2. Quantum Numbers:
specify the properties of atomic orbitals and their electrons.

3. Four Quantum Numbers Principal Quantum Number Orbital Quantum Number
Magnetic Quantum Number
Spin Quantum Number

4. Principal Quantum Number, n
Indicates main energy levels
n = 1, 2, 3, 4…
Each main energy level has sub-levels

5. The maximum number of electrons in a principal energy level is given by:
Max # electrons = 2n2
n= the principal quantum number

6. Orbital Quantum Number, ℓ (Angular Momentum Quantum Number)
Indicates shape of orbital sublevels
ℓ = n-1
ℓ sublevel
0 s
1 p
2 d
3 f
4 g

7. l : The secondary quantum number
If n can be thought of as shells, l can be thought of as “subshells” dividing each shell into subsections … (l = 0  n - 1)
n = 1
l = 0 (s)
n = 3
l = 0 (s)
l = 1 (p)
l = 2 (d)
n = 2
l = 0 (s)
l = 1 (p)
Use QN WS as study tool

8. Atomic Orbital s 2s

9. II. Orbital Shapes and Energies
Atomic orbital shapes are surfaces that surround 90% of the total probability of where its electrons are
Look at l = 0, the s-orbitals
Basic shape of an s-orbital is spherical
centered on the nucleus
Basic shape is same for same l values
Nodes = areas of zero probability
Number of nodes changes for larger n
We will usually just use outer surface
to describe the shape of an orbital

10. Degenerate Orbitals

11. The 3 p orbitals

12. p-orbitals There are no 1p orbitals (n = 1, l = 0 only)
2p orbitals (n = 2, l = 1) have 2 lobes with a node at the nucleus
There are three different p-orbitals (l = 1, ml = -1, 0, 1)
2px lies along the x-axis
2py lies along the y-axis
2pz lies along the z-axis
All three 2p orbitals have the same energy = degenerate
3p, 4p, 5p, etc… have the same shape and number, just larger

13. The d orbitals

14. d-orbitals There are no 1d or 2d orbitals (d needs l = 2, so n = 3)
5 degenerate d-orbitals (ml = -2, -1, 0, 1, 2)
4 of the d-orbitals have 4 lobes which lie in planes on or between the xyz axes: 3dxy, 3dxz, 3dyz, 3dx2-y2
1 is composed of 2 lobes and a torus- shaped area: 3dz2
The 4d orbitals etc…are the same shape, only larger

16. f orbitals

17. f-orbitals n = 4, l = 3, ml = -3, -2, -1, 0, 1, 2, 3
7 f-orbitals in the fourth shell are degenerate
The f-orbital are only used for the lanthanides and actinides and are complex shapes. We won’t use them.

18. Magnetic Quantum Number, ml
Indicates the orientation of the orbital in space.
Values of ml : integers -l to l
The number of values represents the number of orbitals.
Example:
for l= 2, ml = -2, -1, 0, +1, Which sublevel does this represent?
Answer: d

19. Electron Spin QN (ms = +1/2, 1/2)
Relates to the spin states of the electrons.
Electrons are –1 charged and are spinning
Spinning charge creates a magnetic field
You can tell the direction of the spin by which way the magnetic moment lines up in an external magnetic field
The two possible spin directions are called +½ and –½

20. Electron Spin Quantum Number, (ms or s)
Indicates the spin of the electron (clockwise or counterclockwise).
Values of ms: +1/2, -1/2

21. Example:
List the values of the four quantum numbers for orbitals in the 3d sublevel.
Answer:
n=3
l = 2
ml = -2,-1, 0, +1, +2
ms = +1/2, -1/2 for each pair of electrons

22. The Electron Cloud
The electron cloud represents positions where there is probability of finding an electron.

23. The Electron Cloud
The higher the electron density, the higher the probability that an electron may be found in that region.

24. The Electron Cloud for Hydrogen
90% probability
of finding the electron within this space

25. Probability Curve for Hydrogen

26. Quantum Mechanical Model
Electrons are located in specific energy levels.
There is no exact path around the nucleus.
The model estimates the probability of finding an electron in a certain position.

27. Let's Summarize Quantum Numbers

28. Principal Quantum Number
Symbol = n
Represents the main energy level of the electron
Range = 1- 7
Ex. = 3s
Principal Quantum number = 3

29. Angular Momentum Quantum Number
Symbol = l (small letter L)
Represents the shape of the orbital (also called sublevel)
Range = 0 – n-1 (whole number)
Shapes:
0 = s (sphere) 1 = p (petal)
2 = d (double petal) 3 = f (flower)

30. Magnetic Quantum Number
Symbol = m
Represents the orientation of the orbital around the nucleus
Each line holds 2 electrons
___ = s
___ ___ ___ = p

31. Magnetic Quantum Number (cont.)
___ ___ ___ ___ ___ = d
___ ___ ___ ___ ___ ___ ___ = f

32. So what is ms (or just “s”)?
The spin (clockwise or counterclockwise) on the electron
It describes which of the 2 possible electrons in any orbital is being described
Values: +/- ½

33. Spin Quantum Number 2 Spin States Clockwise spin = +1/2 (upward arrow)
Counterclockwise spin = -1/2 (downward
arrow)
A Single orbital can hold two electrons, but they must have opposite spins

34. Unit 2 – Electrons and Periodic Behavior Cartoon courtesy of NearingZero.net