1. Quantum Theory Schrodinger Heisenberg
Quantum Theory
Schrodinger
Heisenberg

2. The Quantum Mechanical Model
Energy is quantized. It comes in chunks.
A quanta is the amount of energy needed to move from one energy level to another.
Since the energy of an atom is never “in between” there must be a quantum leap in energy.
Schrodinger derived an equation that described the energy and position of the electrons in an atom

3. The Quantum Mechanical Model
Heisenberg Uncertainty Principle---it is impossible to know both the exact position and momentum of an object at the same time.
Can’t know position if e- is moving.
Can’t know momentum if e- is not moving.

4. The Quantum Mechanical Model
Has energy levels for electrons.
Orbits are not circular.
It can only tell us the probability of finding
an electron a certain distance from the nucleus.

5. The Quantum Mechanical Model
The atom is found inside a blurry “electron cloud”
A area where there is a chance of finding an electron.
Draw a line at 90 %

6. Schrodinger’s Quantum #’s
(n) Principal quantum #
n = 1, 2, 3 … -1
the energy level of the electron.
Formula: 2(n)2 = # of electrons per energy level
(l) Azimuthal or Secondary quantum #
l = 0,1, 2, (n-1)
the sublevels or shape within an energy level.
s,p,d,f (names of sublevels)
s,p,d, & f each have a unique shape.

7. Quantum #’s (cont.) (ml) magnetic quantum # (ms) spin quantum #
ml = +l –l (2l +1) = total orbitals
regions where there is a high probability of finding an electron
each orbital can hold 2 e-
(ms) spin quantum #
ms = +1/2 or –1/2
in each orbital there can be up to 2 electrons spinning in opposite directions.
Clockwise  +1/2 Counter clockwise  –1/2

8. Quantum Numbers n Principle Azimuthal m l Magnetic ms Spin l
l = 0, 1, 2, 3 … (n-1)
m l
Magnetic
m l = +l ..+2,+l, 0,. –l, l ms
Spin
ms = +1/2 or –1/2 s p d f

9. Arrangement of Electrons in Atoms
Electrons in atoms are arranged as
LEVELS (n)
SUBLEVELS (l)
ORBITALS (ml)

10. Energy Levels
Each energy level has a number called the PRINCIPAL QUANTUM NUMBER, n
Currently n can be 1 thru 7, because there are 7 periods on the periodic table

11. Energy Levels
n = 1
n = 2
n = 3
n = 4

12. Orbitals and the Periodic Table
Orbitals grouped in s, p, d, and f orbitals
(sharp, proximal, diffuse, and fundamental)
s orbitals
d orbitals
p orbitals
f orbitals

13. s orbitals 3s 2s 1s 1 s orbital for every energy level
Spherical shaped
Each s orbital can hold 2 electrons
Called the 1s, 2s, 3s, etc.. orbitals. 3s 2s 1s

14. p orbitals Start at the second energy level 3 different directions
3 different shapes
Each can hold 2 electrons

15. d orbitals Start at the third energy level 5 different shapes
Each can hold 2 electrons

16. f orbitals Start at the fourth energy level
Have seven different shapes
2 electrons per shape

17. f orbitals

18. Summary # of orbitals Max electrons Starts at energy level s 1 2 1 p 36 2 d 5 10 3 7 14 4 f

19. Number of Electrons that can be held in each orbital
s = 2 e-
p = 6 e-
d = 10 e-
f = 14 e-

20. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p

21. Electron Configurations
The way electrons are arranged in atoms.
Aufbau principle- electrons enter the lowest energy first.
This causes difficulties because of the overlap of orbitals of different energies.
Pauli Exclusion Principle- at most 2 electrons per orbital - different spins
Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .

22. Electron Configuration
Let’s determine the electron configuration for Phosphorus (P)
Need to account for 15 electrons

23. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The first to electrons go into the 1s orbital
Notice the opposite spins
only 13 more

24. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The next electrons go into the 2s orbital
only 11 more

25. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p
The next electrons go into the 2p orbital
only 5 more

26. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p
The next electrons go into the 3s orbital
only 3 more

27. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s
The last three electrons go into the 3p orbitals.
They each go into seperate shapes
3 upaired electrons
1s22s22p63s23p3

28. The easy way to remember
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2
2 electrons

29. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2
4 electrons

30. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2 2p6 3s2
12 electrons

31. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2 2p6 3s2 3p6 4s2
20 electrons

32. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
38 electrons

33. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
56 electrons

34. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2
88 electrons

35. Fill from the bottom up following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p 1s
108 electrons

36. Effective Nuclear Charge
Electrostatic repulsion between negatively charged electrons
Influences the energies of the orbitals.
The effect of repulsion is described as screening or shielding.
The combined effect of attraction to the nucleus and repulsion from other electrons gives an effective nuclear charge, Zeff, which is less than that of the ‘bare’ nucleus.
Zeff = Z - S +
# Protons
# Shielding
electrons

