Transcript Quantum Mechanics - Derry Area School District

Quantum Mechanics
Chapters 4 & 5
1
WAY WAY BACK IN
TIME...
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Greek philosopher
Democritus (460370 BCE.)
substances that
comprised nature
– empty space
– tiny particles

“atoms”
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Democritus
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different kinds of atoms existed
not able to be broken down by
ordinary means
3
Aristotle
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More popular
a contemporary of Democritus
matter was a continuous substance
which he called "hyle“
this idea was accepted without
support for nearly two thousand years.
4
pseudo- science

explained natural phenomena in
philosophical ways
– without experimentation
– without logic
maggots come from rotting meat
 frogs cause warts

5
Isaac Newton, Robert
Boyle and John Dalton

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Questioned natural occurrences
conducted experiments
– controlled variables

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made observations
collected data
data and observations used to support
hypotheses
6
John Dalton
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matter is particulate in nature
atoms of a single element are identical
atoms of different elements are
different from each other
Dalton's hypothesis explained the
observations
first modern atomic theory
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J.J. Thomson
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Are atoms really the smallest particles?

Cathode ray tubes
Rays originated at the cathode (negative
electrode) and traveled toward the anode
(positive electrode).

Produced rays composed of negatively
charged subatomic particles

– he called particles electrons (e-).
– mathematically calculated the electron's mass to
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charge ratio
Oil Drop Experiment
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Robert Millikan
determined the charge of a single
electron (-1)
Oil Drop Experiment
9
Thomson Atom

Plum Pudding Model
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Electrons
10
Atomic Research

Ernest Rutherford
– Niels Bohr
– Hans Geiger
– Ernest Marsden

Experiment to study structure of atom
– Gold Foil Experiment
11
Gold Foil Experiment

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Ernest Rutherford
positively charged helium nuclei (alpha () particles) propelled
at high speed toward a thin sheet (tissue paper-like) of gold
foil surrounded by a fluorescent screen
12
Experimental Results:

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1. Most of particles pass straight
through foil
2. Some particles are slightly
deflected
3. A few particles (1 per 8000) are
deflected greatly. Nearly bounce back
to origin.
13
Conclusions based on
experimental data:
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1. The atom is mostly space.
2. Mild deflection was caused by
repulsion of similar electrostatic charge.
Therefore, the atom has a positive region.
'Protons“
3. The positive core is very small (1 x
10-12 of total atomic volume) and
contains most of the atom's mass.
'Nucleus'
14
Rutherford Atom
15
The Atom is mostly empty space…..
16
Eugene Goldstein

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showed that protons created rays in a
cathode ray tube just as the electrons had
done
traveled in the opposite direction. (anode to
cathode)
concluded that a proton is equal but
opposite in charge to the electron, or 1+,
and approximately 1836 times more
massive
17
Thomson's observation

Atoms that are
– chemically identical can have variable
mass
18
James Chadwick
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credited with the discovery of the neutral
subatomic particle - the neutron
Walter Bothe obtained initial evidence nearly
two years before Chadwick's experiments
Neutrons have a mass nearly identical to
that of the proton, but no electrical charge.
19
Explanation lies with the
neutrons
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Isotopes
– Atoms of the same element containing different
numbers of neutrons.
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Nuclide
– a particular isotope
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Each isotope acts the same in chemical
reaction
Each nuclide will produce a product of
different mass.
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Hydrogen isotopes
Proton +
Protium
1 proton, 1 electron
Neutron
Deuterium
1 proton, 1 electron, 1 neutron
Electron -
Tritium
1 proton, 1 electron, 2 neutrons
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TO SUMMARIZE...
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The atom is the smallest particle of matter
that cannot be chemically subdivided.
Composed of two regions and three primary
subatomic particles.
– Nucleus
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very small
positively charged
dense.
– Protons
– Neutrons

Electron Cloud
– Electrons
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orbit the nucleus.
Small point-like negative charges
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IN PERFECT BALANCE
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The atom is electrically neutral
contain equal number of:
– protons (positive charges) and
– electrons (negative charges).
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Remind you of anything?
24
Niels Bohr
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1913
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Introduced ‘Planetary Model’
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Planetary Model
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Gravity and Inertia
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Solar System
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Attractive force:
Atom
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– Gravity
– Pulls planet toward
sun
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+ / - charges
– + nucleus pulls
– electrons toward
it
Repulsive force:
– Inertia
– Pushes planet in a
straight line away
from sun
Attractive force:
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Repulsive force:
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It Ought to Go SPLAT!

