1. Modern Electron Structure

2. 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

3. 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

4. Schroedinger’s Wave Function - Y
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

5. 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

6. 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

7. 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

8. 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

9. 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 = l = Subshell
For n = l = 0, Subshells
For n = l = 0, 1, Subshells
For n = l = 0, 1, 2, Subshells
l values have a corresponding letter (older system)
0 = s = p 2 = d 3 = f

10. l = S Subshell

11. l = 1 p subshell

12. 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 = orbital
For l = 1 ml = -1, 0, orbitals
For l = 2 ml = –2,-1,0,+1, orbitals
For l = 3 ml = –3,-2,-1,0,+1,+2, orbitals

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

14. 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 px or 2py or 2pz

15. 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

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

17. 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

18. Quantum Number Calculations
Relation between Quantum Numbers and Atomic Orbitals

19. 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

20. 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

21. Calculations Shortcuts -2
Number of orbitals in a subshell = 2 l + 1
For l = # 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 = # e-/ l = 2(2*2 + 1) = 10

22. 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

23. 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

24. 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

25. 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

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

27. 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

28. Aufbau Order of e- Configurations

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

30. 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
= 12 electrons
Abbreviated as [Ne]3s2
[Ne]=1s22s22p6
What is the electron configuration of Sc?
Sc 21 electrons
1s22s22p63s23p64s23d1 or [Ar]4s23d1
= 21 electrons

31. 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

32. 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]

33. Learning Check - 3 V: [Ar]4s2 3d3 V2+:
[Ar] 4s0 3d 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 4p P e-s before S , at same level

34. 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

35. 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

36. 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)

37. 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

38. 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)

39. 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
1s s p 2p 2p

40. 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

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

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

43. 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