Chemistry 1A
Chapter 7
Atomic Theory
• To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
William Blake Auguries of Innocence
• Thus, the task is not so much to see what no
one has yet seen, but to think what nobody
has yet thought, about that which everybody
sees.
Erwin Schrodinger
Ways to deal with
Complexity and Uncertainty
• Analogies In order to communicate
something of the nature of the electron,
scientists often use analogies. For
example, in some ways, electrons are
like vibrating guitar strings.
• Probabilities In order to
accommodate the uncertainty of the
electron’s position and motion, we refer
to where the electron probably is within
the atom instead of where it definitely is.
Electron like Light
• Dual Nature
– Particle
• Massless photons of varying energy for
light.
• Negatively charged particles with a mass of
9.1096 × 10−28 g for the electron.
– Wave – related to the effect on the
space around them
• Oscillating electric and magnetic fields for
light.
• 3-D Wave of varying negative charge for
electron.
Guitar String Waveform
Allowed
Vibrations
for a
Guitar
String
Determination of the Allowed
Guitar String Waveforms
• Set up the general form of the wave
equation that describes the vibrating string.
• Determine the forms of the general equation
that fit the boundary conditions.
• Each possible equation is solved over and
over again for the amplitude at many
different positions.
• We plot the values determined in Step 3 and
get an image of the possible wave forms.
• Steps 3 and 4 can be repeated for other
equations that meet the boundary
conditions.
Equation for Guitar
String
nπ x
A X = AO sin
a
• AX = the amplitude at position x
• AO = the maximum amplitude at any
point on the string
• n = 1, 2, 3, ...
• x = the position along the string
• a = the total length of the string
Guitar String Amplitudes
A1
A0
A2
Guitar String Waveform 1
A X = A O sin
πx
a
Guitar String Waveform 2
2π x
A X = A O sin
a
Guitar String Waveform 3
3π x
A X = A O sin
a
Determination of the Allowed
Electron Waveforms
• Set up the general form of the wave equation that
describes the electron in a hydrogen atom.
Ψx,y,z = f(x,y,z)
• Determine the forms of the general equation that
fit the boundary conditions. Each equation has its
own set of three quantum numbers: n, l, and ml.
Ψ1s = f1s(x,y,z) with 1,0,0 for quantum numbers
Ψ2s = f2s(x,y,z) with 2,0,0 for quantum numbers
Ψ2p = f2p(x,y,z) with 2,1,1 or 2,1,0
or 2,1, −1 for quantum numbers
Etc.
Determination of the Allowed
Electron Waveforms (cont.)
• Each allowed equation is solved to
get the values for the wave function
for many different positions.
• When we plot the solutions for one
of the possible wave functions on a
three-dimensional coordinate
system, we get an image of one of
the possible waveforms.
Waveform for 1s Electron
(with quantum numbers 1,0,0)
Other Allowed Waveforms
1s Orbital
Particle Interpretation of
1s Orbital
Wave Character of the
Electron
• Just as the intensity of the movement
of a guitar string can vary, so can the
intensity of the negative charge of the
electron vary at different positions
outside the nucleus.
• The variation in the intensity of the
electron charge can be described in
terms of a three-dimensional standing
wave like the standing wave of the
guitar string.
Wave Character of the
Electron
• Although both the electron and the
guitar string can have an infinite
number of possible waveforms, only
certain waveforms are possible.
• We can focus our attention on the
waveform of varying charge intensity
without having to think about the
actual physical nature of the
electron.
Summary
• The electron in a H atom can be described
with a 3-dimensional wave equation.
• This equation has 3 quantum numbers
associated with it.
• Each unique set of 3 quantum numbers
(e.g. 1,0,0 for the 1s orbital) yields an
equation that when calculations are done
using this equation for various positions
outside the nucleus and when the results
of these calculations are plotted on a 3dimensional coordinate system, we get an
image of the variation in the intensity of
negative charge generated by the electron.
• This image is called an orbital.