“A charged particle constrained to move in
curved path … radiates energy according to
Maxwell equations.”
Some basic principles of synchrotron radiation.
(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)

Electrons – constant orbit
Energy drain
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and the atom goes
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SPLAT!
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Electromagnetic
Radiation
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Electromagnetic
Radiation

c = 3.0 X 108 m/s
Wavelength = λ
Frequency = f (υ)
30
Electromagnetic
Radiation

Louis de Broglie
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Dual Nature of
Light
Wave Nature
– Travels through space in
waves
– Travels at speed of light
(c)
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Particle Nature
– Interacts with matter as
a particle
– Quanta (unit of energy)
transferred to matter in
packets of light
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(photons)
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Electromagnetic
Radiation
Light →
33
Electromagnetic
Radiation
Light → Excited atomic
state
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Electromagnetic
Radiation
e- jumps to
Higher Energy
level
Light → Excited atomic
state
35
Electromagnetic
Radiation
e- jumps to
Higher Energy
level
e- jumps to
Lower Energy
level
Light → Excited atomic →→→→→→
state
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Electromagnetic
Radiation
e- jumps to
Higher Energy
level
e- jumps to
Lower Energy
level
Light → Excited atomic →→→→→→
state
37
Electromagnetic
Radiation
e- jumps to
Higher Energy
level
Light →Excited atomic
state
e- jumps to
Lower Energy
level
→→→→→→ Atom in Ground State
photon released
38
Electromagnetic
Radiation
e- jumps to
Higher Energy
level
e- jumps to
Lower Energy
level
Light →Excited atomic
state
→→→→→→ Atom in Ground State
photon released
Bright-line Spectrum
39
Electromagnetic
Radiation

Speed of wave
Energy of photon
E=hf

c=fλ
solving for frequency
c=f
λ
c=
λ
ch=
E=
solving for frequency
E=f
h
E
h
Eλ
ch
λ
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Electromagnetic
Radiation
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Irwin Schrodinger
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Developed the ‘Wave Equation’
to support de Broglie’s idea of
the dual nature of light
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Quantum Leap
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Bohr’s Planetary Model is used to
explain the spectral lines produced by
atoms.
Quantum leap animation
42
Quantum Leap
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The color of light indicates its
wavelength
A particular wavelength has a definite
frequency
A particular wavelength has a definite
amount of energy
43
Riding the Wave (Equation)
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The Wave Equation
– confirmed Bohr’s theory of quantized
energy levels.
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Treating electrons as waves, explains
why the tiny negative electrons are
not drawn into the more massive and
positive nucleus
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Riding the Wave
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“A charged particle constrained to move in curved path … radiates energy
according to Maxwell equations.”
Some basic principles of synchrotron radiation.
(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)
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As the e- approach the
nucleus, their wavelengths
become shorter.
E = ch
λ
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Solar System
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Attractive force:
Atom
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– Gravity
– Pulls planet toward
sun
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Repulsive force:
– Inertia
– Pushes planet in a
straight line away
from sun
Attractive force:
+ / - charges
– + nucleus pulls
– electrons toward
it
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Repulsive force:
– Energy produced
form the shorter λ
pushes the e- away
from the nucleus
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QUANTUM MECHANICS

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Electrons do not obey the laws of
classical or Newtonian physics
A new science to describe the laws of
small particles was established
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LOOK! IT ISN'T THERE!
Uncertainty principle
Not possible to locate an electron's exact
position
Position and momentum cannot be
determined at the same time
to determine one you effect a change in
the other
Electrons - only "seen” when they jump from
a higher to lower energy level.
once electron is "seen," its direction and Werner Heisenberg
speed are different from what they were
prior to observation.
Determining position changes its
momentum.
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Applies to electron when it is considered a
particle
WAVE REVIEWS!
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Irwin Schrodinger
Wave equation
– helps locate probable regions of electron
population if considered it to be like a
wave.
– general paths of the electrons around the
nucleus can be determined
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50
MAP IT OUT!
Electrons may be described by a
set of four quantum numbers
which serve as 3-D for electron
location.
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D.C. Map Activity

Find
– Union Station
– Nat’l Air & Space
Museum
– Watergate Complex
– Capitol
– Ford’s Theater
– White House
– Lincoln Memorial
– Kennedy Center

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A-B 5+
C-D 4
A-B
C
B
B
C
B
0
5
3-4
2
1
0
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The Quantum Numbers
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principle quantum number (n)
– n = 1, 2, 3...
– Distance of electron from nucleus.
– Electrons exist ONLY in the energy levels.
– No electrons have energies to exist between energy levels
[nodes].

angular momentum (azimuthal) quantum number (l)
– l = s, p, d, f
– Shape of paths, subshells, sublevels,
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magnetic quantum number (m)
– m = 1, 3, 5, 7
– Spatial orientation to x, y, z axes
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spin quantum number (s)
– s = clockwise, counterclockwise
– Electron spin
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FIRST PRINCIPLE of
QUANTUM MECHANICS
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Only specific energy levels are possible for
electrons.
The principle quantum number that
corresponds to the energy levels begins
with 1, 2, 3, etc. beginning with the level
closest to the nucleus
–
–
–
–
K energy level is 1
L energy level is 2
M energy level is 3
N energy level is 4, etc.
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SECOND PRINCIPLE of
QUANTUM MECHANICS

