Quantum Mechanics

1
Quantum Mechanics

• Chapters 4 5

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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

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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

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Oil Drop Experiment

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

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Thomson Atom

• Plum Pudding Model
• Electrons

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Atomic Research

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

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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

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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'

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Rutherford Atom
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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

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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.

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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.

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Hydrogen isotopes
Tritium 1 proton, 1
electron, 2 neutrons
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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

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IN PERFECT BALANCE

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

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Remind you of anything?
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Niels Bohr

• 1913
• Introduced Planetary Model

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Planetary Model

• Gravity and Inertia

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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

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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
• and the atom goes SPLAT!

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Electromagnetic Radiation
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Electromagnetic Radiation

• c 3.0 X 108 m/s

Wavelength ?
Frequency f (?)
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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)

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Electromagnetic Radiation

• Light ?

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Electromagnetic Radiation

• Light ? Excited atomic
• state

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Electromagnetic Radiation

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

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Electromagnetic Radiation

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

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Electromagnetic Radiation

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

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Electromagnetic Radiation

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

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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

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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

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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

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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
• ?

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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

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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

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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 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
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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

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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

• 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

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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

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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.

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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!

• 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
• 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

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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

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

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Wolfgang Pauli

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

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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.

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North Pole

• South Pole

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Energy Levels are Subdivided
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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

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Summary Chart
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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

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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

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OUTERMOST Energy Level
Nucleus
K Energy Level
NEXT to the OUTERMOST Energy Level
2nd from the OUTERMOST Energy Level
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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.

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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

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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.

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ORBITAL NOTATION

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

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ELECTRON CONFIGURATION NOTATION

• compare this method to the orbital notation.
• 1s2 2s2 2p4

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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)

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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.