Download Quantum Number Review Heisenberg Uncertainty Principle

Heisenberg Uncertainty
Principle
• Heisenberg uncertainty principle states
that it is impossible to know exact position
and speed of an electron simultaneously.
• The best we can do is to describe the
probability of finding an electron in a
specific location.
Quantum Number Review
Principal quantum number, n,
size and energy of an orbital
• Has whole-number values
• Spaces between shells are not equal
Second quantum number, l,
Shape of orbitals
l
Name of
orbital
Shape
0
1
2
s
sharp
p
principal
d
diffuse
Sphere
(1 lobe)
2 lobes
4 lobes
Arrangement of orbitals in an
atom
3
f
fundamental
8 lobes
1
Magnetic quantum number, ml
describes orientation of orbital in 3D space
Identifying orbitals using
quantum numbers
• The number of different ml values, equals the number of
orbitals that are possible
n
l
Sublevel
designation
ml
Number of
orbitals
Number of
electrons in each
orbital 2n2
1
0
1s
0
1
2
2
0
2s
0
1
2
1
2p
-1, 0, +1
3
6
0
3s
0
1
2
1
3p
-1, 0, +1
3
6
2
3d
-2, -1, 0, +1, +2
5
10
3
Spin quantum number, ms
direction of spin of an electron
Summary of Electrons and
Orbitals
• Each shell or principal level of quantum number
n contains n subshells
– Eg. If n=2, l=0,1
• Each subshell of quantum number l contains
2l+1 orbitals
– Eg. If l=1, there are 3 p orbitals
• Not more than 2 electrons can be placed in each
orbital therefore the maximum number of
electrons is twice the number of orbitals
• There are 2n2 electrons in each quantum level
The Periodic Table
Atomic Structure and the
Periodic Table
• Arranged according to the way electrons
are arranged around the nucleus
• Electron arrangement determines
chemical behaviour of every element
(recall the reactivity of elements based on
the number of electrons in their valence
shells)
2
Relationship Between Quantum Numbers and the Periodic
Table
The number of
the period
corresponds to
the principal
quantum
number.
n=1
n=2
n=3
n=4
n=5
n=6
n=7
This is similar to
the shells that
were drawn in
B-R diagrams.
Relationship Between Quantum Numbers and the Periodic
Table
The secondary
quantum number
corresponds to the
different blocks on
the periodic table.
These blocks show
the shape of the
orbitals that the
electrons occupy.
2 lobe
4 lobe
spherical
8 lobe
Notice that there are several sublevels with the same principal
quantum number. This means that each energy level has orbitals of
different shapes. Each principal quantum number has n2 orbitals.
Relationship Between Quantum Numbers and the Periodic
Table
Relationship Between Quantum Numbers and the Periodic
Table
The tertiary quantum
number indicates how many
orbitals there are.
The s sublevel has one
orbital, ml=0.
The p sublevel has 3 orbitals,
ml= -1, 0, +1
The d sublevel has 5 orbitals,
ml= -2, -1, 0, +1, +2
The fourth quantum
number simply
indicates that when
electrons are paired in
an orbital, each one
spins opposite to the
other.
Each orbital is able to hold 2
electrons. The number of
electrons per principal
quantum number is 2n2.
Where do we go from here?
• The quantum numbers are used to
designate the energies and positions of
electrons in an atom
• We can draw energy level diagrams to
indicate which energy levels are occupied
by the electrons
3
Creating Energy-Level Diagrams
• Used as a tool to predict and understand the
concepts of reactivity and chemical bonding
• Indicate which energy levels are occupied by
electrons for a particular atom or ion
• Show the relative energies of electrons in
various orbitals under normal conditions
Maximum Number of Electrons
In Each Sublevel
Maximum Number of Electrons In Each Sublevel
Sublevel
Number of Orbitals
Maximum Number
of Electrons
s
1
2
p
3
6
d
5
10
f
7
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LeMay Jr, Beall, Robblee, Brower, Chemistry Connections to Our Changing World , 1996, page 146
The energy levels and
orbitals can be expressed
in a diagram like this.
Notice that the energy
levels get closer together
as the principal quantum
number increases.
Notice the overlapping of
the sublevels in the
fourth, fifth and
subsequent orbitals – the
effect is that an electron
has a lower overall
energy if the 4s sublevel
is of lower energy than
the 3d sublevel.