Electron-Wave Quantum Numbers for
the Hydrogen Electron
• Principal quantum number – n
– Describes the PE and relative size of orbital.
• Angular momentum quantum number
(orbital shape quantum number) – l
– Describes the general shape of orbital.
• Magnetic quantum number (orbital
orientation quantum number) – ml
– Describes the direction the orbital points
relative to other orbitals of the same energy.
• Magnetic spin quantum number – ms
– Necessary for describing electrons, not orbitals.
Electron-Wave Quantum
Numbers for the Hydrogen
Electron (cont.)
• Possible values
n = 1, 2, 3,…
l = 0, 1, 2,…, (n − 1)
ml = +l,…, 0,…, −l
ms = +1/2 and −1/2
• What they describe
n – principle energy level (shell)
n, l – sublevel (subshell)
n, l, ml – orbital
n, l, ml, ms - electron
Possible Sublevels for the First
4 Principal Energy Levels of the
Hydrogen Electron
1,0 1s
2,0 2s
2,1 2p
4,0 4s
4,1 4p
4,2 4d
4,3 4f
3,0 3s
3,1 3p
3,2 3d
Orbitals Within
Sublevels
• Any “s” sublevel – one orbital
n,0,0
• Any “p” sublevel – three orbitals
n,1,+1
n,1,0
n,1,−1
• Any “d” sublevel – five orbitals
n,2,+2
n,2,+1
n,2,0
n,2,−1
n,2,−2
• Any “f” sublevel – seven orbitals
n,3,+3
n,3,−2
n,3,+2
n,3,−3
n,3,+1
n,3,0
n,3,−1
Cutaway of 1s and 2s Orbitals
(with quantum numbers 2,0,0)
Realistic and Stylized 2py Orbital
2px, 2py, and 2pz Orbitals
3d Orbitals
Other Allowed
Waveforms
Grand Orbital Table
• The website below, created by David
Manthey, shows many more orbitals.
http://www.orbitals.com/orb/orbtable.htm
Orbitals for Ground States of
Known Elements
Orbital Energies for Hydrogen
Calculating Frequencies for
Hydrogen Spectrum
Lyman (UV portion of hydrogen spectrum)
⎛1
1 ⎞
frequency = ν = 3.289 x 10 1/s ⎜ 2 nhigh = 2, 3, 4, ...
2 ⎟
⎜1
⎟
nhigh ⎠
⎝
Balmer (visible portion of hydrogen spectrum)
15
⎛ 1
1 ⎞
ν = 3.289 x 10 1/s ⎜ 2 nhigh = 3, 4, 5, ...
2 ⎟
⎜2
⎟
nhigh ⎠
⎝
Paschen (IR portion of hydrogen spectrum)
15
⎛ 1
1 ⎞
ν = 3.289 x 10 1/s ⎜ 2 2 ⎟
⎜3
⎟
n
high
⎝
⎠
15
nhigh = 4, 5, 6, ...
Line Spectrum of Hydrogen
Continuous
and Line
Spectrum
Frequency, Wavelength,
and the Speed of Light
speed of light (c) = wavelength(λ ) • frequency(ν )
distance cycles
distance
c = λν =
=
cycle
time
time
m cycles
8 m
or c = λν =
= 2.9979 × 10
cycle
s
s
Lab
• Goal – to determine wavelengths of
lines in the visible portion of the
hydrogen spectrum
–From Calculation
⎛1
1 ⎞
frequency = ν = 3.289 x 10 1/s ⎜ n high = 3, 4, 5, 6, and 7
⎟
2
⎜ 4 nhigh ⎟
⎝
⎠
2.9979 × 108 m/s ⎛ 109 nm ⎞
wavelength = λ =
⎜
⎟
ν
1
m
⎝
⎠
15
–From Experiment
Wave Interference
Wave Diffraction Patterns
Lab – With He Spectrum
• View lines and measure angle
of diffraction for each.
• Assign to wavelengths on table
based on color, intensity and
relative position.
