Download Chapter 3 Atomic Structure

Chapter 3
Atomic Structure
Chemistry
Mr. Bass
Atomic Structure
3-1 How are elements organized?
 3-2 What is the basic structure of an atom?
 3-3 How do the structures of atoms differ?

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3.1 How are elements organized?
Objectives
 Periodic Table
 Basic Components of an Atom
 Basic Definitions

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3.2 What is the basic structure of
an atom?
Creating Atomic Models by Inference
 3 Laws of Nature
 John Dalton’s Atomic Theory
 J.J. Thompson’s Atomic Theory
 Ernest Rutherford’s Atomic Theory
 The Physics of Energy
 Niels Bohr’s Atomic Theory.

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3.2 What is the basic structure of
an atom?

1.
2.
3.
Objectives: (SWBAT)
infer the existence of atoms from the laws
of definite composition, conservation of
mass, and multiple proportions.
list the five basic principles of Dalton’s
atomic theory.
describe Dalton’s, Rutherford’s, and
Bohr’s atomic models.
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3.2 What is the basic structure of
an atom?

4.
5.
6.
Objectives (continued): SWBAT
compare and contrast the properties of
electrons, protons, and neutrons.
explain the particle-wave nature of
electrons.
describe the quantum model of the atom.
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Creating Atomic Models by
Inference
Indicator 1.4.8
Study the patterns of nature.
 Develop models that fit the information.
 Test/Refine the models.

– Wind: It can’t be seen, but its force can be felt.
» The evidence of the wind is indisputable. This is
inference.
– Straw Men: Develop a model and then try to
destroy it.
– Models should reflect the properties of nature.
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3 Known Laws of Nature

Law of Definite Composition

Law of Conservation of Mass

Law of Multiple Proportions
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Known Laws of Nature
1.
Law of definite composition: a
compound contains the same elements in
exactly the same proportions by mass
regardless of the size of the sample or
source of the compound.
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Law of Definite Composition
Sugar (Sucrose) has the same composition regardless of
the size of the sample or source of the sample.
100 g of sugar: 42.1 % carbon, 51.4 % oxygen, 6.5 %
hydrogen.
100 Mg of sugar: 42.1 % carbon, 51.4 % oxygen, 6.5 %
hydrogen.
Sugar from Sugar Beats: 42.1 % carbon, 51.4 %
oxygen, 6.5 % hydrogen.
Sugar from Sugar Cane: 42.1 % carbon, 51.4 % oxygen,
6.5 % hydrogen.
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Law of conservation of mass:

In a chemical reaction, the mass of the
reactants is equal to the mass of the
products.
– Restated: In a chemical reaction, mass is
neither created nor destroyed.
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Law of Conservation of Mass

Combination of Atoms:
– 32 g of S and 32 g of O2  64 g of SO2

Separation of Atoms:
– 434 g of HgO  402 g of Hg and 32 g of O2

Rearrangement of Atoms:
– 62 g of H2CO3  18 g H2O and 44 g CO2
» In every case, the mass of the products is equal to
the mass of the reactants!
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Law of Multiple Proportions

The mass ratio for one of the elements that
combines with a fixed mass of the other
element can be expressed in small whole
numbers.
– This compares two substances made of the
same elements. For example, water and
hydrogen peroxide (both composed of
hydrogen and oxygen).
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Law of Multiple Proportions
16g O2 + 2g H2  18g Water
 32g O2 + 2g H2  34g Hydrogen Peroxide

