1. Quantum Mechanics & Electron Configuration
Chapter 5: Electrons in Atoms

2. Part 1: Models of the Atom
1897: Thompson Model (Plum Pudding) 1911: Rutherford Model – Small, dense, + charged nucleus Electrons orbit around 1913: Bohr Model 1926: Quantum Mechanical Model – Erwin Schrodinger & his math equations

3. Bohr Model (aka the versions you’ve learned before)
Electrons move around the nucleus in fixed spherical orbits with fixed energies
Fixed energies = orbits / energy levels
Aka rungs of a ladder
Electrons can go to a higher or lower energy level
Either gain or lose energy to move levels
Electrons CANNOT be between levels

4. Atomic Emission Spectra
** When atoms absorb energy (i.e. electric current), they move to a higher energy level …
… these electrons emit light when they return back to a lower energy level
Emission spectra is unique for each element
The light emitted consists of only a mixture to specific frequencies…
If you pass the light through a slit and then a prism, you can separate the resulting light into its frequencies (aka colors)
Gas: Run electricity through it … gives off light and run that light through a prism to get the spectra
Metal: Heat it and it gives off light (glowing flame). Run this light through a prism to get the spectra
Barium

5. Light Has properties of both:  a Particle ( ____________)  a Wave
Light Waves:
Amplitude: crest of the wave (height from 0)
Wavelength: distance between crests (λ)
Frequency: # of waves per unit time (ν)
Units: Hertz (Hz) aka s-1

7. C = speed of light (constant) = 2.998 x 108 m/s
Math Time!!!
c = λν
C = speed of light (constant) = x 108 m/s
λ = Wavelength (m)
ν = Frequency (Hz or s-1)

9. More Math… E = h x v E = energy (joules – J)
The energy (E) of a photon is directly proportional to its frequency.
Higher freq = More Energy
Lower Freq = Less Energy
E = h x v
E = energy (joules – J)
H = Plank’s constant = 6.626E-34 J/s
v = Frequency (Hz or s-1)

10. Example:
What is the energy of a quantum of light with a frequency of 7.39 x 1014 Hz?

11. Think about this… E = h x v c = λν
What would you do if you were asked to solve for the frequency of light if you are given a wavelength of 700nm?
What would you do if you were asked to find the energy of light if you are given a wavelength of 480nm?

12. Emission Spectra Lab
Look at the gas tubes and follow directions provided.

13. Continuous Spectrum v. Line Spectrum
What did you observe in the Emission Lab?

14. Light has Wave-Particle Duality (& so do electrons)
Particle & Wave-like Nature
Depends on experiment / what we try to observe
Throws a wrench in Bohr Model…
New method of describing the motion of subatomic particles
= foundation of quantum mechanics = movement/organization of subatomic particles
Bohr Model = two dimensional description of what was going on
This does not work for atoms with more than one electron. For atoms with more than one electron, a model that showed movement in a three-dimensional space was needed.

15. The Quantum Mechanical Model
This is what we use today
Describes: LOCATION & ENERGY of electrons
Electrons do not have a direct orbit around nucleus
Based on probability
Electron clouds
Electrons do have energy levels

16. Hog Hilton Sample Problem
Book 15 hogs into their rooms
6th floor ____ ____ ____ _____ _____
6th floor ______
5th floor ______ ______ ______
4th floor ______
3rd floor ______ ______ ______
2nd floor ______
1st floor ______

17. Hog Hilton Sample Problem Place 15 electrons into their spaces
3d_____ _____ _____ _____ ____
4s _____
3p ______ ______ ______
3s ______
2p ______ ______ ______
2s ______
1s ______

18. But…all of these electrons are not organized into hotel rooms, but ATOMIC ORBITALS

19. So, what exactly is an ATOMIC ORBITAL?
Atomic Orbital = region of space in which there is a high probability of finding an electron
They come in different SHAPES, SIZES & ENERGY LEVELS!!
These are described by Quantum Numbers…

20. Quantum Numbers Get ready…here we go…
Part 2
Quantum Numbers
Get ready…here we go…

21. Quantum Numbers
Used to describe the location of electrons Electrons in an atom CANNOT have the same quantum numbers  Unique for each electron  Like an address

22. Principle Quantum Number (think…Energy Level)
Allowable values = 1, 2, 3 … n (positive, integer values)
Describes energy level
Position of the electron w/ respect to nucleus
As n increases = further from nucleus

23. Angular Momentum Quantum Number (Azimuthal Quantum Number) (think…energy sublevel) Pay attention…this is where it starts to get complicated l
Allowed values: 0, 1, 2, … (n-1)
Describes the sublevel
SHAPE of the orbital
SHAPES:
l = 0 = s orbital = spherical cloud
l = 1 = p orbital = dumbbell cloud
l = 2 = d orbital = clover cloud
l = 3 = f orbital = … too complicated

24. Example
If I had a principal quantum number of 2, what are my possible angular momentum quantum numbers?
n = 2
l =

25. Angular Momentum Quantum Number: Orbital Shapes

26. Magnetic Quantum Number (ml)
Determines spatial orientation (x, y, z, plane)
Possible Values: - l to + l
Examples: if it is a d orbital
d orbital:
l =
ml =
L = 2
M = -2, -1, 0, 1, 2

