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Quantum Numbers
Section 3.
Quantum Numbers
- a set of four numbers used to describe each electron in an atom.
- each number identifies one characteristic of that electron
For example, the valence electron of Be has the following set of numbers: n = 2 l = 0 ml = 0 ms = +½
first three: describe an orbital
fourth: describes a specific electron
m (^) l m (^) s
Principal quantum number, n
- specifies: the energy level and size (together aka “shell”)
- possible values: positive whole number (range = 1, 2, ... ∞)
- higher value of n = higher energy level = larger shell
n = 1 (^) n = 2 n = 3
The energy levels are kind of like the shells from the Bohr- Rutherford diagrams you learned in previous studies!
Every shell (n) contains smaller sub-shells.
- All sub-shells within a shell are part of the same principal energy level.
(n) (l)
(m (^) l )
Secondary quantum number, l
Specifies: the sub-shell’s shape (i.e., the orbital type)
value of l 0 1 2 3 4 orbital s p d f g
s orbital
p orbitals
d orbitals
Possible values of l : 0 to (n-1)
- range of values depends on the value of n
Principal number, n
Possible values of l Orbital name
1 0 1s 2 0 1 2p 3
value of l 0 1 2 3 4 orbital s p d f g
Always named using energy level and orbital shape
A 3f orbital cannot exist… use quantum numbers to explain why.
Sub-shells contain individual orbitals.
- Recall: the orbitals are the region where one is likely to find a particular e -.
- Each orbital can hold a maximum of 2 electrons.
(n) (l)
(m (^) l )
Third quantum number, ml
- called the “magnetic quantum number”
- specifies: the orbital within the sub-shell, by identifying its 3-D orientation
Example 1 There are three 2p orbitals:
n = 2, l = 1
m (^) l = -1 m (^) l = 0 m (^) l = +
Example 2 There are five 3d orbitals: n = ____, l = ____
m (^) l = -2 m (^) l = -1 m (^) l = 0 m (^) l = +1 m (^) l = +
Can you figure out an expression that relates l to the possible values of ml****?
Possible values of m l: -l to +l, including 0
Principal number, n
Possible values of l Possible values of m^ l
1 0 0 2 0 1 -1, 0, + 3 0 1 2
Use quantum numbers to figure out: How many 4f orbitals are possible?
- The maximum number of orbitals that a principal energy level
can contain is n^2.
- Since every orbital can hold a maximum of 2 electrons, this
means, that the total number of electrons a principal energy
level can contain is 2n^2.
Verify these relationships for principal energy level n = 2.