Rules for Constructing
Energy-Level Diagrams
• When drawing an energy
level diagram, an atom is
assumed to be its lowest,
or ground state, without
any excited electrons
• Construct the diagram
showing the energy levels
with increasing energy
• Begin filling the energy
levels with the number of
electrons that the atom
has
Rules for Energy-Level Diagrams
• An atom is assumed to be its
lowest, or ground state
• There are 3 rules for drawing
energy – level diagrams
1. Pauli Exclusion Principle
2. Aufbau Rule
3. Hund’s Rule
• Follow the rules until the
number of electrons placed in
the energy-level diagram for
the atom is equal to the
atomic number for the
element
1. Pauli Exclusion Principle
– In a given atom, no two electrons can have
the same set of 4 quantum numbers
– An electron in an orbital is shown by drawing
an arrow, pointed up or down to represent the
electron spin
– An orbital can hold a maximum of 2 electrons
– An orbital can be empty or have one electron
4
Energy Level Diagrams for the First
5 Elements of the Periodic Table
2. Aufbau Principle
– Fill the lower energy levels first
(the ones closest to the
nucleus, with the lowest
energies)
– 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
– “aufbau” means “building up” in
German
Energy Level Diagram of a Many-Electron Atom
6s
6p
5d
32
5s
5p
4d
18
4s
4p
3d
18
Arbitrary
Energy Scale
3s
3p
2s
2p
3. Hund’s Rule
4f
• Place one electron into each orbital of the
same energy before pairing the electrons
• Electrons filling a subshell will have
parallel spins before the shells start filling
up with a second electron of opposite spin
8
8
1s
2s
2p
1s
2
NUCLEUS
O’Connor, Davis, MacNab, McClellan, CHEMISTRY Experiments and Principles 1982, page 177
Energy Level Diagram Rules
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
Carbon
• For an atom with unfilled orbitals, the most
stable energy level is achieved when
electrons occupy separate orbitals with
parallel spins
3. Hund’s Rule: Place one electron into each
orbital of the same energy before pairing the
electrons.
5
4d
5s
Energy
4p
3d
4s
3p
3s
2p
2 unpaired
electrons
Nickel
2s
28Ni
1s
How do I know which order to list
the energy levels?
Electron Filling in Periodic Table
H
• The energy descriptions of the quantum
numbers fit perfectly with both the
arrangement of electrons and the structure
of the periodic table
s
s
p
1
H
He
1s1
1s2
1s1
Li
Be
B
C
N
O
F
Ne
2p1
2p2
2p3
2p4
2p5
2p6
Al
Si
P
S
Cl
Ar
3p1
3p2
3p3
3p4
3p5
3p6
Ga
Ge
As
Se
Br
Kr
4p1
4p2
4p3
4p4
4p5
2
2s1
2s2
Na
Mg
3s1
3s2
K
Ca
Sc
4s2
3d1
d
3
Ti
V
Cr
3d2
3d3
3d5
Mn
Fe
Co
3d5
3d6
3d7
Ni
Cu
Zn
3d8
3d10
3d10
4
4s1
4p6
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
5s1
5s2
4d1
4d2
4d4
4d5
4d6
4d7
4d8
4d10
4d10
4p1
5p1
5p2
5p3
5p4
5p5
5p6
5
Cs
Ba
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
6s1
6s2
5d2
5d3
5d4
5d5
5d6
5d7
5d9
5d10
5d10
6p1
6p2
6p3
6p4
6p5
6p6
Fr
Ra
H
H
H
H
H
H
7s1
7s2
1s1
1s1
1s1
1s1
1s1
1s1
La
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
5d1
4f2
4f3
4f4
4f5
4f6
4f7
4f7
4f9
4f10
4f11
4f12
4f13
4f14
4f114
Ac
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
6d1
6d2
5f2
5f3
5f4
5f6
5f7
5f7
5f8
5f10
5f11
5f14
5f13
5f14
5f14
6
7


f


Overlapping of energy levels
6
Electron Configurations
• Practice..
• Draw the energy level diagram for oxygen
Electron configurations
Electron Configuration
1s22s22p63s23p64s23d104p65s24d104p65s24d105p66s24f145d106p6…
• Energy-level diagrams are a good way to
visualize the different energy levels of
electrons in atoms, but they are very
cumbersome
• Electron configurations provide the same
information as energy-level diagrams but
in a much more concise format
• It is a list of the number and kinds of
electrons in order of increasing energy
Principal quantum
number “n”
Secondary quantum
number “l”
Example – electron configuration
for the oxygen atom
1s22s22p4
Energy-level diagram for the
oxygen atom
Electron configuration for the
Oxygen atom
7
Writing electron configurations
• Follow the periodic
table writing out
the filled orbitals,
then carefully
count the final
number of
electrons in the
outer orbital and
make sure it
corresponds with
the atomic number
Electron Configuration
• The total of the superscripts must equal the
atomic number (number of electrons) of that
atom
• The differentiating electron is the electron that is
added which makes the configuration different
from that of the preceding element.
• The “last” electron.
