Download Lecture 5 - Help-A-Bull

1/20/2014
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CH2045, Gen. Chem. I, Section: 004
Spring 2014
Dr. Shengqian Ma
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Define the term periodic property
Define and apply the Pauli exclusion principle
Define the term degenerate as it applies to orbitals
Indicate the roles of Coulomb’s Law, shielding and
penetration in sublevel splitting
Define and apply the aufbau principle and Hund’s rule
Determine the expected electron configuration for any
atom on the periodic table (complete configuration and
noble gas abbreviation)
Describe an orbital filling diagram for any element on
the periodic table
Relate orbital filling diagrams, electron configurations
and quantum numbers
Determine number of valence electrons and core
electrons for any atom on the periodic table
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Compare the terms nonbonding atomic radius, bonding
atomic radius and atomic radius
Describe the trends in atomic radii on the periodic table and
relate the observed trends to the structure of the atom
Define and make predictions for diamagnetic and
paramagnetic
Relate the radius of an atom to an ion of the same element
Describe the trends in ionization energy on the periodic table
and relate the observed trends to the structure of the atom
Predict the expected trends in successive ionization energies
Define electron affinity
Describe what is meant by metallic character and relate it to
trends on the periodic table
Characterize the alkali metals, halogens and noble gases and
their trends on the periodic table
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Baseball Cards:
year, team, player, card number, value ($).
Elements:
when
they weremass,
discovered,
family, reactivity,
alphabetically,
value, density,
state
of liquid
matter,ormetal
solid or
gas vs. non-metal, atomic mass,
atomic number.
Which way is CORRECT to organize the elements?
Is it possible to organize the elements correctly in more than one way?
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Dmitri Mendeleev
and Lothar Meyer
independently came
to the same
conclusion about
how elements
should be grouped.
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Ordered elements by atomic mass
Saw a repeating pattern of properties
Put elements with similar properties in the same
column
Used pattern to predict properties of undiscovered
elements (Germanium, Gallium, etc)
Where atomic mass order did not fit other properties,
he re-ordered by other properties
◦ Te & I
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This is an older style
table.
The rows are called
“periods.”
The
columns
e co
u
s are
a e
“families” or “groups.”
◦ Type A: representative
◦ Type B: transition
◦ The guys at the bottom
are inner transition
elements.
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This is especially true of type A
(representative) elements.
 But, there are changes in reactivity, etc., as
one goes down a column.
 This link gives group IA as an example
example...
http://www.youtube.com/watch?v=Ft4E1eCUItI
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The rows are called periods.
How they fill gives insight into the atomic
structures.
In particular, we shall examine the idea of
electron configurations.
More about vertical trends later!
As just stated, rows of the periodic table are
called periods.
These have the following lengths:
o2
o8
o 18
o 32
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2=
8=
18 =
32 =
2
2
2
2
x
x
x
x
12
22
32
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This gives some insight into quantum
numbers!
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3 quantum numbers, n, l, and ml.
For each value of n we have n2 orbitals.
We play some number games here:
n
n
n
n
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=
=
=
=
1
2
3
4
→
→
→
→
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1 orbital
4 orbitals (4 = 1 + 3)
9 orbitals (9 = 1 + 3 + 5)
16 orbitals (16 = 1 + 3 + 5 + 7)
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These are all ½ the lengths of the periods!
What’s wrong?
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Calculations with Schrödinger’s equation show
hydrogen’s one electron occupies the lowest energy
orbital in the atom
Schrödinger’s equation calculations for multielectron
atoms cannot be exactly solved
◦ due to additional terms added for electron-electron
interactions
Approximate solutions show the orbitals to be
hydrogen-like
Two additional concepts affect multielectron atoms:
electron spin and energy splitting of sublevels
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H has just one electron.
The Schrödinger equation seen earlier needed
another quantum number to handle multielectron atoms. (Technical detail: This
comes naturally if relativity included
included.))
This new quantum number is ms, the electron
spin. This has values of = +1/2 and -1/2.
The physical explanation is left for lecture!
Experiments by Stern and Gerlach
showed a beam of silver atoms is split
in two by a magnetic field
The experiment reveals that the
electrons spin on their axis
As they spin, they generate a magnetic
field
◦ spinning
i i
charged
h
d particles
ti l generate
t a
magnetic field
If there is an even number of electrons,
about half the atoms will have a net
magnetic field pointing “north” and the
other half will have a net magnetic field
pointing “south”
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Spin is a fundamental property of all electrons
All electrons have the same amount of spin
The orientation of the electron spin is
quantized, it can only be in one direction or its
opposite
◦ spin up or spin down
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In the 1920s, it was discovered that two electrons in
the same orbital do not have exactly the same
energy.
The “spin” of an electron describes its magnetic
