Quantum Mechanical Theory
-
Allows us to predict the probability of finding an electron at various points in space
Allows us to explain both the atomic spectra of elements better, the arrangement of elements on the
periodic table of elements, and understand chemical bonding
Bohr’s theory
Term used: orbits
2-D path
Fixed distance from the nucleus
Quantum Mechanical theory
Term used: orbital
3-D region in space
Variable distance from the nucleus
Circular or elliptical path
No path: varied shape of region
2n2 electrons per orbit
2 electrons per orbital
Quantum Numbers
- Used to describe an electron in an atom
- There are four quantum numbers:
1)
2)
Principal Quantum Number (n)
- Aka: Principal energy level
- Tells you the energy of the electron in an atom
- Positive number (1,2,3,…)
- The smaller the n, the lower the energy
- The size of an orbital also depents on n
- Orbitals with the same n are said to belong to the same shell
- Are sometimes designated by letters
Letter
K
L
M
N…
n
1
2
3
4…
Secondary Quantum Number (l)
- Aka: Sublevel
- Distinguishes orbitals of a given n as having different shapes
- An integer value from 0 to n – 1
- For a given n, the energy of an orbital increases with l
- Orbitals of the same n but different l are said to belong to different subshells of a given shell
Letter
s
p
d
f
l
0
1
2
3
The subshells are split up into 4 different types
s subshell – hold a max of 2 electrons
p subshell – hold a max of 6 electrons
d subshell – hold a max of 10 electrons
f subshell – hold a max of 14 electrons
-
Shapes of the subshells
s subshell – sphere
p subshell – 3 dumbbells
The shape of the subshells become harder to predict and the mathematical calculations are
more complex as the principal quantum number increases
s (l=0)
p (l=1)
m=0
m=0
s
pz
d (l=2)
m=±1
px
m=0
py
dz2
f (l=3)
m=±1
dxz
m=±2
dyz
dxy
dx2-y2
m=0
fz3
m=±1
fxz2
fyz2
m=±2
fxyz
m=±3
fz(x2-y2) fx(x2-3y2) fy(3x2-y2)
n=1
n=2
n=3
n=4
n=5
n=6
n=7
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
3) Magnetic Quantum Number (ml)
-
Distinguishes one orbital from another in the same sublevel
Distinguishes orbitals given n and l → that is, given energy and shape but having a different
orientation in space
Integers from –l to +l
Each orbital of a given subshell has the same energy
Table 1. Permissible Values of Quantum Numbers for Atomic Orbitals
n
l
ml *
Subshell
Notation
Number of
Orbitals in the
Subshell
1
0
0
1s
1
2
0
0
2s
1
2
1
-1, 0, +1
2p
3
3
0
0
3s
1
3
1
-1, 0, +1
3p
3
3
2
-2, -1, 0, +1, +2
3d
5
4
0
0
4s
1
4
1
-1, 0, +1
4p
3
4
2
-2, -1, 0, +1, +2
4d
5
4
3
-3, -2, -1, 0, +1, +2, +3
4f
7
* Any one of the mi quantum numbers may be associated with the n and l quantum numbers on the
same line.
- NOTE: there are 2l + 1 orbitals in each subshell of quantum number l
4)
Spin Quantum Number (ms)
- Refers to the two possible orientations of the spin axis of an electron
- Possible values are + ½ or – ½
Table 2. Key Experimental Work in Creating the Four Quantum Numbers
Key Experimental work
low-resolution line spectra
Theoretical Explanation
principal quantum number (n)
high-resolution line spectra
secondary quantum number (l)
spectra in magnetic field
magnetic quantum number (ml)
ferro- and paramagnetism
spin quantum number (ms)
Quantum Theory
All electrons in all atoms can
be described by four quantum
numbers
Electron Configuration
- Shows the order of filling of the orbitals
1s2
Energy level
(n)
Sublevel/subshell
(l)
Do examples: sulphur, iron, bismuth
Number of electrons in that sublevel
Shorthand of Electron Configurations
- Write the symbol of the preceding noble gas in square brackets
- Just the remaining electrons following that noble gas need to be included