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Quantum Mechanics

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Title: Quantum Mechanics


1
Quantum Mechanics
  • Chapters 4 5

2
WAY WAY BACK IN TIME...
  • Greek philosopher Democritus (460-370 BCE.)
  • substances that comprised nature
  • empty space
  • tiny particles
  • atoms

3
Democritus
  • different kinds of atoms existed
  • not able to be broken down by ordinary means

4
Aristotle
  • 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.

5
pseudo- science
  • explained natural phenomena in philosophical ways
  • without experimentation
  • without logic
  • maggots come from rotting meat
  • frogs cause warts

6
Isaac Newton, Robert Boyle and John Dalton
  • Questioned natural occurrences
  • conducted experiments
  • controlled variables
  • made observations
  • collected data
  • data and observations used to support hypotheses

7
John Dalton
  • 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

8
J.J. Thomson
  • 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
    charge ratio

9
Oil Drop Experiment
  • Robert Millikan
  • determined the charge of a single electron (-1)
  • Oil Drop Experiment

10
Thomson Atom
  • Plum Pudding Model
  • Electrons

11
Atomic Research
  • Ernest Rutherford
  • Niels Bohr
  • Hans Geiger
  • Ernest Marsden
  • Experiment to study structure of atom
  • Gold Foil Experiment

12
Gold Foil Experiment
  • 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

13
Experimental Results
  • 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.

14
Conclusions based on experimental data
  • 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'

15
Rutherford Atom
16
The Atom is mostly empty space..
17
Eugene Goldstein
  • 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

18
Thomson's observation
  • Atoms that are
  • chemically identical can have variable mass

19
James Chadwick
  • 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.

20
Explanation lies with the neutrons
  • Isotopes
  • Atoms of the same element containing different
    numbers of neutrons.
  • Nuclide
  • a particular isotope
  • Each isotope acts the same in chemical reaction
  • Each nuclide will produce a product of different
    mass.

21
Hydrogen isotopes
Tritium 1 proton, 1
electron, 2 neutrons
22
TO SUMMARIZE...
  • The atom is the smallest particle of matter that
    cannot be chemically subdivided.
  • Composed of two regions and three primary
    subatomic particles.
  • Nucleus
  • very small
  • positively charged
  • dense.
  • Protons
  • Neutrons
  • Electron Cloud
  • Electrons
  • orbit the nucleus.
  • Small point-like negative charges

23
IN PERFECT BALANCE
  • The atom is electrically neutral
  • contain equal number of
  • protons (positive charges) and
  • electrons (negative charges).

24
Remind you of anything?
25
Niels Bohr
  • 1913
  • Introduced Planetary Model

26
Planetary Model
  • Gravity and Inertia

27
Solar System Atom
  • Attractive force
  • Gravity
  • Pulls planet toward sun
  • Repulsive force
  • Inertia
  • Pushes planet in a straight line away from sun
  • Attractive force
  • / - charges
  • nucleus pulls electrons toward it
  • Repulsive force

28
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
  • and the atom goes SPLAT!

29
Electromagnetic Radiation
30
Electromagnetic Radiation
  • c 3.0 X 108 m/s

Wavelength ?
Frequency f (?)
31
Electromagnetic Radiation
  • Louis de Broglie
  • Dual Nature of
  • Light
  • Wave Nature
  • Travels through space in waves
  • Travels at speed of light (c)
  • Particle Nature
  • Interacts with matter as a particle
  • Quanta (unit of energy) transferred to matter in
    packets of light (photons)

32
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33
Electromagnetic Radiation
  • Light ?

34
Electromagnetic Radiation
  • Light ? Excited atomic
  • state

35
Electromagnetic Radiation
  • e- jumps to
  • Higher Energy
  • level
  • Light ? Excited atomic
  • state

36
Electromagnetic Radiation
  • e- jumps to e- jumps to
  • Higher Energy Lower Energy
  • level level
  • Light ? Excited atomic ??????
  • state

37
Electromagnetic Radiation
  • e- jumps to e- jumps to
  • Higher Energy Lower Energy
  • level level
  • Light ? Excited atomic ??????
  • state

38
Electromagnetic Radiation
  • e- jumps to e- jumps to
  • Higher Energy Lower Energy
  • level level
  • Light ?Excited atomic ?????? Atom in Ground
    State
  • state
  • photon
    released

39
Electromagnetic Radiation
  • e- jumps to e- jumps to
  • Higher Energy Lower Energy
  • level level
  • Light ?Excited atomic ?????? Atom in Ground
    State
  • state
  • photon
    released
  • Bright-line
    Spectrum

40
Electromagnetic Radiation
  • Speed of wave
  • cf?
  • solving for frequency
  • cf
  • ?
  • c
  • ?
  • ch
  • E
  • Energy of photon
  • Ehf
  • solving for frequency
  • Ef
  • h
  • E
  • h
  • E?
  • ch
  • ?