• Graph angle of diffraction vs.
wavelength on graph paper
provided.
Calibration Curve
When Graphing
• Label graph and axes.
• Set scale to
– use as much of the graph paper as
possible. (Do not start numbering the
scale at 0.)
– Make each box a value that makes the
graph easy to read, e.g. 3 nm per box,
not 2.4356 nm.
• Indicate each data point with a clear x.
• Draw the best straight line that
averages the points.
Lab – for H Spectrum
• View lines and measure
angle of diffraction for each.
• Use the graph created from
the helium data to determine
the wavelength for each line.
Electron Spin
Pauli Exclusion Principle
• No two electrons in an atom can be the same in all
ways. (No two electrons in an atom can have the
same set of four quantum numbers, n, l, ml, and
ms.)
• There are four ways that electrons can be the
same:
• Electrons can be in the same principal energy level (same n).
• They can be in the same sublevel (same n and l).
• They can be in the same orbital (same n, l, and ml).
• They can have the same spin (same ms).
• Leads to the conclusion that there can only be
2 e−/orbital…2 e−/s sublevel, 6 e−/p sublevel,
10 e−/d sublevel, and 14 e−/f sublevel.
Electron Configurations
• The sublevels are filled in such a way as to
yield the lowest overall potential energy for
the atom.
• No two electrons in an atom can be the
same in all ways. This is one statement of
the Pauli Exclusion Principle.
• When electrons are filling orbitals of the
same energy, they prefer to enter empty
orbitals first, and all electrons in half-filled
orbitals have the same spin. This is called
Hund’s Rule.
Orbitals for Ground States of
Known Elements
Why is 1s
before 2s?
Electron Configurations (cont.)
Why 2s before 2p?
Electron Configurations
through Neon
1s1
• H• He - 1s2
• Li - 1s2 2s1
• Be - 1s2 2s2
•
•
•
•
•
•
B - 1s2 2s2 2p1
C - 1s2 2s2 2p2
N - 1s2 2s2 2p3
O - 1s2 2s2 2p4
F - 1s2 2s2 2p5
Ne - 1s2 2s2 2p6
Orbital Overlap
Why 4s
before
3d?
Order
of
Orbital
Filling
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p
Writing Electron
Configurations
• Determine the number of electrons in the
atom from its atomic number.
• Add electrons to the sublevels in the correct
order of filling.
• Add two electrons to each s sublevel, 6 to
each p sublevel, 10 to each d sublevel, and
14 to each f sublevel.
• To check your complete electron
configuration, look to see whether the
location of the last electron added
corresponds to the element’s position on
the periodic table.
Order of Filling from the
Periodic Table
Long Periodic Table
Drawing Orbital Diagrams
• Draw a line for each orbital of each
sublevel mentioned in the complete
electron configuration. Draw one line for
each s sublevel, three lines for each p
sublevel, five lines for each d sublevel,
and seven lines for each f sublevel.
• Label each sublevel.
• For orbitals containing two electrons,
draw one arrow up and one arrow down
to indicate the electrons’ opposite spin.
• For unfilled sublevels, follow Hund’s Rule.
Abbreviated Electron
Configurations
• The highest energy electron are most
important for chemical bonding.
• The noble gas configurations of electrons
are especially stable and, therefore, not
important for chemical bonding.
• We often describe electron configurations to
reflect this representing the noble gas
electrons with a noble gas symbol in
brackets.
• For example, for sodium
1s2 2s2 2p6 3s1 goes to [Ne] 3s1
Writing Abbreviated
Electron Configurations
• Find the symbol for the element on a
periodic table.
• Write the symbol in brackets for the noble
gas located at the far right of the preceding
horizontal row on the table.
• Move back down a row (to the row
containing the element you wish to
describe) and to the far left. Following the
elements in the row from left to right, write
the outer-electron configuration associated
with each column until you reach the
element you are describing.
