Lesson 18 Quantum Numbers
and Electron Configurations
Objectives:
1. The student will define and explain the four
quantum numbers.
2. The student will explain and apply Hund’s Rule
and the Pauli Exclusion Principle.
3. The student will write electron configurations for
elements, as well as determine what element is
represented by a specific electron configuration.
I. Scientists whose theories led to
the understanding of the electron:
a.
b.
c.
Louis deBroglie: French graduate student in physics
who proposed The DeBroglie Hypothes, which states
that particles have properties of waves as well as
properties of particles, “the wave particle duality of
nature” Formula ( λ= h/mv ) λ=wavelength, h=
Planck’s constant, m= mass in kg, v= velocity in m/s
Werner Heisenberg: German physicist who published
the Heisenberg Uncertainty Principle: it is impossible to
know the exact location and exact momentum of a
particle at the same time.
Erwin Schrodinger: 1926, Austrian physicist who
treated electrons as waves to help determine probability
of location within an atom. This led to the creation of
the quantum mechanical model that we use to explain
the structure of the atom today.
II. Labeling Electrons in atoms
a.
`
Quantum numbers are used to differentiate
between electrons
i. In quantum theory, each electron in an atom
is assigned a set of four quantum numbers.
ii. Three of these give the location of the
electron, and the fourth gives the orientation
of the electron within the orbital
iii. Definitions of numbers
1.
Principle Quantum Number – n – This number
describes the energy level that the electron occupies. It
can have a value of 1-7 – This defines the “level” of the
electron.
2. Orbital Quantum Number – l – (Azimuthal) this
number describes the shape of the orbital that the electron is
found in. It can have a value from 0-3. This defines the
“sublevel” of the electron. Also, the numbers can be replaced
by letters according to the following:
a.
0=s
b.
1=p
c.
2=d
d.
3=f
f orbital shapes:
3.
Magnetic Quantum Number - ml – this number
describes the orientation of the electrons in the orbitals. This
defines the “orbital” of the electron. There are 2l+1 orbitals in
each sublevel. This quantum number can have the following
values: (-l to +l)
a.
b.
c.
d.
If l = 0, ml can equal 0
If l = 1, ml can equal –1, 0, +1
If l = 2, ml can equal –2, -1, 0, +1, +2
If l = 3, ml can equal –3, -2, -1, 0, +1, +2, +3
4.
Spin Quantum Number – ms – this number describes the
direction of spin of the electron in the orbital – electrons in the
same level and sublevel must spin in opposite directions. This
can have a value or +1/2 or –1/2 only.
iv. According to the Pauli Exclusion Principle, no two
electrons can have the same four quantum numbers in the same
atom.
v.
Think of these as City, Street, House Number, and
upstairs/downstairs apartment. No two people could have the
same complete address, but they could live in the same city, on
the same street, or even in the same house, but not the same
apartment.
b.
Orbital diagrams and electron configurations are models
for electron arrangements.
i. Orbital diagrams are used to show how electrons
are distributed among the different sublevels and also to
show the direction of spin.
ii. For orbital diagrams, you must fill in orbitals in the
same energy level with one electron each before pairing
up any electrons. This is known as Hund’s Rule.
iii. Electron configurations are used to show similar
information, but are a much more abbreviated form.
iv. How many electrons can go in any level?
(Maximum)
1.
s=2
2.
p=6
3.
d = 10
4. f = 14
v.
What order do I fill the levels in? The Aufbau Principle
states that when predicting an atoms ground state electron
configuration, electrons will occupy the lowest energy
orbital available first.
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
vii.
This also could be written: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s,
4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
c. Electron configurations can be written in
terms of noble gases
i.
Instead of writing out the long configurations that
some of the larger elements would have, you can
abbreviate by using the next smallest noble gas to
the element in question to replace most of the
electron configuration.
ii. Only noble gases can be used for this. Don’t
replace part of an electron configuration with any
other element.
iii. Example Configurations with the noble gas
shortcut:
1. Cl
2. W
3. Ra
4. K
5. Zn
6. At
7. Cf
III. Writing Lewis Structures or Lewis Dot
Diagrams for elements
a. This is a kind of short hand that
illustrates how many outer shell electrons
an atom contains.
b. The purpose behind all of the
configurations is because the number of
electrons and their placement in the
atom, strongly influences how the atom
will react, bond and the properties it will
demonstrate.
c. Rules for writing dot diagrams:
i.
ii.
iii.
iv.
Write configuration.
How many e- are in the outer energy level?
Write the elements symbol.
Draw dots around the symbol to represent
outer level electrons, each of the 4 sides
represents an orbital.
v. “s” electrons must be paired (1st two e-)
vi. Other three sides cannot be paired until each
has at least one e-. (Hund’s Rule)
d. Example:
e.
Dot diagram examples:
i. C
ii.
Br
iii. Ar
iv. H
v.
Mg
vi. Ag
vii. P
viii. O
IV. Exceptions to electron configuration
using the Aufbau Diagram
a.
b.
c.
d.
A half full level is the next stable thing to a
full level.
Some atoms will violate our predictions in
order to achieve stability. This can occur in
the transition metals when the predicted
configuration ends in a d4 or d9.
It will steal a single electron from the full s
shell that came before it to obtain 2 half full
shells or one half and one full shell.
(s2 d4) becomes (s1 d5) and (s2 d9)
becomes (s1 d10)
e.
Actual exceptions:
* 5d1 fills before starting the 4f sequence
* 6d1 fills before starting the 5f sequence
Predicted configurations
Cr:[Ar]4s2, 3d4
Cu:[Ar] 4s2, 3d9
Nb:[Kr]5s2,4d3
Mo:[Kr] 5s2, 4d4
Tc:[Kr] 5s2, 4d5
Ru[Kr] 5s2, 4d6
Rh[Kr] 5s2, 4d7
Pd[Kr] 5s2, 4d8
Ag[Kr] 5s2, 4d9
Pt[Xe] 6s2, 4f14, 5d8
Au[Xe] 6s2, 4f14, 5d9
Actual configurations
Cr:[Ar] 4s1, 3d5
Cu[Ar] 4s1, 3d10
Nb:[Kr] 5s1, 4d4
Mo[Kr] 5s1, 4d5
Tc[Kr] 5s1, 4d6
Ru[Kr] 5s1, 4d7
Rh[Kr] 5s1, 4d8
Pd[Kr] 5s0, 4d10
Ag[Kr] 5s1, 4d10
Pt[Xe]6s1, 4f14, 5d9
Au[Xe] 6s1, 4f14, 5d10
Questions:
1. Make a chart, with the following columns:
Quantum number name, symbol, possible
values. Fill in the information for each of
the four quantum numbers.
2. What is the reason that an element cannot
have all four quantum numbers the same?
3. What is the rule which means “spread
them out before you pair them up”?