– Ratio of Oxygen in two compounds is:
32 g O2 = 2:1 ratio of oxygen
16 g O2
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How do these 3 laws infer the
existence of atoms?
1.
Law of definite composition infers that
there must be small units (atoms) because
compounds always have the same percent
composition.
 In order for compounds to always have the
same percent composition, there must be a
“smallest unit” or particle of an element that
makes up the compound.
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Atomic Inference
2.
Law of conservation of mass infers that
there must be atoms because the sum of
the reactants mass is equal to the sum of
the mass of the products.
–
–
This law is always true no matter how many
(or few) units of mass are used.
This infers that there must be a basic small
unit of nature (atom) that is being swapped
around during a chemical reaction.
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Atomic Inference
3.
Law of Multiple Proportions infers that
there must be a small unit of nature
(atoms) because every compound
composed of the same elements can be
reduced to a simple mass ratio.
 That simple ratio is caused by the fact that
compounds are made of atoms, and when
atoms combine in small whole number ratios
it is reflected in the mass ratio.
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Atomic Inference

Law of Multiple Proportions (Continued)
– This also infers that atoms of different elements
have different masses.
– This also infers that different atoms of the same
element have the same mass.
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John Dalton; 1776 - 1844
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John Dalton
Together the 3 experimental laws
represented much of the quantitative data
that chemists had in the 1700’s.
 They implied the existence of what was to
become known as the atom.

– Atom is from greek “atomos” meaning
indivisible.

John Dalton was the first one to put all the
pieces together in 1805.
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John Dalton’s Atomic Theory
1.
2.
3.
4.
All matter is made of indivisible and
indestructible atoms.
Atoms of a given element are identical in
their physical and chemical properties.
Atoms of different elements have different
physical and chemical properties.
Atoms of different elements combine in
simple, whole-number ratios to form
chemical compounds.
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John Dalton’s Atomic Theory
5.
Atoms cannot be subdivided, created, or
destroyed when they are combined,
separated, or rearranged in chemical
reactions.
–
–
Dalton’s theory brought much attention from
other scientists who tested it.
While some exceptions were found, Dalton’s
Atomic Theory has not been discarded, just
modified and expanded.
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Definition of Element
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Testing the atomic theory

During the next 200 years the atomic theory
was tested over and over again.
– One of the main ways of testing the atomic
theory was a device used during the 1800’s
called a Cathode Ray tube.
•The Cathode ray tube was essentially a
low pressure tube that had electricity
put through it. It produced a light
called a cathode ray.
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Cathode Ray Tube
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Cathode Ray Tube
Cathode: a negative electrode through
which current flows.
 Anode: a positive electrode through which
current flows.

– The reason for calling the light a cathode ray
was because it appeared to start at the cathode
and go to the anode.
– The cathode ray is the basis for today’s TVs
and monitors.
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Cathode Ray Tube Experiments
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The search for smaller particles

Basic Discoveries made with the cathode
ray tube.
1. The ray originated at the cathode and goes to
the anode.
–
This infers that the ray is negative in charge.
Principles of Nature:
1. The electric charge of matter is normally neutral.
2. Opposite Charges Attract
Like Charges Repel
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The search for smaller particles
2. When a paddle wheel was placed in front of the
cathode ray it moved toward the anode.
–
–
This infers that the cathode ray must be composed of small,
individual particles that could push the paddle wheel down
the cathode-ray tube.
Late in the 19th century G. Johnstone Stoney named the
small, negatively charged particles electrons.
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J.J. Thomson



1.
2.
English physicist.
Discovered the
electron in 1897.
Nobel Prize Winner
1906.
Negative in charge.
Almost no mass.
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J. J. Thomson
In His Own Words
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J. J. Thomson

When a magnet or
charged plates were
placed above the
cathode ray, the ray
was deflected.
– This implied that the
mass of an electron
was small.
– Also that an electron
had a negative charge.
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J. J. Thomson
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J. J. Thomson’s Atomic Theory

Based upon his
experiments and
observations, J. J. believed
that the atom was a solid
ball with electrons located
on the outer skin of the
ball.
– This was called the plum
pudding model because of
the appearance of raisins in
pudding are like the
electrons in the theory.
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Earnest Rutherford





A student of J. J. Thomson.
From Australia originally.
Determined that atoms are
composed mainly of space,
with a small dense center.
Discovered the proton.
Won the Nobel Prize in
1908.
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Ernest Rutherford