27. Example: p-orbital
n = 2 l = ml = This means, there are _______ p-orbitals and that they are in three directions (x, y, z axes):

28. What orbital corresponds to : n = 2 l = 1 ml = 0
Energy level = Sublevel = _____ - orbital Orientation: Orbital:
Energy level: 2
Sublevel: p orbital
Orientation: z
Orbital: 2pz

29. Number of orbitals within an energy level: n2
Examples: How many orbitals are in energy level 2?
n =
l =
ml =
Orbitals =
Each orbital holds 2 electrons:So, how many electrons can energy level 2 hold?
# Electrons = 2n2
N = 2
Orbitals = 0 , 1  s orbital , 3 p orbitals (px, py, pz)
# Electrons = 2 per orbital = 8 total electrons can be held at energy level 2
2n^2  2 (4) = 8  They are the same!!

30. Spin Quantum Number ms
Describes the direction of the electrons spin within an orbital (remember, each orbital only holds 2 electrons)
Possible Values: ½ or -½ (spin up, spin down)
Think back to hogs…

31. Ahhh…it’s too much information…HELP!!!
Solution: STUDY and PRACTICE!!!
Quantum #
Symbol
Possible Values
Description
Principle Quantum Number n
1, 2, 3, etc
Energy level
Angular Momentum Quantum Number l
0 … n-1
Sublevel & shape
Magnetic Quantum Number ml
-l … +l
Spatial Orientation of orbital (x,y,z)
Spin Quantum Number ms
+½ or -½
Direction of Spin

32. Examples n = 3 (what are the possible quantum numbers?)
What orbital corresponds to n = 4 & l = 2?

33. What orbital corresponds to
n = 4 , l = 1, ml = -1
Energy Level =
Sublevel =
Orbital orientation =
Orbital =

34. How Many Types of Orbitals (orientations) How Many Electrons in Shape
Re-iterate:
Orbital
How Many Types of Orbitals (orientations)
How Many Electrons in Shape s 1 p 3 d 5 f 7

35. Principle Quantum Number Angular Momentum Quantum Number (sublevels)
Shapes of Sublevels
# electrons (2n2) 1 2 3 4 5 6 7

36. Principle Quantum Number Angular Momentum Quantum Number (sublevels)
Shapes of Sublevels
# electrons (2n2) 1 s 2
0, 1
s p 8 3
0, 1, 2
s p d 18 4
0, 1, 2, 3
s p d f 32 5
0, 1, 2, 3, 4
s p d f (g) 50 6
0, 1, 2, 3, 4, 5
s p d f (g h) 72 7
0, 1, 2, 3, 4, 5, 6
s p d f (g h i) 98

37. STOP Do You Have Any Questions?

38. PART 3
Rules of Electron Configuration

39. Aufbau Principle Electrons enter orbitals of lowest energy first
Orbitals within a sublevel have equal energy
(3px, 3py, 3pz)
Exceptions: Cr , Cu
Which hog rules is this?

40. Pauli Exclusion Principle
An atomic orbital may only hold two electrons
Electrons must have opposite spin
Clockwise or counterclockwise spin
Denoted with arrows
Prevents two electrons from having same quantum numbers
Which hog rule is this?

41. Hund’s Rule
Every orbital of the same energy is singly occupied before any orbital is doubly occupied
Electrons have the same spin
Second electrons added have opposite spins
Which hog rule is this?

42. PART 4
Writing Electron Configurations

43. Electron Configuration Diagonal Rule
Starting with the top arrow, follow the arrows one by one in the direction they point, listing the sublevels as you pass through them.
Stop when you get to the sublevel you need.

44. Electron Orbital Diagram
3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

45. Example: Fill Orbitals w/ 7 electrons
3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

46. Review: How many electrons fill an s orbital?
How many electrons fill a p orbital ?(remember subshells…)
How many electrons fill a d orbital?
How many electrons fill an f orbital?

47. Example: Cl 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___
Give the final E.C:

48. With a partner: Examples: Give the E.CLi Be B C N F

49. No more…Make it
Write the electron configuration for Barium:
Ahhhhhhhhhh!!! Too many electrons!!
But wait…there’s a shortcut…
Noble gas / shorthand configuration:
Find the nearest noble gas that came before the element you are interested in
Write the symbol of that noble gas in [brackets]
Write the configuration as normal from there…

50. Examples: Sb

51. Stop & Practice
E.C. Worksheet

52. All Together Now… Mendeleev didn’t know quantum numbers Blocks
BUT…our periodic table is related to HOW electrons fill the levels in the different shells
Blocks
s block
Groups 1 & 2
p Block
Groups 3 – 8
d block
Transition Elements
f Block
Rare earth metals
Meaning, the electron configuration ends with this type of electron.
I.e. Vanadium: ends w/ 3 d

53. It ends w/…
It ends w/ the indicated orbitals…count across for number of neutrons…

54. Another Example: Ba (shorthand)

55. Stop & Practice
Patterns in Electron Configuration Worksheet

56. Columns Elements have similar properties Why? Examples
Similar ground state electron configurations
Examples
Noble gases
Complete sublevel
Favorable - do not react
Halogens
One electron short of completely filled sublevel
Readily react with elements who have a single electron