Download Chapter 6 Electronic Structure of Atoms

The Modern
Model of
the Atom
History of the Atomic Model
• Democritus (400 B.C.)
• Believed that matter was composed
of invisible particles of matter he
called atoms.
• Antoine Lavoisier (1700’s)
• Law of Conservation of Mass –
Matter is not created or destroyed.
• Joseph Proust (1700’s)
• Law of constant composition –
compounds are composed of
atoms in definite ratios.
History of the Atomic Model
• John Dalton (Late 1700’s)
• First atomic theory explaining
chemical reactions
• J.J. Thomson (1897)
• Discovered the electron using
cathode ray tubes
• Robert Millikan (1909)
• Found the charge and mass of the
electron in his famous “oil-can”
experiment.
In Bohr’s atom (1913), electrons had a
single energy state, described by its Principle
Quantum Number, corresponding to an
orbit at a specific distance from the nucleus
as observed from the spectral lines of
hydrogen.
However, It was soon
discovered that electrons
could not be described so
simply.
Experimental
data began to suggest that
not all electron energy
levels fit into nice and neat
integers.
History of the Atomic Model
• Ernest Rutherford (1911)
• Discovered the nucleus, and later
the proton, in his famous “gold
foil” experiment.
• James Chadwick (1932)
• Discovered neutrons studying
atomic masses.
• Neils Bohr (1913)
• His atomic model accounted for the
atomic emission spectrum of the
hydrogen atom
History of the Atomic Model
• Arnold Sommerfeld (1916)
•
•
Used Einstein's Theory of Relativity to
expand Bohr’s single electron orbit into two
possible electron orbits that an electron can
attain to explain the “Fine Structure” of the
hydrogen line spectrum, or the doubling of
the spectral lines.
Electrons were then thought to not only
have a principle energy, but also could exist
with different sub-energies.
•
Eventually, Sommerfeld introduced a
second quantum number, the
Azimuthal Quantum Number, to
describe the angular momentums of
an electron giving rise to the observed
Fine Structure of hydrogen.
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History of the Atomic Model
History of the Atomic Model
• Arnold Sommerfeld (1916)
• Samuel Goudsmit [top] and Geroge
Uhlenbeck (1916)
•
•
•
•
Accounted for how a magnetic field affects the Fine
Structure by widening the gap between the spectral
lines of hydrogen, known as the Zeeman Effect. This
led them to the understanding that electrons must
have a spin property and that spin will affect the
energy of the electron as it moves around the nucleus.
The result was the inclusion
of a third quantum number,
called the Magnetic
Quantum Number, to
describe further divisions in
electron energies.
However, the Zeeman Effect
could not be explained.
History of the Atomic Model
• Wolfgang Pauli (1924)
•
•
•
proposed a new quantum number, Spin
Quantum Number, with two possible values in
order to resolve inconsistencies between
observed molecular spectra and the BohrSummerfeld model.
This brought the total quantum numbers
required to describe the energy of an electron
to four.
Formulated the Pauli exclusion principle
which stated that no two electrons could exist
in the same quantum state; meaning, no two
electrons can have the same set of four
quantum numbers.
History of the Atomic Model
• Louis de Broglie (1924)
•
Introduced the Wave Theory of Matter where
he proposed that all moving particles,
particularly subatomic particles such as
electrons, exhibit a degree of wave-like
behavior.
h

mv
Where:
m = mass
v = velocity
h = planck’s constant
Equation sheet
•
•
•
Added elliptical orbits to the Bohr model to
explain the apparent discrepancy between
Bohr’s single electron energy state and the noninteger energy levels being observed from
spectral data.
Electrons in these “elliptical” orbits
would have energies more in line with
the experimental evidence being
collected and were described rather
nicely by the two new quantum
numbers; Azmuthal and Magnetic.
The inclusion of elliptical orbits into “shells” of electrons
made the model very difficult to use, and it still couldn't
explain more complex atoms.
Nor could it explain the Zeeman Effect.
Electron Shell Model
Collectively, the Rutherford-Bohr model and
the Bohr-Summerfeld model are referred to as
“Old-Quantum Theory,” or more commonly the
Electron Shell Model.
Where the Rutherford-Bohr model predicted
circular obits described by a single quantum
number, the Bohr-Summerfeld model describes
electron orbits that are elliptical and require three
quantum numbers.
However, they had one thing in common, they
depended solely on the particle nature of electrons.
History of the Atomic Model
• Erwin Schrödinger (1926)
•
•
fascinated by de Broglie's idea, Schrödinger
explored whether or not the movement of an
electron in an atom could be better explained as
a wave function rather than as a point particle
in his famous equation.
This approach elegantly predicted many of the
spectral phenomena that Bohr's model failed to
explain.
 h2   2  2  2 