Coined the names of many atomic particles.
– alpha, beta, and gamma rays
– proton, neutron
– half life, daughter atoms

Many influential scientists studied under
him.
– Neils Bohr
– James Chadwick
– Robert Oppenheimer
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Rutherford’s Gold Foil Apparatus
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Gold Foil Apparatus
1.
2.
3.
4.
The atom is composed primarily of space.
All of the positive charges are in a dense
center.
The center of the atom contains the vast
majority of the mass of an atom.
Discovered the nucleus.
 Nucleus: from Latin word meaning “little
nut”
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Ernest Rutherford’s Atomic
Theory
Electrons travel in the space surrounding
the nucleus in a way similar to the motion
of the planets around the sun.
 Called the planetary model.

– There is a total of 7 Primary Shells.
– The difference between these shells is the
distance from the nucleus.
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Ernest Rutherford’s Atomic
Theory
Electrons orbit the nucleus like the
planets orbit the sun.
7 primary orbits (or shells)
More than one electron can be in an
orbit.
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James Chadwick

In 1932 a British
scientist discovered
the neutron.
– He recognized that
these particles had the
same properties as
those proposed by
Ernest Rutherford.

Neutral particles that
have a mass equal to
that of protons.
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The Physics of Energy

As scientists came to have a more complete
understanding of the atom, they began to
study because they thought it might hold the
answer to the structure of an electron.
– Waves: a characteristic pattern of energy.

Dual Nature of Light: Light behaves both
as a mass particle (called a photon) and as
energy (called a wave).
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Electromagnetic Spectrum
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Electromagnetic Spectrum


Electromagnetic Spectrum: all wavelengths of
light.
Visible Spectrum: only visible wavelengths of
light.
– Prism: separates light into the different wavelengths.
– Diffraction Grating: separates light into the different
wavelengths.
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Electromagnetic Spectrum

Continuous Spectrum: All wavelengths of
light are seen.
ROY G BIV: Order of colors.
Red, Orange, Yellow, Green, Blue, Indigo, Violet.
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Electromagnetic Spectrum
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Electromagnetic Spectrum

Absorption Spectrum: Wavelengths of light are
absorbed by a substance.
– Produced by passing light through cool gases.
– White Absorption: No light absorbed, all light
reflected.
– Black Absorption: All light absorbed. No light
reflected.
– Absorption Movie:
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Electromagnetic Spectrum

Emission Spectrum: Only certain
wavelengths of light are seen.
– Produced by passing electricity through
hot/excited gases.
– Color seen is characteristic for element.
– Color seen is a blend of the specific
wavelengths of light.
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Electricity and Magnetism

If the blue portion is the wave created by
electricity, the green portion is the magnetic
field generated at a 90o angle.
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Standing Wave

Standing Wave: A wave with nodes that do
not move.
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Wave Terms



Wavelength (λ): The distance between two
identical portions of a wave.
Frequency (f): The number of times a wave
passes a particular spot in a set period of time.
The unit for this is hertz (Hz = 1/s)
Axis: The midline of a wave.
Peak
Amplitude
Wavelength
Axis
Trough
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Wave Terms




Node: Where the wave crosses the axis.
Peak: The top of the wave.
Trough: The bottom of the wave
Amplitude: The measurement from axis of a
wave to either the peak or the trough.
Peak
Amplitude
Wavelength
Axis
Trough
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Relationship between Frequency
and Wavelength

Wavelength is inversely proportional to
frequency. f  1/
Math Principle:
Whenever two factors are
proportional, they can be made equal
by multiplying by a constant.
The
constant for this relationship is velocity
(speed) so f = v/
For light f = c/, where c = speed of light
–c = 3.00E8 m/s
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Max Planck; 1858-1947



Nobel Prize Award:
1918
Discovered the value of
the constant that relates
energy to wavelength.
Discovered the
fundamental concept of
quanta, which lead to the
quantum theory.
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Plank’s Constant
Energy was discovered to be proportional to
frequency. E  f
 Plank discovered the constant that made it
equal, and the constant was named after
him. E = hf where h = Plank’s Constant
 Since E = hf, and f = c/, then E=hc/

– This is the main math we will use in the bright
line experiment (Exp 3C)
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The deBroglie Hypothesis
From Einstein we know E=mc2
 From Planck we know E=hc/
 Therefore mc2=hc/
 Cancel c and mc=h/
 Now solve for 
  = h/mc
 This implies that moving particles have
wavelength. Interesting, eh???