37. Periodicity of Effective Nuclear Charge
Z* on valence electrons

38. Effective Nuclear Charge, Zeff
Atom Zeff Experienced by Electrons in Valence Orbitals
Li +1
Be +2
B +3
C +4
N +5
O +6
F +7
Increase in Zeff across a period

39. Electron Configurations
A list of all the electrons in an atom (or ion)
Must go in order (Aufbau principle)
2 electrons per orbital, maximum
We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons.
The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

40. Electron Configurations
2p4
Number of electrons in the sublevel
Energy Level
Sublevel
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

41. Let’s Try It!
Write the electron configuration for the following elements: H Li N Ne K Zn Pb

42. Shorthand Notation A way of abbreviating long electron configurations
Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

43. Shorthand Notation
Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ].
Step 2: Find where to resume by finding the next energy level.
Step 3: Resume the configuration until it’s finished.

44. Shorthand Notation [Ne] 3s2 3p5 Chlorine
Longhand is 1s2 2s2 2p6 3s2 3p5
You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces 1s2 2s2 2p6
The next energy level after Neon is 3
So you start at level 3 on the diagonal rule (all levels start with s) and finish the configuration by adding 7 more electrons to bring the total to 17
[Ne] 3s2 3p5

45. Practice Shorthand Notation
Write the shorthand notation for each of the following atoms: Cl K Ca I Bi

46. Valence Electrons
Electrons are divided between core and valence electrons
B 1s2 2s2 2p1
Core = [He] , valence = 2s2 2p1
Br [Ar] 3d10 4s2 4p5
Core = [Ar] 3d10 , valence = 4s2 4p5

47. Rules of the Game
No. of valence electrons of a main group atom = Group number (for A groups)
Atoms like to either empty or fill their outermost level. Since the outer level contains two s electrons and six p electrons (d & f are always in lower levels), the optimum number of electrons is eight. This is called the octet rule.

48. Keep an Eye On Those Ions!
Electrons are lost or gained like they always are with ions… negative ions have gained electrons, positive ions have lost electrons
The electrons that are lost or gained should be added/removed from the highest energy level (not the highest orbital in energy!)

49. Keep an Eye On Those Ions!
Tin
Atom: [Kr] 5s2 4d10 5p2
Sn+4 ion: [Kr] 4d10
Sn+2 ion: [Kr] 5s2 4d10
Note that the electrons came out of the highest energy level, not the highest energy orbital!

50. Keep an Eye On Those Ions!
Bromine
Atom: [Ar] 4s2 3d10 4p5
Br- ion: [Ar] 4s2 3d10 4p6
Note that the electrons went into the highest energy level, not the highest energy orbital!

51. Try Some Ions! Write the longhand notation for these: F- Li+ Mg+2
Write the shorthand notation for these:
Br-
Ba+2
Al+3

52. Exceptions to Electron Configuration

53. Exceptions to the Aufbau Principle
Remember d and f orbitals require LARGE amounts of energy
If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel)
There are many exceptions, but the most common ones are
d4 and d9
For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d4 or d9 are exceptions to the rule. This may or may not be true, it just depends on the atom.

54. Exceptions to the Aufbau Principle
d4 is one electron short of being HALF full
In order to become more stable (require less energy), one of the closest s electrons will actually go into the d, making it d5 instead of d4.
For example: Cr would be [Ar] 4s2 3d4, but since this ends exactly with a d4 it is an exception to the rule. Thus, Cr should be [Ar] 4s1 3d5.
Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.

55. Exceptions to the Aufbau Principle
OK, so this helps the d, but what about the poor s orbital that loses an electron?
Remember, half full is good… and when an s loses 1, it too becomes half full!
So… having the s half full and the d half full is usually lower in energy than having the s full and the d to have one empty orbital.

56. Exceptions to the Aufbau Principle
d9 is one electron short of being full
Just like d4, one of the closest s electrons will go into the d, this time making it d10 instead of d9.
For example: Au would be [Xe] 6s2 4f14 5d9, but since this ends exactly with a d9 it is an exception to the rule. Thus, Au should be [Xe] 6s1 4f14 5d10.
Procedure: Same as before! Find the closest s orbital. Steal one electron from it, and add it to the d.

57. Orbitals fill in order Lowest energy to higher energy.
Adding electrons can change the energy of the orbital.
Half filled orbitals have a lower energy.
Makes them more stable.
Changes the filling order

58. Write these electron configurations
Titanium(Ti) - 22 electrons
1s22s22p63s23p64s23d2
Vanadium(V) - 23 electrons 1s22s22p63s23p64s23d3
Chromium(Cr) - 24 electrons
1s22s22p63s23p64s23d4 is expected
But this is wrong!!

59. Chromium is actually 1s22s22p63s23p64s13d5 Why?
This gives us two half filled orbitals.
Slightly lower in energy.
The same principal applies to copper.

60. Copper’s electron configuration
Copper has 29 electrons so we expect
1s22s22p63s23p64s23d9
But the actual configuration is
1s22s22p63s23p64s13d10
This gives one filled orbital and one half filled orbital.
Remember these exceptions