 2  2   V  E
8 2 m  x 2
y
z 
Where:
V = potential energy of electron
E = total energy of electron
 = wave function of electron
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History of the Atomic Model
• Max Born (1926)
History of the Atomic Model
• Werner Heisenberg (1927)
• A consequence of describing electrons as
waveforms is that it is mathematically
impossible to simultaneously derive the
position and momentum (mν) of an
electron.
• The Heisenberg Uncertainty Principle:
•
•
•
proposed that Schrödinger's wave function
described not the electron but rather all its
possible energy states, and thus could be used
to calculate the probability of finding an
electron at any given location around the
nucleus.
He formulated the now-standard interpretation of the
probability density function for ψ2 in the Schrödinger
equation.
This reconciled the two opposing theories of particle versus
wave electrons and the idea of wave–particle duality was
introduced. This theory stated that the electron may exhibit
the properties of both a wave and a particle.
x  m v 
h
4
• The Uncertainty Principle invalidated Bohr's model,
with its neat, clearly defined circular orbits and
ushered in the newly emerging Quantum Mechanics
Model of the atom.
New-Quantum Theory
Quantum Mechanic Atomic Orbitals
• Electrons behave as waves in their motions around the nucleus.
• The question then becomes how do the electron wave functions
and probability distributions translate into 3-D spaces
according to the Quantum Numbers used to describe them?
• An electron’s wave function (ψ) is found by the Schrödinger
Equation and describes its energies corresponding to the four
quantum numbers.
 ψ is a function of distance (Principle Quantum Number) and
angular momentum according to its vector components
(Angular-Momentum Quantum Number and Magnetic
Quantum Number).
 Each ψ corresponds to a region of space within which an
electron is found, called an orbital.
• does NOT describe the exact location of the electron.
 No one orbital may contain more than two electrons and
they must be of opposite spin (Spin Quantum Number).
• ψ 2 is proportional to the probability of finding an e- at a given
point.
1. Principal Quantum
Number, n
• The principal quantum
number, n, describes the
principle energy level in
which the electron resides.
• The values of n are
integers ≥ 1.
• The energy of the level
increases away from the
nucleus
• Answer:
 The Principle Quantum Number gives us the overall size of the electrons
probability density; distance from the nucleus.
 The Azmuthal Quantum Number (Angular-Momentum) describes the
number of probability densities at any given main energy level; the
number and shapes of electron sublevel energies.
 The Magnetic Quantum Number tells us how many orientations a
particular set of probability densities will have within each sublevel; the
number of electron orbitals.
 The Spin Quantum Number denotes the spin an electron will have in any
one orbital.
2. Azimuthal Quantum Number, l
• This quantum number
defines the sublevels and
the shape of each orbital in
the sublevels in each
principle energy level.
d Sublevel
p Sublevel
Principle
Quantum #
Azimuthal
Quantum #
1
s
2
s
p
3
s
p
d
4
s
p
d
f
s Sublevel
3
3. Magnetic Quantum Number, ml
• Describes the
number of
orbitals in each
sublevel and the
threedimensional
orientation of
each orbital.
Sublevel
# Orbitals
s
1
P
3
d
5
f
7
The s Sublevel
has only one s
Orbital
• Spherical in
shape.
• Radius of
sphere
increases with
increasing
value of n.
The p Sublevel
has 3 Orbitals
• Each p orbital has two lobes with a node
between them.
• The shape of a p orbital is known as
dumbell.
The d Sublevel
has 5 Orbitals
• Four of the
five orbitals
have 4 lobes;
the other
resembles a
p orbital with
a doughnut
around the
center.
•There are 7 f orbitals
•The f orbitals are much to
complicated to represent
graphically.
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4. Spin Quantum Number, ms
• The “spin” of an
electron describes
its magnetic field,
which affects its
energy.
• The electron spin is
either +1/2 or -1/2.
•From our understanding of the quantum model, we
can describe the location of each electron around the
nucleus of an atom.
Principle
Quantum #
Azimuthal
Quantum #
AngularMomentum
Quantum #
# electrons
per sublevel
# electrons
per main
energy level
1
s
s
2
2
2
s
p
s
px,py,pz
2
6
8
3
s
p
d
s
px,py,pz
d1,d2,d3,d4,d5
2
6
10
18
4
s
p
d
f
s
px,py,pz
d1,d2,d3,d4,d5
f1,f2,f3,f4,f5,f6,f
2
6
10
14
32
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Electron Configurations
According to the Quantum
Molecular Model
Electron Configurations
Therefore, 4th
main energy level
or n = 1
Electron Configurations
Therefore, p
sublevel in the 4th
main energy level
• Distribution of
all electrons in
an atom
• Consist of
– Number
denoting the
energy level
– Letter
denoting the
type of orbital
• Distribution of
all electrons in
an atom
• Consist of
– Number
denoting the
energy level
Electron Configurations
• Distribution of all
electrons in an atom.
• Consist of
– Number denoting the
Therefore, 5th
energy level.
electron of the
– Letter denoting the
possible 6 filling
type of orbital.
the 3 orbitals of – Superscript denoting
the p sublevel in
the number of
electrons in those
the 4th main
orbitals.
energy level
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Three rules guide the filling
of electrons in the main energy
levels, sublevels and orbitals to
determine the electron
configuration of an atom:
Aufbau principle:
States that electrons will
occupy the lowest possible energy
level possible.
This gives rise to the Order-of-Fill:
1.Aufbau principle
2.Pauli Exclusion Principle
3.Hund’s Rule.
Following the arrows on the diagram
gives rise to the following Order-of-Fill:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s
4f 5d 6p 7s 5f 6d 7p 8s
•Notice, 4s is
lower in
energy than 3d
and fills first.
Using the order of fill, we can designate the
electron configuration for any element. Observe:
Given that an s orbital only holds 2
electrons, p orbital holds 6 electrons, d
holds 10 and f holds 14, the electron order
of fill also designates the number of
electrons in each sublevel:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 8s2
1.Use the order of fill to write the electron
configuration for the following elements:
•Chlorine has 17 electrons in its electron cloud
Nitrogen
•From the order of fill:
Sulfur
2 + 2 + 6 + 2 + 5 = 17
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 8s2
Magnesium
Potassium
Krypton
•Therefore:
17Cl
1s2 2s2 2p6 3s2 3p5
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A second method of writing electron
configurations, know as orbital fill notation,
shows not only the main energy level, sublevels
and electrons in each sublevel, but also includes
the individual orbitals.
• Each box represents
one orbital.
• Half-arrows represent
the electrons.
• The direction of the
arrow represents the
spin of the electron.
To write electron configurations using the
orbital fill notation, the Pauli Exclusion
Principle and Hund’s Rule must be followed.
HUND'S RULE
• According to Hund's rule, electrons will not join
So, where electron configurations look like:
1s2 2s2 2p5
9F
Orbital fill looks like:
9
F  
1s
2s
  