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Heisenberg Uncertainty Principle

The problem with the wave-particle duality
of nature: both natures cannot be tested at
the same time with the same experiment.

Heisenberg stated it this way: It is
impossible to know the exact position and
the exact momentum at the same time.
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Niels Bohr; 1885 - 1962





1913 proposed that electrons could
only reside in certain energy levels
(quanta).
Danish physicist.
Proposed the step ladder analogy.
Took all of the available information
and synthesized it into the proposed
quantum theory.
Nobel Prize: 1922
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Niels Bohr

What he saw:
6
bright lines of light for the atomic emission
of hydrogen.
Using Plank’s equation he related the lines of
light to specific quantities of energy.
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Hydrogen Emission Spectrum

Bohr stated that the electron usually stays at
the lowest energy level possible.
– He called this the ground state.
Principles of Nature
1. The sum of electric charges are usually equal in
nature.
2. Opposites Attract; Likes Repel
3. Entropy: Things tend to go to the lowest energy
level possible.
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Hydrogen Emission Spectrum

Bohr stated that when energy is passed
through a sample of gas most of the energy
is not absorbed.
– Electrons only absorb the energy when it is
exactly the same amount as the next higher
energy level for the electron.
– Excited State: When an electron has absorbed
energy to go to a higher energy level.
– Electrons stay in the excited state for only
moments before falling back to ground state.
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Niels Bohr
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Hydrogen Emission Spectrum
Ground State
e-
Energy
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e-
Excited State
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Neils Bohr: Hydrogen Emission
Spectrum
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Hydrogen Emission Spectrum
Quantum: A specific amount of energy.
 Bohr stated that electrons could only absorb
specific quanta of energy. When this energy
is absorbed the electron is in an excited
state for a moment. It quickly returns to the
ground state because of its instability.
 Entropy: Things tend to go to the lowest
energy level possible.

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Hydrogen Emission Spectrum
Bohr studied a series of 6 lines called the
Balmer series. Because there was 6 lines he
hypothesized that there must be 7 principle
shells.
 Later other series of lights confirmed what
Bohr had hypothesized.
 Still later it was hypothesized that there
must be another energy level called subshells.

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Confirmation
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Bohr’s Atomic Theory
1.
2.
3.
Electrons can only exist in certain energy
levels.
Primary Shell: Distinguished by the
distance from the nucleus (7 primary
shells) same as Rutherford’s model.
Sub-shell: Distinguished by the shape of
the electron cloud.
 Four sub-shells, s, p, d and f
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Electron Cloud
Area of high
probability of
finding an
electron.
 Each of the subshells are different
types of electron
clouds

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Electron Orbitals

Each orbital can contain up to two different
electrons (in a normal situation).
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s Sub-Shell
s Sub-Shell: round
ball shape region.
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p Sub-Shell
p Sub-Shell: Pear shaped pairs of lobes on all
three axis.
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d Sub-Shell
d Sub-Shell:
Each sub-shell
has four pairs
of pear-shaped
lobes.
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f Sub-Shell
f Sub-Shell: Seven sets of four pear-shaped
lobes around the different planes of the atom.
This is extremely difficult to draw.
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Sub-Shells Chart
# of e- Possible
Principle
#
of
Multiply
Sub-Shells
Shell
Orbitals by 2 = (in Sub-Shell)
s
Some
1
1
X2=
2
p
People
2
3
X2=
6
d
Do
3
5
X2=
10
4
7
X2=
14
f
Fine
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3.3 How do the structures of
atoms differ?
Objectives
 Shorthand Notation
 Valence Notation
 Electron Configuration (Orbital Diagram)
 Quantum Numbers

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Objectives (SWBAT)
write the shorthand notation for any
element.
 write the valence notation for any element.
 write the electron configuration for any
element.
 write the quantum numbers for any electron.
 discuss the total possible number of
electrons for any principle or sub-shell.

