PHY1003 Properties of Matter
1
Atomic and molecular structure
The wave functions for the hydrogen atom are
determined by the values of three quantum numbers
n, l and m
l
.
n principal quantum number (determines the energy)
l orbital quantum number (determines the magnitude of
the orbital angular momentum)
m
l
magnetic quantum number (determines the component
of orbital angular momentum in a specified axis direction)
I. Quantum number notation
A fourth quantum number, m
s
(the spin quantum
number) is necessary to label completely the state of the
electron
in a hydrogen atom
(determines
the
z-component of the spin angular momentum).
Quantum number notation
For many-electron atoms, in the central-field
approximation, we can still label a state using the four
quantum numbers (n, l, m
l
and m
s
). In general, the
energy of the state now depends on both n and l.
Restrictions on the values of the quantum numbers
(the same as for the hydrogen atom)
ms = ±
1
2
l = 0, 1,2 . . . (n − 1)
ml = −l . . .+ l
n ≥ 1
n = 1, 2, 3...
The exclusion principle
The exclusion principle states that
no two electrons can occupy the same
quantum-mechanical state in a given system.
This means that
no two electrons in an atom can have the
same values of all four quantum numbers
n, l, m
l
and m
s
.
Wolfgang Ernst Pauli
(1900-1958)
PHY1003 Properties of Matter
2
Quantum number notation
The radial extent of the wave functions increases with the
principal quantum number n, and we can speak of a region
of space associated with a particular value of n as a shell.
States with the same n but different l form subshells.
These subshells are often lebelled with letters.
Remember that
n = 1 K shell
n = 2 L shell
n = 3 M shell
n = 4 N shell
l = 0, 1,2 . . . (n − 1)
l = 0 s state
l = 1 p state
l = 2 d state
l = 3 f state
l = 4 g state
Quantum states of electrons
The maximum number of electrons in a shell is 2n2
14
4f
-3,-2,-1,0,1,2,3
3
4
N
10
4d
-2,-1,0,1,2
2
4
6
4p
-1,0,1
1
4
2
4s
0
0
4
10
3d
-2,-1,0,1,2
2
3
M
6
3p
-1,0,1
1
3
2
3s
0
0