1. Modern Theory of the Atom: Quantum Mechanical Model

3. Recap of Bohr Model electrons:
particles moving in circular orbits with specific speed, position, & energy
quantization of energy levels is imposed
electrons can move between energy levels
higher energy levels farther from nucleus
moving up to higher E level: electron absorbs energy
moving down to lower E level: electron emits light energy
Ground state:
electrons located in lowest possible energy levels
closest can be to nucleus

5. 1924: De Broglie Proposed this Idea:
if light can show both particle and wave behavior, maybe matter can too

9. 2 kinds of waves Traveling wave wave not confined to given space
travels from one location to another
interrupted by hitting
boundary or another
wave
Standing wave
confined to given space (ends are pinned)
interference between incident & reflected waves
at certain frequencies:
certain points seem to be standing still
other points - displacement changes in regular way

10. Traveling Wave

11. Standing wave

12. DeBroglie Electron-Wave
wavelength describing electron depends on energy of electron
at certain energies, electron waves make standing waves in atom
wave does not represent path of electron

13. Modern Theory electron treated as wave
cannot specify both position & speed of electron
can determine probability of electron’s location in given region of space
Quantized energy levels arise naturally out of wave treatment

14. Bohr Model vs. Modern Theory
electron = particle
e- path is orbit
holds 2n2 electrons
circular path
each orbit has specific energy
can find exact position/ speed
electron = wave
e– path is orbital
holds 2 electrons
not necessarily circular
each orbit has specific energy
probable location

15. Heisenberg uncertainty principle
Fundamentally impossible to know velocity & position of particle at same time
Impossible to make observation without influencing system

16. What can orbitals do for us?
Physical structure of orbitals explain:
Bonding
Magnetism
Size of atoms
Structure of crystals

17. Orbital – Modern Theory
orbital: term describes region where e- might be found
each orbital:
specific energy & specific shape
described by 4 parameters of wave function (like an address)
quantum numbers = n, l, m, s

18. n: principal quantum number
specifies atom’s principal energy levels
whole number values: 1, 2, 3, 4, …
maximum # electrons in any principal energy level = 2n2

19. l = Describes sublevels
principal energy levels have sublevels
# sublevels depends on principal energy level
1st principal energy level has 1 sublevel
2nd “ “ “ “ “
3rd “ “ “ “ “
4Th “ “ “ “ “ , etc.

20. Naming sublevels Sublevels are labeled by shapes:
s, p, d, f
s orbitals: spherical
p orbitals: dumbbell shaped
d & f orbitals: more complex shapes

21. m = 3rd quantum number sublevels made up of orbitals
each sublevel has specific # of orbitals
sublevel
# of orbitals s 1 p 3 d 5 f 7

22. s orbital shapes

23. p orbital shapes

24. d orbital shapes

25. f orbital shapes

26. 4th quantum number = s e- spin: 2 possible values
clockwise and counter clockwise

27. Address for each electron
4 quantum numbers
no 2 e- can
occupy the same space in atom
can have same 4 quantum numbers
therefore only 2 electrons per orbital
(Pauli exclusion principle)

28. principle energy level
sublevels
# orbitals
total # e- 1 s 2 p 3 6 d 5 10 4 f 7 14

29. Each box represents an orbital and holds 2 electrons
3rd principal energy level, 3 sublevels
2nd principal energy level, 2 sublevels – s & p
1st principal energy level, 1 sublevel – s
Each box represents an orbital and holds 2 electrons

30. Order of fill: Aufbau Principle
each electron occupies lowest energy orbital available
learn sequence of orbitals from lowest to highest energy
some overlap between sublevels of different principal energy levels

31. Aufbau Principle Follow arrows 1s 2s 2p sequence of orbitals: 3s 3p 3d
1s, 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, …
exceptions do occur: half-filled orbitals
have extra stability
- magic # is 8 1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p

32. Electron Configurations

33. Compare Bohr & Schrodinger

34. Frequencies in Chemistry

35. Electron Configuration & PT

37. Principle
Energy
Levels
hold 2
electrons max 
Sublevels 
Orbitals  
1st E level has 1 sublevel : s
2nd “ “ 2 sublevels : s and p
3rd “ “ “ : s, p, and d
4th “ “ “ : s, p, d, and f 
n = 1,2,3,4
holds 2n2
electrons max
s sublevel holds 1 orbital
p sublevel holds 3 orbitals
d sublevel holds 5 orbital
f sublevel holds 7 orbitals