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Shorthand Notation

Shorthand Notation: describes the
sub-shell location of every electron of
an element.
Sub-shell electrons are
found in:
1S2
Total number of electrons in
sub-shell:
Primary Shell that sub-shell is
located in:
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Locating Sub-Shells on Periodic
Table
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Primary/Sub-Shells
1
1st
Primary Shell Seen
S 1
P 2
Consecutive #s
D 3
F 4
2
2
3
3
4
3
4
5
4
5
6
5
6
7
6
7
4
5
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Shorthand Notation Guidelines
1. Treat the atomic number as the electron #.
2. Always count electrons in numerical order.
3. The superscript is always the number of electrons
in that sub-shell and that principle shell.
4. The sum of the superscripts should add up to the
atomic number of the element.
5. Electrons are listed in order of increasing
energy. This is called the Aufbau Principle
(means building up in German).
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Shorthand
H 1s1
 He 1s2
Noble Gas
 Li 1s2 2s1
 Be 1s2 2s2
 B 1s2 2s2 2p1
 C 1s2 2s2 2p2
 N 1s2 2s2 2p3

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Shorthand
O 1s2 2s2 2p4
 F 1s2 2s2 2p5
 Ne 1s2 2s2 2p6
-Noble Gas
 Na 1s2 2s2 2p6 3s1
 Mg 1s2 2s2 2p6 3s2
 Al 1s2 2s2 2p6 3s2 3p1
 Si 1s2 2s2 2p6 3s2 3p2

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Shorthand
P
S
 Cl
 Ar
K
 Ca
 Sc

1s2 2s2 2p6 3s2 3p3
1s2 2s2 2p6 3s2 3p4
1s2 2s2 2p6 3s2 3p5
1s2 2s2 2p6 3s2 3p6 Noble Gas
1s2 2s2 2p6 3s2 3p6 4s1
1s2 2s2 2p6 3s2 3p6 4s2
1s2 2s2 2p6 3s2 3p6 4s2 3d1
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Shorthand – Alternative Method
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Valence Notation
Valence Electrons: Electrons in the
outermost shell of the atom.
 Noble Gases: The outermost shell of the
atom is always full for a Noble Gas.
 Valence Notation: Start with the last Noble
Gas before the element and do the
shorthand notation from there.

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Valence Notation
H 1s1
 He 1s2
Noble Gas
 Li 1s2 2s1
 Be 1s2 2s2
 B 1s2 2s2 2p1
 C 1s2 2s2 2p2
 N 1s2 2s2 2p3

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H 1s1
 He [He]
 Li [He] 2s1
 Be [He] 2s2
 B [He] 2s2 2p1
 C [He] 2s2 2p2
 N [He] 2s2 2p3

87
Valence Notation
O 1s2 2s2 2p4
 F 1s2 2s2 2p5
 Ne 1s2 2s2 2p6 -Noble Gas
 Na 1s2 2s2 2p6 3s1
 Mg 1s2 2s2 2p6 3s2
 Al 1s2 2s2 2p6 3s2 3p1
 Si 1s2 2s2 2p6 3s2 3p2

Last Modified 10-18-01
(c) 2001 Tim Bass
O [He] 2s2 2p4
 F [He] 2s2 2p5
 Ne [Ne]
 Na [Ne] 3s1
 Mg [Ne] 3s2
 Al [Ne] 3s2 3p1
 Si [Ne] 3s2 3p2