field, which affects its energy.
The electron’s spin adds a fourth quantum
number to the description of electrons in an
atom, called the Spin Quantum Number, ms
◦ not in the Schrödinger equation
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ms can have values of +½ or −½
Orbital Diagrams use a square to
represent each orbital and a halfarrow to represent each electron in
the orbital
By convention, a half-arrow pointing
up is used to represent an electron in
an orbital with spin up
Spins must cancel in an orbital
◦ paired
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We often represent an orbital as a square
and the electrons in that orbital as arrows
◦ the direction of the arrow represents the spin
of the electron
unoccupied
orbital
orbital with
one electron
orbital with
two electrons
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• No two electrons in an atom may have the same
set of four quantum numbers
Quantum
Number
Principal, n
• Therefore no orbital may have more than two
electrons, and they must have with opposite spins
• Knowing the number orbitals in a sublevel allows
us to determine the maximum number of
electrons
l t
in
i th
the sublevel
bl
l
 s sublevel has 1 orbital, therefore it can hold 2 electrons
 p sublevel has 3 orbitals, therefore it can hold 6
electrons
 d sublevel has 5 orbitals, therefore it can hold 10
electrons
 f sublevel has 7 orbitals, therefore it can hold 14
electrons
Wolfgang
Pauli
Values
Number Significance
of Values
1, 2, 3, ...
size and
energy of the
orbital
shape of
Azimuthal, l 0, 1, 2, ..., n n
1
orbital
orientation of
Magnetic, -l,...,0,...+ l
2l + 1
orbital
ml
direction of
Spin, m s
-_ , +_
2
electron sp in
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Helium has two electrons
Both electrons are in the first energy level
Both electrons are in the s orbital of the first energy level
Because they are in the same orbital, they must have opposite
spins
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For a one-electron
hydrogen atom,
orbitals on the
same energy level
have the same
energy.
That is, they are
degenerate.
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As the number of
electrons increases,
though, so does the
repulsion between
them.
Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate.
The sublevels in each principal energy shell of
Hydrogen all have the same energy
 or other single electron systems
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We call orbitals with the same energy degenerate
For multielectron atoms, the energies of the
sublevels are split
◦ caused by charge interaction, shielding and penetration
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The lower the value of the l quantum number, the
less energy the sublevel has
◦ s (l = 0) < p (l = 1) < d (l = 2) < f (l = 3)
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Coulomb’s Law describes the attractions and repulsions between
charged particles
“ The potential energy (E) of two charged particles depends on their
charges (q1 and q2) and on their separation (r)”
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For like charges, the potential energy (E)
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For opposite charges, the potential energy
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◦ positive
◦ decreases as the particles get farther apart
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◦ negative
◦ more negative as the particles get closer together
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Strength of interaction increases with increasing charge
◦ electrons are more strongly attracted to a nucleus with a 2+ charge than a
nucleus with a 1+ charge
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In a many-electron
atom, electrons are both
attracted to the nucleus
and repelled by other
electrons.
The nuclear charge
g that
an electron
l
experiences
depends on both
factors.
The total amount of
attraction that an
electron feels for the
nucleus is called the
effective nuclear charge
of the electron
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Each electron in a multielectron atom
experiences both the attraction to the nucleus
and repulsion by other electrons in the atom
These repulsions cause the electron to have a
net reduced attraction to the nucleus – it is
shielded from the nucleus
The total amount of attraction that an electron
feels for the nucleus is called the effective
nuclear charge of the electron
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The closer an electron is to the nucleus, the
more attraction it experiences
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The better an outer electron is at penetrating
th
through
h th
the electron
l t
cloud
l d off iinner electrons,
l t
the more attraction it will have for the nucleus
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The degree of penetration is related to the
orbital’s radial distribution function
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According to the radial
distribution function…
◦ the 2s orbital penetrates more deeply
into the 1s orbital than does the 2p
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Electrons in the 2p sublevel
◦ experience more repulsive force
◦ they are more shielded from the
attractive force of the nucleus
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Electrons in the 2s sublevel
◦ experience a greater attractive force
to the nucleus
◦ are not shielded as effectively
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7s
6s
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Penetration causes the energies of sublevels in the
same principal level to not be degenerate
5s
◦ In the fourth and fifth principal levels, the s orbital lies
lower in energy than the d orbitals of the previous principal
level
4s
Ene
ergy
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2s
1s
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principal energy level of
