The location of an electron in an atom can be described by four quantum numbers.
Quantum Number
Principal Quantum Number
Symbol
n
Range
n = 1 to n = ∞
Secondary Quantum Number
l
l = 0 to l =n – 1
Magnetic Quantum Number
ml
ml = - l to ml = + l
Spin Quantum Number
ms
ms = + ½ or ms = - ½
ENERGY LEVELS (1, 2, 3, 4…) or SHELLS (K, L, M, N)
Are subdivided into
SUBLEVELS (s, p, d, f…) or SUBSHELLS
Are subdivided into
ORBITALS
Bohr’s theory was based on the idea that electrons travel in some kind of orbit or path,
a more modern view is that of an electron orbital. An electron orbital is a region
(volume) of space where an electron is most likely to be found. Below is a table that
indicates some of the differences between an orbit and an orbital.
Orbits
2-D path
Fixed distance from nucleus
Circular or elliptical path
2n2 electrons per orbit, where n is the
principal quantum number
Orbitals
3-D region in space
Variable distance from nucleus
No path; varied shape of region
2 electrons per orbital
Principal Quantum Number, n
This refers to the energy level. Energy levels range from n = 1 to n = ∞. As n
increases, the energies of the orbtials also increase. The maximum number of
electrons in an energy level can be determined using the formula 2n2.
Secondary Quantum Number, l
This refers to the type of sublevel/subshell. Each subshell has a different shape.
Subshells range from l = 0 to l =n – 1.
value of l
0
1
2
3
4
5
letter designation
for subshells
s
p
d
f
g
h
…
The number of subshells is equal to the principal quantum number. For instance,
when n = 1, l = 0, therefore 1 subshell (s) [Refer to chart above.]
when n = 2, l = 0, 1, therefore 2 subshells (s, p)
Question 1: Which subshell has the following quantum numbers?
(a) n = 2, l =1 _____________
(b) n = 3, l = 2 _____________
Question 2: What subshells can be found in the following shells?
(a) n = 3
(b) n = 4
Magnetic Quantum Number ml
This refers to the region of space in which electrons in the energy subshells are most
likely to be found. Magnetic quantum number can range from ml = - l to ml = + l
value of l
0
1
2
3
…
subshell
s
p
d
f
…
# of orbitals
1
3
5
7
When l =0, ml = 0, therefore the s subshell has only one orbital.
When l = 1, ml = -1, 0, +1, therefore the p subshell has three orbitals.
Question 3: How many orbitals in a g subshell?
Spin Quantum Number ms
This is best described as the spin of the electrons in an orbital, although scientists do not think
the electron is actually spinning. The spin quantum number can only be ms = + ½ or ms = - ½.
Only two electrons can share the same orbital, one spinning clockwise and the other spinning
counterclockwise.
Electron Configuration
Electron configuration is a method for communicating the location and each number of electrons
in electron energy levels. Example: Mg: 1s22s22p63s2
Question 4: Interpret the following:
3p5
Steps for Writing Electron Configuration
1. Determine the position of he element in the periodic table and the total number of electrons
in the atom or simple ion.
2. Start assigning electrons in order of increasing order of main energy levels and sublevels
(using aufbau diagram or the periodic table).
3. Continue assigning electrons by filling each sublevel before going to the next sublevel, until
all the electrons are assigned.


For anions (negatively charged ions), add the extra electrons to the total number in the
atom.
For cations (positively charged ions), write the electron configuration for the neutral atom
first and then remove the required number of electrons from the highest quantum
number, n.
4. To write shorthand electron configuration, start at the noble gas immediately preceding the
atom or ion.
aufbau Principle
“aufbau” is German for building up; each electron is added to the lowest energy orbital available
in an atom or ion.
Example 1: Write the electron configuration for the tin atom and the tin (II) ion.
Example 2: Write the shorthand electron configuration for the lead atom and lead (II) ion.
Example 3: Write two permissible quantum numbers for the electron found in the outermost
energy level of a potassium atom.
Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum numbers; no two electrons in the
same atomic orbital can have the same spin; only two electrons with opposite spins can occupy
any one orbital.
Anomalous Electron Configuration
Some elements are exceptions to the rules for writing electron configuration. Two examples are
chromium and copper
Element
chromium
Predicted Electron Configuration
[Ar] 4s23d4
Actual Electron Configuration
[Ar] 4s13d5
copper
[Ar] 4s23d9
[Ar] 4s13d10
This suggests that half-filled and filled subshells are more stable (lower energy) than unfilled
subshells. In the case of chromium, an s electron is promoted to the d subshell to create two
half-filled subshells. In the case of copper, an s electron is promoted to the d subshell to create
a half-filled s subshell and a filled d subshell.
Energy Level Diagrams
aufbau Principle
“aufbau” is German for building up; each electron is added to the lowest energy orbital available
in an atom or ion.
Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum numbers; no two electrons in the
same atomic orbital can have the same spin; only two electrons with opposite spins can occupy
any one orbital.
Hund’s Rule
When electrons are placed in a set of orbitals of equal energy, there are spread out as much as
possible to give as few paired electrons as possible.
Example 1:
Draw the electron energy level diagram for:
(a) an oxygen atom
(b) an iron atom
(c) a sulfide ion
(d) a zinc ion