The Four Quantum NumbersIn the quantum mechanical model of the atom, each electron is described by four quantum numbers, and no two electrons in an atom can have the same numbers.
The quantum numbers are:
n: the principle quantum number. n = 1, 2, 3, 4…
l: the angular quantum number. It describes the ‘shape’ of the orbital…the electronic distribution about the nucleus. l = n-1, n-2,… to 0
If l = 0, it’s an s orbitalIf l = 1, it’s a p orbitalIf l = 2, it’s a d orbitalIf l = 3, it’s an f orbital (and so on)
ml: the magnetic quantum number. It describes the orientation of the orbital on an xyz-coordinate axis. ml = -l…0…+l in integral values.
ms: the spin quantum number. It equals +½ or -½. Conventionally, the +½ is always given first.
A few examples:
1
n l ml
0 0
(all ms’s are ± ½, so won’t be shown here)
Notes
The 1s orbital
2 1
0 0
-1, 0, 1 The three 2p orbitals.
2 The 2s orbital
3 2 -2, -1, 0, +1, +2 The five 3d orbitals.
3 1 -1, 0, +1 The three 3p orbitals.
3 0 0 The 3s orbital
x
y
z
x
y
z
x
y
z
px pz py
The three p-orbitals are oriented along the x, y and z axes and can hold a maximum of 2 electrons each.
It’s been suggested that the p-orbitals look like peanuts if that helps you to remember their shape.
The d-orbitals
dxy dxz dyz
Even though the d-orbitals look like two p-orbitals, it is important to remember that each orbital can hold a maximum of 2 electrons regardless of how many lobes it has.
dx2-y2 dz2
The freaky (or flowery) f-orbitals
And Electron Configurations
Orbital Diagrams
H: 1 electron, 1s1
Electron configuration
Electrons behave as though they are spinning on their axis. A half arrow is used to indicate if the direction of the spin is up ( ) or down ( ).
Electrons behave as though they are spinning on their axis. A half arrow is used to indicate if the direction of the spin is up ( ) or down ( ).
He: 2 electrons, 1s2
Pauli Exclusion Principle:Each orbital can contain 2 electrons ONLY if the electron spins are in opposite directions.
Pauli Exclusion Principle:Each orbital can contain 2 electrons ONLY if the electron spins are in opposite directions.
Li: 3 electrons, 1s2 2s1
Auf bau principle: the electrons fill the orbitals starting with the lowest energy level and working their way up the energy ‘ladder’
Auf bau principle: the electrons fill the orbitals starting with the lowest energy level and working their way up the energy ‘ladder’
Be: 4 electrons, 1s2 2s2
B: 5 electrons, 1s2 2s2 2p1
C: 6 electrons, 1s2 2s2 2p2
Hund’s Rule: all sublevel orbitals of the same energy must be filled with a single electron before the electrons can begin to pair up.
Hund’s Rule: all sublevel orbitals of the same energy must be filled with a single electron before the electrons can begin to pair up.
Sc: 21 electrons , 1s2 2s2 2p6 3s2 3p6 4s2 3d1
Total electrons
241012182021
complete configuration
Shorthand notation: noble gas core configuration4s2 3d1[Ar]
n
1
2
3
4
5
6
7
n -1
n -2
d-block metals
f-block metals
s-block metals
p-block elements
1s1 1s2
2s1 2s2 2p1 2p2 2p3 2p4 2p5 2p6
3s1 3s2 3p1 3p6
4s1 4s2 3d1 3d10 4p1 4p6
4d1 4d10
5d1
We’ll look at the f-block tomorrow
4f14
5f14
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p4
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d8
Chemical reactivity depends upon the number of electrons in the highest energy level (the largest n).
• Electron dot structures show only the outermost electrons so that reactivity can be easily predicted.
• The outermost electrons are also called the valence electrons.
Electron Dot Structures
Rules to Drawing Electron Dot Structures
1. Electrons 1-4 are added singly.2. Exception: If there only two electrons, they’re
shown as a pair.3. Electrons 5-8 are paired with the single
electrons that are already there.
Xe
Sr
N
Examples:
1. What is the electron configuration of strontium (Sr)?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 3p6 5s2
The highest energy level is n=5 and there are 2 electrons in it. Therefore, Sr has 2 valence electrons.
2. What is the electron configuration of nitrogen (N)?
1s2 2s2 2p3
The highest energy level is n=2 and there are 5 electrons in it. Therefore, N has 5 valence electrons.
3. What is the electron configuration of xenon (Xe)?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 3p6 5s2 4d10 5p6
The highest energy level is n=5 and there are 8 electrons in it. Therefore, Xe has 8 valence electrons.
Excluding a few exceptions, how many valence electrons would all of the d-block and f-block elements have?
1
2 3 4 5 6 7
8
# Valence electrons
Electron Configuration Exceptions
Hund’s Rule (part 2): For n ≥ 4, the energy of the electrons decreases (and stability increases) when all of the boxes for a sublevel are either half-filled OR completely filled.
4s 3d
All of the orbitals are half-filled
Cr
4s 3d
Cu
[Ar]
[Ar] All of the 3d orbitals are filled and the 4s orbital is half-filled
Where would the exceptions be in the 5th through 7th periods?