• H 1s1
He 1s2
Li 1s2, 2s1
Be 1s2, 2s2
B 1s2, 2s2, 2p1
Electron Configuration
• Fe (Atomic Number = 26)
• Mg (Atomic Number = 12)
• Ne (Atomic Number = 10)
• Ti (Atomic Number = 22)
• Zr (Atomic Number=40)
Example
• Identify the element whose atoms have the
following electron configuration:
Example
• Write the electron configuration for the tin
atom and the tin (II) ion
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
8
Shorthand Electron Configurations
• The core electrons of an atom are
expressed by using a symbol to represent
all of the electrons of the preceding noble
gas (kernal)
• This reflects the stability of the noble
gases and the theory that only the
electrons beyond the noble gas are
chemically important for explaining
chemical properties
• Cl: 1s22s22p63s23p5
Shorthand
• Sn: 1s22s22p63s23p64s23d104p65s24d105p2
Shorthand
Energy-Level Diagrams for Anions
• Same procedure as for atoms, but add the
extra electrons corresponding to the ion
charge to the orbitals
• Example:
• Draw the energy level diagram for the
sulfide ion S2-
Energy-level diagrams for Cations
• Draw the energy-level diagram for the
corresponding neutral atom first, and then
remove the number of electrons (corresponding
to the ion charge) from the orbitals with the
highest principal quantum number, n.
• The electrons removed might not be the highestenergy electrons, but, in general, this produces
the correct arrangement of energy levels based
on experimental evidence.
Ion Configurations
P [Ne] 3s2 3p3 - 3e-  P3+ [Ne] 3s2 3p0
3p
3p
3s
3s
2p
2p
2s
2s
1s
1s
9
Explaining Ions of Transition
Metals
• Example:
• Draw the energy-level diagram for the zinc
ion Zn2+
Ion Configurations
Transition metal ions:
remove ns electrons and then (n - 1)d electrons.
Fe [Ar] 4s2 3d6 loses 2 electrons  Fe2+ [Ar] 4s0 3d6
2+
Fe
4s
3d
E4s ~ E3d - exact energy
of orbitals depend on
whole configuration
Fe
4s
3d
Fe3+
4s
3d
Anomalous Electron Configurations
(Exceptions to the order of filling)
• Zn: [Ar]4s23d10
Zn2+: [Ar]3d10
• It seems logical that Zn would lose 2 e-‘s to gain
an ionic charge of 2+.
• It loses the electrons from the 4s orbital because
it would be too difficult to lose them from the 3d
orbital. The 3d orbital is still full which is a very
stable state, like those atoms with filled subshells.
• (unlikely Zn would lose 10 e-‘s and leave a full
4s shell)
Explaining Ions of Transition
Metals
• Pb: [Xe]6s24f145d106p2
• Lead can form 2+ or 4+ ions
• Lead loses the two 6p electrons to form a 2+ ion
or loses four electrons, 2 from 6s and 2 from 6p
orbitals to form a 4+ ion
• (look at energy level diagram you see that all of
the outer electrons are very similar in energy
and it is easier to remove fewer electrons than
large numbers such as 10 and 14)
Anomalous Electron Configurations
• Electron configurations can be found experimentally
• In general, the experimental evidence follows the
predicted electron configurations as we have drawn
them, but there are some exceptions eg. Chromium and
Copper
• This is due to the fact that half-full and full subshells are
more stable
• Overall energy state of the atom is lower after the
promotion of the electron
10
Stability Pyramid
Explaining Magnetism
Explains why anomalous configurations exist
Ferromagnetic = strongly magnetic
• One full and one halffull sublevel make an
atom more stable than
do one full sublevel
with no special
arrangement.
• Most of the exceptions
from predicted
configurations can be
explained in this way.
• Ferromagnetism is based
on the properties of a
collection of atoms
• Effective magnets are able
to orient themselves in the
presence of a magnetic
field. Groups of tightly
packed domains are aligned
in the same direction
Explaining Ferromagnetism
Explaining Paramagnetism
Ferromagnetism = strong magnetic fields caused
by alignment of groups of atoms called domains
Paramagnetism = weak magnetism based on
unpaired electrons in an individual atom
•Iron, cobalt, and nickel are all strong
ferromagnetic materials and they have unpaired
electrons.
•However, ruthenium, rhodium, and palladium
are not ferromagnetic, yet they are weakly
magnetic and considered paramagnetic.
• Caused by the presence of unpaired electrons
whose forces are not cancelled out by the opposite
spin of another electron in the same orbital
• Unpaired electrons account for weak magnetism
but not for strong ferromagnetism
• Domains do not form as in ferromagnetism
• Found in:
– any atom with an odd number of electrons
– Some atoms with even numbers of electrons if their
electrons are unpaired in p, d or f orbitals
11