orbital occupied by the
electron
1s1
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4f
4d
3d
3p
Notice the following:
1. because of penetration, sublevels within
an energy level are not degenerate
2. penetration of the 4th and higher energy
levels is so strong that their s sublevel is
lower in energy than the d sublevel of
the previous energy level
3. the energy difference between levels
becomes smaller for higher energy levels
(and can cause anomalous electron
configurations for certain elements)
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The electron configuration of an atom is a
shorthand method of writing the location of
electrons by sublevel.
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The ssublevel
ble el is written
ritten followed
follo ed b
by a ssuperscript
perscript
with the number of electrons in the sublevel.
◦ If the 2p sublevel contains 2 electrons, it is written 2p2
number of electrons in
the orbital
sublevel of orbital
occupied by the
electron
5f
5d
4p
2p
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Quantum-mechanical theory describes the
behavior of electrons in atoms
The electrons in atoms exist in orbitals
A description of the orbitals occupied by
electrons is called an electron configuration
5p
3s
The energy separations between one set of orbitals
and the next become smaller beyond the 4s
 the ordering can therefore vary among elements
 causes variations in the electron configurations of the transition
metals and their ions
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6d
6p
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The electron sublevels are arranged according
to increasing energy.
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• Energy levels and sublevels fill from lowest energy
Electrons are arranged about the
nucleus in a regular manner. The
first electrons fill the energy
sublevel closest to the nucleus.
to high
 s→p→d→f
 Aufbau Principle
◦ lowest in energy
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Electrons continue filling each
sublevel until it is full and then
start filling the next closest
sublevel.
• Orbitals that are in the same sublevel have the
same energy
• No more than two electrons per orbital
◦ Next lowest in energy (Aufbau
principle)
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 Pauli Exclusion Principle
A partial list of sublevels in order
of increasing energy is:
• When filling orbitals that have the same energy,
place one electron in each before completing pairs
 1s < 2s < 2p < 3s < 3p < 4s <
3d < 4p < 5s < 4d …
 Hund’s Rule
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First, determine how many electrons are in the atom. Lithium
has 3 electrons.
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Arrange the energy sublevels according to increasing energy:
 1s 2s 2p 3s 3p 4s 3d …
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Fill each sublevel with electrons until you have used all the
electrons in the atom:
 Li: 1s2 2s1
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The sum of the superscripts equals the atomic number of lithium
(3)
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Each box in the
diagram represents
one orbital.
Half-arrows
represent the
electrons.
The direction of the
arrow represents the
relative spin of the
electron.
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The electron configuration is a listing of the
sublevels in order of filling with the number of
electrons in that sublevel written as a
superscript.
Kr = 36 electrons =
1s22s22p63s23p64s23d104p6
 A short-hand way of writing an electron
configuration is to use the symbol of the
previous noble gas in [] to represent all the
inner electrons, then just write the last set.
Rb = 37 electrons =
1s22s22p63s23p64s23d104p65s1 = [Kr]5s1
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Friedrich Hund
“For degenerate
orbitals the
orbitals,
lowest energy is
attained when the
number of
electrons with the
same spin is
maximized.”
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Start by drawing a diagram
putting each energy shell on
a row and listing the sublevels,
(s, p, d, f), for that shell in
order of energy
gy ((left-to-right)
g )
Next, draw arrows through
the diagonals, looping back
to the next diagonal
each time
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
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All electrons in noble gases occupy completely
filled orbitals
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• core electrons – electrons are more stable (less
reactive) when belonging to completely filled orbitals
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 Noble gas electron configuration used to abbreviate core
electrons
• Condensed Electron Configuration– electron
configuration uses noble gas from previous row
[He] = 1s2
[Ne] = 1s2 2s2 2p6
[Ar] = 1s2 2s2 2p6 3s2 3p6
[Kr] = 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6
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Mn
Electron configuration for K using full notation: 1s2 2s2
2p6 3s2 3p6 4s1
Electron configuration for K using condensed notation:
[Ar] 4s1
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Electron configuration for In using full notation:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p1
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Electron configuration for In using condensed notation:
[Kr] 5s2 4d10 5p1
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Z = 25, therefore 25 e−
s sublevel holds 2 e−
p sublevel holds 6 e−



d sublevel holds 10
1s
2s
e−
f sublevel holds 14 e−

2p


1s
  
−
2 e
2s
+2 = 3s
4e−
+6
 +2 =
12e−

+6 +2 = 20e−
3d
3s
4s

3p
 
2p

3p
3d
4p
4d
4s
4f
+10 = 30e−
Therefore the electron configuration is 1s22s22p63s23p64s23d5
Based on the order of sublevel filling, we will need the first seven sublevels
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