2px
2py
2pz
THE PAULI EXCLUSION PRINCIPLE
• An atomic orbital may describe at most two
electrons, each behaving as if they spin on an
axis.
• According to the Pauli exclusion principle, only
electrons spinning in opposite directions can
occupy the same orbital within a sublevel.
other electrons in an orbital of a sublevel if an
empty orbital of the same energy is available in
the sublevel.
•Thus, the second electron entering a p sublevel
will go into an empty p orbital of the sublevel
rather than into the orbital that already contains
an electron.
2. Use the order of fill to write the orbital fill
notation for the following elements:
The question now becomes:
Sulfur
Why is it so important to know the
location of electrons around the nucleus of
the atom?
Magnesium
The answer?
Nitrogen
Potassium
Krypton
Valence electrons
Valence electrons are the electrons
located in the highest main energy level (or
valence shell) of an atom.
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Notice:
Group 2 atoms had how many valence
electrons?
Group 3?
Group 7?
Group 8?
What trend can be identified on the
periodic table related to valence electrons?
What about the transition metals (d
and f block elements)?
Electron
Distribution
in Molecules
G. N. Lewis
1875 - 1946
Valence electrons (the outer most
electrons) are responsible for the interaction
between atoms when forming chemical
compounds.
Another way to say that is that valence
electrons are the electrons that participate in
chemical bonding.
The Octet Rule explains that every atom
seeks a full valence shell. It is the attaining or
loss of valence electrons that will satisfy the
octet rule.
For example:
• Valence Electron
distribution is
depicted with Lewis
electron dot
notation
Electron Dot Notation
shows the number
of valence electrons
of an atom around
the atoms nuclear
symbol.
Oxygen has 6 valence electrons (group 6)
16
8

O 

or for convenience

O

1. When assigning valence electrons to an
atomic symbol, each side of the symbol
should receive one electron before a second
electron is placed on a side.
2. Always assign electrons across from each
other when possible.
Obtain the number of valence
electrons for each of the following atoms
from its group number and draw the
correct Electron Dot Notation (a.k.a.
Lewis Dot Structures).
1.
2.
3.
4.
5.
K
N
Cl
B
Be
6. S
7. C
8. Ar
9. P
10.H
Write the electron configuration and
orbital fill notation for each atom on the
periodic table from element 1 (H) to element 36
(Kr).
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