Abbreviated Electron
Configurations – Optional
Step
• Rewrite the abbreviated
electron configuration, listing
the sublevels in the order of
increasing principal energy
level (all of the 3’s before the
4’s, all of the 4’s before the 5’s,
etc.)
Group 1
Abbreviated
Electron
Configurations
Abbreviated Electron Configuration Steps for Zinc
Common Mistakes
• Complete electron configurations –
miscounting electrons (Use the periodic
table to determine order of filling.)
• Orbital diagrams – forgetting to leave
electrons unpaired with the same spin
when adding electrons to the p, d, or f
sublevels (Hund’s Rule)
• Abbreviated electron configurations
– Forgetting to put 4f14 after [Xe]
– Forgetting to list sublevels in the order of
increasing principal quantum number
– For cations, forgetting to remove highest
energy level electrons first
Anomalies
•
•
•
•
•
•
Cu
Ag
Au
Cr
Mo
Pd
[Ar] 3d10 4s1
[Kr] 4d10 5s1
[Xe] 4f14 5d10 6s1
[Ar] 3d5 4s1
[Kr] 4d5 5s1
[Kr] 4d10
Paramagnetic and
Diamagnetic Atoms
• Diamagnetic atoms have no permanent
net magnetic field because all of their
electrons are paired.
– Uncharged palladium atoms and the
uncharged atoms that are in columns that end
either the s, p, d, or f blocks are diamagnetic.
• Paramagnetic atoms have a permanent
net magnetic field due to having at least
one unpaired electron.
– All uncharged atoms are paramagnetic except
palladium atoms and the uncharged atoms
that are in columns that end either the s, p, d,
or f blocks.
Writing Abbreviated Electron
Configurations for Transition
Metal Monatomic Cations
• Draw the abbreviated electron
configuration for the uncharged
atom, listing the sublevels in the
order of increasing principal
quantum number.
• Remove the number of electrons
equal to the charge, removing
them from the right to left in the
electron configuration.
Factors that Affect Ionic
Charge (1)
• Ions form in such a way as to yield the
most stable, lowest potential energy
ionic compound.
• Ions are less stable than their neutral
counterparts. Therefore, it takes energy
to form ions.
• The higher the charges are, the less
stable they are and the more energy it
takes to form them.
• Therefore, this factor favors low
charges.
Factors that Affect
Ionic Charge (2)
• The formation of ionic bonds
stabilizes the ions, so energy is
released when the cations and
anions form ionic bonds.
• The higher the charges are, the
stronger the bonds and the more
energy is released when they
form.
• Therefore, this factor favors higher
charges.
Factors that Affect Ionic
Charge (3)
• Ions form the charges that yield the
best balance between (1) the
tendency to keep charges low to
minimize the energy necessary to
form ions and (2) the tendency to
maximize charge to yield the
strongest, most stable ionic bond.
• The best balance is often reached
when the ions form stable electron
configurations, which require the least
energy to form.
Very Rough
PE Diagram
for NaCl
Formation
Very Rough
PE Diagram
for AlN
Formation
Stable Configurations
• 1s2 (2 electrons)
– H−, Li+, Be2+
• ns2np6 (10, 18, 36, 54, and 86 electrons)
– All monatomic anions, except H−
– Cations from Group 1, 2, or 3 and Al3+
• nd10(n+1)s2 (30, 48, and 80 electrons)
– Ga+, In+, Tl+, Sn2+, Pb2+, and Bi3+
• nd10 (28, 46, and 78 electrons)
– Cu+, Ag+, Au+, Zn2+, Cd2+, Hg2+, Ga3+, In3+, and
Tl3+
Monatomic Ion Charges
Trends on the
Periodic Table
Chemistry 1A
Atomic Size
• Covalent Radius for Covalently Bonded
Atoms
– F-F bond length is 144 pm, so F covalent
radius is 72 pm.
– H-F bond length is 109 pm, so H covalent
radius is 37 nm.
• Atomic Radius for Elements like the
Noble Gases
– Ar atomic radius is 131 pm
• Metallic Radius for Metals
– Al metallic radius is 143 pm.