88
Valence Notation
P
S
 Cl
 Ar
K
 Ca
 Sc

P
1s2 2s2 2p6 3s2 3p3
S
1s2 2s2 2p6 3s2 3p4
 Cl
1s2 2s2 2p6 3s2 3p5
1s2 2s2 2p6 3s2 3p6-Noble Gas  Ar
K
1s2 2s2 2p6 3s2 3p6 4s1
 Ca
1s2 2s2 2p6 3s2 3p6 4s2
 Sc
1s2 2s2 2p6 3s2 3p6 4s2 3d1
Last Modified 10-18-01
(c) 2001 Tim Bass
[Ne] 3s2 3p3
[Ne] 3s2 3p4
[Ne] 3s2 3p5
[Ar]
[Ar] 4s1
[Ar] 4s2
[Ar] 4s2 3d1
89
Quantum Mechanics
As the Quantum Theory of Atoms advanced
it soon became apparent that locating an
electron was going to be impossible (see
Heisenberg’s Uncertainty Principle and
Electron Cloud).
 Soon a branch of math called Quantum
Mechanics was developed to help identify
areas of high probability of finding an
electron.

Last Modified 10-18-01
(c) 2001 Tim Bass
90
Quantum Mechanics

As the quantum mechanics developed it
was soon apparent that there were four
energy levels instead of two:
1.
2.
3.
4.
Principle Shell (1-7)
Sub-Shell (s, p, d, f)
Orbital: different lobes of the sub-shells
Spin: clockwise and counter-clockwise
Last Modified 10-18-01
(c) 2001 Tim Bass
91
Electron Configuration
A new way developed to describe all the
energy levels of electrons in an atom.
 Electron Configuration: Location of all the
different energy levels for all the atoms of
an element. (Also called Orbital Diagram)

– Orbital: Different lobes of the sub-shells.
– Spin: either clockwise ( ) or counterclockwise ( )
» Clockwise is lower energy, always goes 1st.
Last Modified 10-18-01
(c) 2001 Tim Bass
92
Electron Configuration
Conventions

There are two basic ways that electron
configurations are drawn.
– Each student may choose which to use.
– There is one box (line) per orbital of the subshell
1s

Using boxes as orbitals:

Using lines as orbitals:
– Arrows are electrons:
Last Modified 10-18-01
(c) 2001 Tim Bass
1s
93
Electron Configuration Rules
1.
2.
3.
4.
Treat the periodic table as a table of
electrons for this exercise. Follow the
same order as the electron configuration.
Each orbital can only hold two electrons.
Electrons are added in order of increasing
energy.
Pauli Exclusion Principle: no two
electrons can have the same energy levels.
Last Modified 10-18-01
(c) 2001 Tim Bass
94
Electron Configuration Rules

Hund’s Rule: the most stable arrangement of
electrons is that with the maximum number of
unpaired electrons, all with the same spin
direction.
– Within a sub-shell each orbital must have one electron
before any can have a second electron.
 Exception: Group 6 and Group 11 elements. These
steal an electron from the s sub-shell to have 5 electrons
in the d sub-shell.
 Apparently the d half-filled and filled sub-shells are a lot lower
in energy level.
Last Modified 10-18-01
(c) 2001 Tim Bass
95
Electron Configuration

H
1s

Be 1s 2s

He
1s

B

Li
1s

C 1s 2s
Last Modified 10-18-01
2s
1s 2s
(c) 2001 Tim Bass
2p
2p
96
Electron Configuration


N 1s
2s
2p
1s
2s
2p
O
1s 2s

F

Ne 1s 2s
2p

Na 1s 2s
2p
3s
1s 2s
2p
3s
2p

Last Modified 10-18-01
Mg
(c) 2001 Tim Bass
97
Electron Configuration


Ar 1s 2s
2p
3s
3p
1s 2s
2p
3s
3p
Kr
4s 3d
4p
Exception!!!!
Exception!!!!
Last Modified 10-18-01
(c) 2001 Tim Bass
98
Orbital Notation
Last Modified 10-18-01
(c) 2001 Tim Bass
99
Quantum Numbers


