SCH4U1
As we have seen, the location of an electron can be identified by its orbital type. These names indicate the energy level, shape and orientation of the electron. For example: 1 s,
2 p x
, 5 d xy
.
Another system used to identify am electron is the quantum number system. With this system, a particular electron is designated by a set of 4 numbers.

Principle Quantum Number (n)
This indicates the energy level of the electron. n =1, 2, 3, 4, 5 etc.

Secondary Quantum Number ( l
)
This indicates the type of orbital the electron is in. l
=0 ( s orbital) l
= 1 ( p orbital) l
= 2 ( d orbital) l
= 3 ( f orbital)

Magnetic Quantum Number (m l or m)
This indicates the orientation of the orbital that the electron is in. Possible values depend on the value for l
.
When l
=0
 m l = 0 (only 1 spherical orientation)
When l
= 1
 m l = +1 ( p x
), m l = 0 ( p y
), m l = -1 ( p z
)
When
l
= 2
 m l = +2, +1, 0, -1, -2
When l
= 3
 m l = +3, +2, +1, 0, -1, -2, -3

Spin Quantum Number (m s or s)
Each orbital can contain 2 electrons. However these 2 electrons must have opposite spin. These are the same for all orbitals. m s
= + ½ and - ½
Examples:
What are the possible quantum numbers of an electron in the following orbitals: a) 1 s b) 2 p x c) 5 d xy
Note that no 2 electrons in an atom can have the same 4 quantum numbers.

SCH4U1
This is a useful tool to visualize orbitals and their relative energies. Electrons are added to an energy level diagram using the same rules describe for writing electron configurations.
Examples: a) Carbon b) Chromium*
* Note that the actual electron configuration of chromium is anomalous. Refer to p.196 of the textbook.
An aufbau diagram (right) is one way to memorize the order in which energy levels are filled. The diagonal arrows indicate the order in which electrons are added to the various orbitals.

SCH4U1
Anions (negatively-charged ions) can be written simply by adding the number of electrons corresponding to the ionic charge and then drawing the electron configuration. e.g. fluorine atom has 9 electrons, therefore the fluoride ion (F
-
) has 10 fluorine atom (F) fluoride ion (F ):
Cations (positively-charged ions) can be written by first drawing the neutral atom and then removing electrons. e.g. sodium atom (Na) sodium ion (Na + )
Note that the fluoride ion, neon atom and sodium ion are all isoelectronic (i.e. they have the same electron configurations).
Transition Metals: Bohr’s model could not explain the charges of the transition metals.
The stable ions of iron can finally be explained by looking at their energy level diagrams.
Electrons are always removed from the orbital with the highest principle quantum number first. e.g. iron atom (Fe): iron ion (Fe
2+
): iron ion (Fe
3+
):

SCH4U1
Quantum Number and Energy Level Problem Set
1. Draw energy level diagrams for: a) F b) Ca c) Co d) Yb e) N
3-
2. Write the short form electron configuration for: a) F b) Ca c) Co d) Yb
3. Identify the orbital corresponding to the following quantum numbers: a) n = 3, l
= 2, m l = 1, m s
=

½ b) n = 5, l
= 3, m l = -3, m s
=

½ c) n = 4, l
= 1, m l = -1, m s
=

½ d) n = 2, l
= 1, m l = 0, m s
=

½ e) n = 4, l
= 2, m l = -2, m s
=

½
4. Which of the following designations are orbitals that are not possible in wave mechanics?
1 d , 4 f, 1 p, 6 d , 2 f
5. Which of the following are sets of quantum numbers for orbitals which are possible in wave mechanics? a) n = 1, l
= 1, m l = 1, m s
=

½ b) n = 2, l
= 1, m l = 2, m s
=

½ c) n = 2, l
= 0, m l = 0, m s
=

½ d) n = 3, l
= 3, m l = 1, m s
=

½ e) f) n n
= 3,
= 4, l l
= 2,
= 3, m m l l = -2,
= 2, m m s s
=
=


½
½
6. Write the quantum numbers for the two electrons in a 3 s orbital.
7. The actual electron configuration of chromium is [Ar]4 s
1
3 d
5
. Read p. 196 and explain why chromium has an anomalous electron arrangement.