Trends
in
Atomic
Size (1)
Trends in
Atomic
Size (2)
Ionization Energy, ΔHi.e.
• First Ionization Energy
A(g) → A+(g) + e−
• Second Ionization Energy
A+(g) → A2+(g) + e−
• Third Ionization Energy
A2+(g) → A3+(g) + e−
Ionization
Energy Trends
(1)
Ionization Energy Trends (2)
Electron Affinity, ΔHe.a.
• First Electron Affinity
A(g) + e− → A−(g)
• Second Electron Affinity
A−(g) + e− → A2−(g)
• Third Electron Affinity
A2−(g) + e− → A3−(g)
Electron Affinity Trends
Trends – Representative Elements
Atomic
Size
ΔHi.e.
ΔHe.a.
EN
Increases
to left
and down
Increases
to right
and up
More
favorable
to right
and up
Increases
to right
and up
Two Factors Used to
Explain Trends
• The principal energy level reflects the
size of orbitals and potential energy of the
electrons in those orbitals.
• All other factors being equal, increased n
for the orbitals in which electrons are
found means increased size of orbitals,
which leads to decreased attraction for
electrons and increased potential energy
of those electrons.
Effective Charge
• Effective charge is the approximate nuclear
charge felt by the highest energy electrons.
– nuclear charge minus #e− in lower energy levels
– The effective charge on the highest energy
electrons of the representative elements is
equal to their A-group number.
– The effective charge on the highest energy
electron of the transition metals (other than the
anomalies) is +2.
• All other factors being equal, increased
effective charge means increased attraction
for electrons, which leads to decreased size
of orbitals and decreased potential energy
of electrons.
Explanation of Trends (1)
Explanation of Trends (2)
Explanation of Trends (3)
Ionic or Molecular?
• Is aluminum iodide, AlI3, ionic or
molecular?
• If you are told that aluminum iodide’s
formula was better described as Al2I6,
would it change your prediction?
• Many metal and nonmetal combinations
are better described as forming
molecular compounds rather than ionic
compounds.
• To see why, a new classification of
chemical bonds is added to our list…ionic
bonds with covalent character.
Ionic Bonds with
Covalent Character
• The attraction for the anion’s negative
charge cloud from the cation draws the
anion’s charge cloud toward the cation
and distorts the anion electron cloud.
• This distortion is described as covalent
character, that is, sharing of electrons.
Bond
Types
Degree of Covalent
Character
• Greater distortion of anion electron cloud
(more covalent character) in an ionic
bond comes from
– More highly charged cation…more attraction
for anion electron cloud.
– Smaller cation…more focused attraction for
anion electron cloud.
– Larger anion…electron cloud less strongly
attracted, so anion is more easily distorted.
– More highly charged anion…more repulsion
between electrons, so anion is more easily
distorted.
Ionic Size
• Cations are much smaller than the
uncharged atoms they come from.
– Fewer electrons means less repulsion
between electrons, allowing the electron
cloud to be pulled closer to the nucleus.
• Anions are much larger than the
uncharged atoms they come from.
– More electrons means more repulsion
between electrons, causing the electron
cloud to expand to minimize this
increased repulsion.
Ionic and Atomic Size
Isoelectronic Series
• A collection of ions and an
uncharged atom with the same
number of electrons is called an
isoelectronic series.
• For isoelectronic atoms or ions,
higher nuclear charge leads to
smaller size.
Predicting Degree of
Covalent Character
• CsF…low covalent character
– Large, low charge cation-low attraction and unfocused
attraction.
– Small, low charge anion…electrons strongly
attracted…hard to distort
• AlI3…high covalent character
– Small, highly charged cation…strong attraction and
focused attraction.
– Large anion…electrons weakly attracted…easy to distort
• Li3P…high covalent character
– Small cation…focused attraction.
– Large anion, highly charged anion…electrons weakly
attracted…easy to distort