding 1 additional e-

1s < 2s < 2p < 3s < 3p < 4s Learning Check What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s22s22p63s2 2 + 2 + 6 + 2 = 12 electrons Abbreviated as [Ne]3s2 [Ne]=1s22s22p6 What is the electron configuration of Sc? Sc 21 electrons 1s22s22p63s23p64s23d1 or [Ar]4s23d1 2 + 2 + 6 + 2 + 6 + 2 + 1 = 21 electrons

Learning Check C: 1s22s22p2 N: 1s22s22p3 O: 1s22s22p4 F: 1s22s22p5 Ne: Na: 1s2 2s2 2p6 3s1 or [Ne]3s1 Mg: 1s2 2s2 2p6 3s2 or [Ne]3s2 Al: [Ne]3s2 3p1

Learning Check - 2 K: [Ar] 4s1 K+: [Ar] 4s0 or [Ar] Ca: [Ar] 4s2 Ca2+: [Ar] 4s0 or [Ar] or 1s2 2s2 2p6 3s2 3P6 Br: [Ar]4s2 3d10 4p5 Br-: [Ar]4s2 3d10 4p6 or [Kr]

Learning Check - 3 V: [Ar]4s2 3d3 V2+: [Ar] 4s0 3d3 Outermost e-s removed first Mn: [Ar]4s2 3d5 Mn2+: [Ar] 4s0 3d5 Ge: [Ar]4s2 3d10 4p2 Ge2+: [Ar]4s2 3d10 4p0 Ge4+: [Ar] 4s0 3d10 4p0 P e-s before S , at same level

Anomalies What anomalies do you notice in the orbital filling order? 4s get filled before 3d and similarly for the other s and d orbitals 6s and 7s get filled before 4f and 5f respectively Explanation Although 4s is physically further out than 3d, its e- actually spend enough time closer to the nucleus to make 4s lower energy than 3d and therefore causing 4s to filled first Same is true for s and f orbitals

Configuration Exceptions Half-filled subshell stability Ti = [Ar] 4s2 3d2 V = [Ar] 4s2 3d3 Cr = [Ar] 4s1 3d5 Mn = [Ar] 4s2 3d5 Filled subshell stability Cu = [Ar] 4s1 3d10

Valence and Core Electrons Valence electrons- e- in outermost energy s and p (not d, typically) level/s e-s involved in chemical reactions Core electrons- Inner e-s – All e- accommodated by previous noble gas configuration including lower level d (typically) and f e-s that screen (shield) valence e-s from full electrostatic attraction of nucleus (Zeff)

Learning Check Which are the valence e-s for K:[Ar] 4s1 4s1 How many valence e-s does Ca have? [Ar] 4s2 – 2 valence e-s Which are the core e-s for Br? [Ar] 4s2 3d10 4p5 – Those contained in Ar & 3d10 How many valence e-s does Br have? [Ar] 4s2 3d10 4p5 – Only s and p: 7 e-s How many valence e-s does Sb have? [Kr] 5s2 4d10 5p3 – 5 e-s

Orbital Diagrams Represents arrangement of e-s within orbitals Orbitals represented as series of boxes or short lines Fill in orbitals with arrows to indicate e-s Fill in all available orbitals before doubling up When e- paired show opposite spin, by showing arrows pointing in opposite directions (opposite spin)

Connection to Aufbau Order Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f Orbital Diagram C 1s2 2s2 2p2 1s2 2s2 2p 2p 2p

3 Rules for Filling Orbital Diagrams Aufbau Principle: e-s occupy lowest energy available orbital Pauli Exclusion Principle: No orbital may contain more than two e-s Hund’s Rule: With orbitals of same energy (i.e., three p orbitals or five d orbitals) must place 1 e- in each orbital before doubling up

Orbital Diagrams - Examples Nitrogen Correct 1s 2s 2p 2p 2p Incorrect 1s 2s 2p 2p 2p 1s 2s 2p 2p 2p Correct [He] 2s 2p 2p 2p

Learning Check Write Orbital Diagrams for: Mg, Al, K, Br, Ti, Au, Pu, Pb Ca2+, Br-, Fe+2, Pb+2, Pb+4

Sources Davis et al. “Modern Chemistry” Brown et al. “Chemistry: The Central Science” Zumdahl and Zumdahl “Chemistry” Chang “Chemistry” North Carolina School of Mathematics and Science online honors chemistry course