41
Electromagnetic Radiation
  • Irwin Schrodinger
  • Developed the Wave Equation
  • to support de Broglies idea of the
    dual nature of light

42
Quantum Leap
  • Bohrs Planetary Model is used to explain the
    spectral lines produced by atoms.
  • Quantum leap animation

43
Quantum Leap
  • The color of light indicates its wavelength
  • A particular wavelength has a definite frequency
  • A particular wavelength has a definite amount of
    energy

44
Riding the Wave (Equation)
  • The Wave Equation
  • confirmed Bohrs theory of quantized energy
    levels.
  • Treating electrons as waves, explains why the
    tiny negative electrons are not drawn into the
    more massive and positive nucleus

45
Riding the Wave
  • 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)
  • As the e- approach the
  • nucleus, their wavelengths
  • become shorter.
  • E ch
  • ?

46
Solar System Atom
  • Attractive force
  • Gravity
  • Pulls planet toward sun
  • Repulsive force
  • Inertia
  • Pushes planet in a straight line away from sun
  • Attractive force
  • / - charges
  • nucleus pulls electrons toward it
  • Repulsive force
  • Energy produced form the shorter ? pushes the e-
    away from the nucleus

47
QUANTUM MECHANICS
  • Electrons do not obey the laws of classical or
    Newtonian physics
  • A new science to describe the laws of small
    particles was established

48
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 speed
    are different from what they were prior to
    observation.
  • Determining position changes its momentum.
  • Applies to electron when it is considered a
    particle

Werner Heisenberg
49
WAVE REVIEWS!
  • 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

50
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51
MAP IT OUT!
Electrons may be described by a set of four
quantum numbers which serve as 3-D for electron
location.
52
D.C. Map Activity
  • A-B 5
  • C-D 4
  • A-B 0
  • C 5
  • B 3-4
  • B 2
  • C 1
  • B 0
  • Find
  • Union Station
  • Natl Air Space Museum
  • Watergate Complex
  • Capitol
  • Fords Theater
  • White House
  • Lincoln Memorial
  • Kennedy Center

53
The Quantum Numbers
  • 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,
  • magnetic quantum number (m)
  • m 1, 3, 5, 7
  • Spatial orientation to x, y, z axes
  • spin quantum number (s)
  • s clockwise, counterclockwise
  • Electron spin

54
FIRST PRINCIPLE of QUANTUM MECHANICS
  • 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.

55
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

56
DIVIDE and CONQUER!
  • 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.

57
  • K energy level
  • principle quantum number is 1.
  • 1 sub level, s
  • L energy level
  • principle quantum number is 2.
  • 2 sublevels, s, p
  • M energy level
  • principle quantum number is 3.
  • 3 sublevels, s, p, d
  • N energy level
  • principle quantum number is 4
  • 4 sublevels s, p, d, f.
  • The energy within a level varies.
  • Lowest Energy Highest Energy
  • s gtgtgt p gtgtgt d gtgtgt f

58
Sublevels have characteristic shapes
  • s

59
  • p

60
  • d

61
f
62
Magnetic Quantum Number
  • 1, 3, 5, 7
  • represents the number of different paths (orbits)
    that the electron can take in relationship to the
    three axes of space

63
Wolfgang Pauli
  • electron spectra affected by magnetic fields
  • indicated that the electrons could be spinning in
    two different directions within the orbital
  • clockwise
  • counterclockwise

64
Pauli Exclusion Principle
  • 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.

65
North Pole
  • South Pole

66
Energy Levels are Subdivided
67
Hierarchy
  • 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

68
Summary Chart
69
I'D RATHER STAY SINGLE
  • most stable state of an atom - ground state
  • actual arrangement of the electrons in atom
    referred to as the electron configuration

70
Hund's Rule
  • 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
    sublevels orbitals do the electrons begin to
    pair up and share the same orbital
  • e- spin oppositely when in same orbital

71
OUTERMOST Energy Level
Nucleus
K Energy Level
NEXT to the OUTERMOST Energy Level
2nd from the OUTERMOST Energy Level
72
POSTULATES of QUANTUM MECHANICS
  • 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.

73
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

74
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.

75
ORBITAL NOTATION
  • Example Oxygen
  • 8 protons, 8 electrons, 8 neutrons
  • Notice the application of Hund's Rule, where
    unpaired electrons are maximized.

76
ELECTRON CONFIGURATION NOTATION
  • compare this method to the orbital notation.
  • 1s2 2s2 2p4

77
ELECTRON DOT NOTATION
  • 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)

78
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79
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.
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