It had been known for some time that it was only
the outermost (valence) electrons that affected
the behavior of the atom.
A shortcut called quantum numbers was
developed to give the energy level of individual
electrons.
1.
2.
Primary Shell (n): There are 7 primary shells and
they are numbered 1-7.
Sub-Shell (l): 4 sub-shells, 0-3
–
–
–
–
s
p
d
f
0
1
2
3
Last Modified 10-18-01
(c) 2001 Tim Bass
100
Quantum Theory
3. Orbital (ml): This is like a number-line, the
center orbital is always numbered 0.
–
–
–
–
–
s
0
p
-1 0 +1
d
-2 –1 0 +1 +2
f -3 -2 -1 0 +1 +2 +3
This relates to the electron configuration diagrams
3d
4f
-2 -1 0 +1 +2
-3 -2 -1 0 +1 +2 +3
Last Modified 10-18-01
(c) 2001 Tim Bass
101
Quantum Numbers

Spin (ms):
– Use +1/2 for clockwise ( ) lowest energy
– Use –1/2 for counter-clockwise ( ) higher
energy
Last Modified 10-18-01
(c) 2001 Tim Bass
102
(n) Principle Quantum Number and Periodic Table
Some
1
1
People
2
2
Do
3
2
3
Fine
4
3
4
3
4
5
4
5
6
5
6
7
6
7
4
5
Last Modified 10-18-01
(c) 2001 Tim Bass
103
Sub-Shell Quantum Number
0
Some s
0
People p
1
Do
d
2
Fine
f
3
1
2
3
Last Modified 10-18-01
(c) 2001 Tim Bass
104
Orbital ml Quantum Number
00
Some
0
People
-1 0 +1
Do
-2 -1 0 +1 +2
-1 0 +1 –1 0 +1
Fine -3 –2 –1 0 +1 +2 +3
-2 –1 0 +1 +2 –2 –1 0 +1 +2
-3 –2 –1 0 +1 +2 +3 –3 –2 –1 0 +1 +2 +3
Last Modified 10-18-01
(c) 2001 Tim Bass
105
Spin Quantum Number & Periodic Table
+1/2
-1/2
+1/2 –1/2
+1/2
Last Modified 10-18-01
+1/2
-1/2
(c) 2001 Tim Bass
-1/2
106
Quantum Number Examples
Electron # n
l
ml
ms
1
5
10
21
81
95
118
0
1
1
2
1
3
2
0
-1
+1
-2
-1
+2
-1
+1/2
+1/2
-1/2
+1/2
+1/2
+1/2
-1/2
1
2
2
3
6
5
7
Last Modified 10-18-01
(c) 2001 Tim Bass
107
Maximum Number of Electrons
Principle
Sublevels
energy level available
Number of orbitals Number of eTotal e- possible
in sublevel (2 l +1) possible in sublevel for energy level
[2 (2 l +1)]
(2n2)
1
s
s-1
2
2
2
s, p
s-1, p-3
s-2, p-6
8
3
s, p, d
s-1, p-3, d-5
s-2, p-6, d-10
18
4
s, p, d, f
s-1, p-3, d-5, f-7
s-2, p-6, d-10, f-14
32
5
s, p, d, f, g s-1, p-3, d-5, f-7,
g-9
s-2, p-6, d-10, f-14, 50
g-18
6
s, p, d, f,
g*, h*
s-2, p-6, d-10, f-14, 72
g-18, h-22
7
s, p, d, f,
g*,10-18-01
h*, I*
Last Modified
s-1, p-3, d-5, f-7,
g-9, h-11
s-1, p-3, d-5, d-7,
s-2, p-6, d-10, f-14, 98 Total Poss =
g-9, h-11, (c)
i-13
g-18, h-22, i-26
280 e- 108
2001 Tim Bass