The maximum number of electrons that can
occupy and energy level is given by the
equation
2(n)2 = maximum number of e– n is the principle quantum number of the energy
level.
– Principle quantum number is 2, the electron
maximum is 2(2)2 = 8
– Principle quantum number is 3, the electron
maximum is 2(3)2 = 18
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DIVIDE and CONQUER!
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energy levels are actually several closely
bound bands of energy
Each of the bands represents a sub level
The number of sublevels is the same as the
principle quantum number
It is represented by the angular momentum
numbers
– s, p, d, and f.
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
K energy level
– principle quantum number is 1.
– 1 sub level, s
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L energy level
– principle quantum number is 2.
– 2 sublevels, s, p
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M energy level
– principle quantum number is 3.
– 3 sublevels, s, p, d
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N energy level
– principle quantum number is 4
– 4 sublevels s, p, d, f.
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The energy within a level varies.
Lowest Energy
Highest Energy
s >>>
p >>> d >>> f
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Sublevels have
characteristic shapes
s
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p
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d
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f
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Magnetic Quantum
Number
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1, 3, 5, 7
represents the number of different
paths (orbits) that the electron can
take in relationship to the three axes
of space
62
Wolfgang Pauli
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electron spectra affected by magnetic
fields
indicated that the electrons could be
spinning in two different directions
within the orbital
– clockwise
– counterclockwise
63
Pauli Exclusion Principle
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Spinning in one direction causes a magnetic
field that is attracted to the north pole of a
magnet
Spinning in the opposite direction causes it
to be attracted to a south pole
If two electrons occupy the same orbital
then they must spin in opposite directions
If they did not they would repel each other
as two like magnetic poles repel each other.
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North Pole
South Pole
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Energy Levels are
Subdivided
ENERGY LEVELS
s
SUBLEVEL
p
SUB SHELL
d
f
ORBITALS
1
1
2
3
1
2
3
4
5
1 2
3
4
5 6 7
ELECTRON PAIRS
1 2
1 21 21 2
1 2 1 21
2 1
21
2 1
21 21 21 21 21
212
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Hierarchy
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no two electrons in same atom can
have same set of four quantum
numbers.
What is the maximum number of
quantum numbers that can be shared
by two electrons?
3
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Summary Chart
ENERGY
LEVEL
PRINCIPLE
QUANTUM NO.
SUBLEVELS
ORBITAL
PER SUBLEVEL
ORBITAL
PER LEVEL
ELECTRONS
PER SUBLEVEL
ELECTRONS
PER LEVEL
K
1
s
1
1
2
2
L
2
s
p
1
3
4
2
6
8
M
3
s
p
d
1
3
5
9
2
6
10
18
N
4
s
p
d
f
1
3
5
7
16
2
6
10
14
32
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I'D RATHER STAY SINGLE

most stable state of an atom - ground
state
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actual arrangement of the electrons in
atom referred to as the electron
configuration
69
Hund's Rule

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
electrons arrange themselves in such a
way as to MAXIMIZE THE NUMBER OF
UNPAIRED ELECTRONS in a sub level
Only after one electron occupies each
of the sublevel’s orbitals do the
electrons begin to pair up and share
the same orbital
e- spin oppositely when in same orbital
70
OUTERMOST
Energy Level
Nucleus
K Energy Level
2nd from the
OUTERMOST
Energy Level
NEXT to the
OUTERMOST
Energy Level
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POSTULATES of
QUANTUM MECHANICS
1.
2.
3.
4.
5.
The K energy level is the most tightly bound in any
atom.
The outermost energy level NEVER has more than 8
electrons.
The next to the outermost level NEVER has more
than 18 electrons.
IF the next to the outermost level does not contain
its maximum number of electrons (18 e-), THEN the
outermost energy level can hold no more than 2
electrons.
IF the second from the outermost energy level does
not contain its maximum amount of electrons
(2n2), THEN the next to the outermost energy level
can hold no more than 9 electrons.
72
The Aufbau Principle


Experimental data indicates that sublevels
within the energy levels sometimes overlap
the sublevels of other energy levels
electrons fill the subshells of the lowest
energies first

Since overlapping occurs, a means of
remembering the order of sub level energies
is helpful
73
Aufbau Diagram
(from German Aufbauprinzip, “building-up principle”)



Electrons enter
atom in this order
Electons are
removed from atom
in the reverse order
Last in first out.
74
ORBITAL NOTATION



Example: Oxygen
8 protons, 8 electrons,
8 neutrons
Notice the application of Hund's Rule, where
unpaired electrons are maximized.
75
ELECTRON CONFIGURATION
NOTATION

compare this method to the orbital notation.

1s2 2s2 2p4
76
ELECTRON DOT
NOTATION

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shows only the electrons in the outer
energy level (valence electrons)
the e- that are involved in chemical
reactions
illustrates the electrons that bond with
other atoms
outer (valence) energy level can hold
no more than eight electrons (2nd
postulate of quantum mechanics)
77
78
Oxygen



8 protons, 8 electrons
chemical symbol is
written in the center of
the notation
right of the symbol
represents the s orbital
top, left and bottom
represent each of the
three orbitals in the p
sub level, respectively.
79