Download The Quantum Number System

SCH4U1
The Quantum Number System
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: 1s, 2px, 5dxy.
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.
 Principal Quantum Number (n)
This indicates the energy level of the electron.
n=1, 2, 3, 4, 5 etc.
 Secondary Quantum Number (l)
Ranges from 0 to n-1
This indicates the shape or sublevel of the orbital the electron is in.
l =0 (s orbital)
l = 1 (p orbital)
l = 2 (d orbital)
l = 3 (f orbital)
 Magnetic Quantum Number (ml)
This indicates the orientation of the orbital that the electron is in.
Ranges from – l to +l.
When l =0  ml = 0 (only 1 spherical orientation)
When l = 1  ml = +1 (px), ml = 0 (py), ml = -1 (pz) (3 possible orientations)
When l = 2  ml = +2, +1, 0, -1, -2 (5 possible orientations)
When l = 3  ml = +3, +2, +1, 0, -1, -2, -3 (7 possible orientations)
 Spin Quantum Number (ms)
Each orbital can contain 2 electrons. However these 2 electrons must have opposite
spin. These are the same for all orbitals.
ms = + ½ and - ½
Examples:
What are the possible quantum numbers of an electron in the following orbitals:
a) 1s
b) 2px
c) 5dxy
Note that no 2 electrons in an atom can have the same 4 quantum numbers.
SCH4U1
Energy Level Diagrams
This is a useful tool to visualize orbitals and their relative energies. Electrons are added to an
energy level diagram using the same rules described for writing electron configurations.
Rules for drawing energy level diagrams:
1. Pauli Exclusion Principle: Represent each electron by an arrow. The direction of the
arrow represents the electron spin. Draw an up arrow to show the first electron in each
orbital.
2. Aufbau Principle: Electrons (arrows) are placed into the orbitals by filling the lowest
energy orbitals first. An energy sublevel must be filled before moving on to the next
higher level
3. Hund’s Rule: Place one electron into each orbital of the same energy before pairing
the electrons.
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.
Examples:
a) Carbon
b) Manganese
(leave lots of room)
c) Neodynium
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Electron Configurations of Ions
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.
Eg. Draw the electron configurations for the following:
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). Draw the neon electron configuration and explain why based
on your previous knowledge of formation of ions.
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 principal quantum number first.
e.g.
iron atom (Fe):
iron ion (Fe2+):
iron ion (Fe3+):
SCH4U1
Quantum Number and Energy Level Practice
1. Draw energy level diagrams for:
a. a) F
b) Ca
c) Co
2. Write the short form electron configuration for:
b. a) F
b) Ca
c) Co
d) Yb
e) N3-
d) Yb
3. Identify the orbital corresponding to the following quantum numbers:
a) n = 3, l = 2, ml = 1, ms =  ½
b) n = 5, l = 3, ml = -3, ms =  ½
c) n = 4, l = 1, ml = -1, ms =  ½
d) n = 2, l = 1, ml = 0, ms =  ½
e) n = 4, l = 2, ml = -2, ms =  ½
4. Which of the following designations are orbitals that are not possible in wave
mechanics?
c. 1d,
4f,
1p,
6d,
2f
5. Which of the following are sets of quantum numbers for orbitals are possible in wave
mechanics? If they are not possible, explain why.
d. a) n = 1, l = 1, ml = 1, ms =  ½
d) n = 3, l = 3, ml = 1, ms =  ½
e. b) n = 2, l = 1, ml = 2, ms =  ½
e) n = 3, l = 2, ml = -2, ms =  ½
f. c) n = 2, l = 0, ml = 0, ms =  ½
f) n = 4, l = 3, ml = 2, ms =  ½
6. Write the quantum numbers for the two electrons in a 3s orbital.
7. a) The actual electron configuration of copper is [Ar]4s13d10 which is different from its
expected configuration. Read p. 168 to explain this anomalous electron configuration.
b) Draw chromium’s electron configuration and predict how it achieves its anomalous
electron arrangement of [Ar]4s13d5. (look up the definition for anomaly if you don’t
understand what the question is asking)
8. The last electron represented in an electron configuration is related to the position of
the element in the periodic table. For each of the following sections of the periodic
table, indicate the sublevel (s, p, d, f) of the last electron:
a) groups 1 and 2
b) groups 3-12 (transition metals)
c) groups 13-18
d) lanthanides and actinides
9. a) When the halogens form ionic compounds, what is the ionic charge of the halide
ions?
b) Describe and explain the similarities and differences in properties of these two
chemical entities.
10. The sodium ion and the neon atom are isoelectronic: i.e., have the same electron
configuration.
a) Write the electron configurations for the sodium ion and the neon atom.
b) Describe and explain the similarities and differences in properties of these two
chemical entities.
11. Use energy level diagrams to explain the common ion charges for antimony, i.e., Sb3+,
Sb5+.
12. Predict the electron configuration for the gallium ion, Ga3+. Provide your reasoning.