Topic 18: The World of Quantum Mechanics

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Topic 18The World of Quantum Mechanics

• A microscopic view of
• the limits of reality

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The Bohr Atom - A New Paradigm for the Nature of
Matter

• Bohr combined quantization of energy in
  electrons with the Rutherford Atom to develop a
  new view of the atom - a real paradigm.
• Protons and neutrons sit in extremely small
  nucleus with electrons occupying 99.999 of space
  surrounding nucleus.
• Electrons moving inside atom and into/out of atom
  describe spectroscopic observations - light
  (energy) is given off as electrons change
  locations.
• Electron configuration explains standard chemical
  reactions.

Important
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Another Dream of Mr. Tompkins
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Gay Tribe of Electrons

• MT sees pairs of (e-) spinning around nucleus, he
  is alone in outer orbit of Na atom (valence
  electron).
• MT joins seven outer electrons in CI atom. Na
  atom tags along.
• electrons in homopolar bonds get tired of
  continuously jumping from one atom to the other.
• An electron jumped from outer to inner orbit,
  gave off light.

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Parallel Stories

• While an understanding of atomic structure and
  the Bohr Atom model were being developed,
  selected ideas and observations appeared that
  ultimately proved the Bohr Atom model to be
  wrong.
• These ideas/observations were not yet an
  alternative paradigm, they were more like warts
  that detracted from the Bohr Atom story.
• They ultimately led to a replacement paradigm -
  Quantum Mechanics.

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Quantization of Light

• Einsteins explanation of the photoelectric
  effect brought back the notion that light has
  particle-like characteristics.
• The particle-like characteristics for light are
  described by Ehn. This suggests that light
  travels as packets (quanta) called photons.
• The STR contains the following mathematical
  relationship E2m2c4p2c4
• For normal matter with mass that becomes Emc2.
• For light it becomes Epc2. This means that light
  has momentum even though it doesnt have mass.
  This is another particle-like characteristic.

Important
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Wave/Particle Duality
Important

• The quantization of light resurrected the
  argument as to whether light is a particle or a
  wave.
• Now, however, scientists were forced to consider
  the fundamental idea that light has BOTH
  characteristics.
• This lead to the notion of wave/particle duality
  - electromagnetic radiation inherently has both
  wave- and particle-like characteristics

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Whats good for the goose is also good for the
gander!
Important

• De Broglie acknowledged the wave/particle duality
  of light, but hypothesized that this
  characteristic might be true of all matter as
  well.
• He developed the mathematics and experiments to
  prove it.
• All objects (even humans) have wave/particle
  duality. The degree of duality is inversely
  proportional to mass.
• Electrons are, by far, most wavelike!

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Quantum Mechanical View of Electrons
Important

• Quantum mechanics replaces billiard ball
  electrons with wave functions.
• The wave functions describe the statistical
  likelihood of the electron location at any time.
• The Wave functions can be defined by four
  quantum numbers.
• Bohr had stumbled onto the first three in order
  to explain electron orbits - 1s1, 1s2, 2s1, 2s2,
  2p1, 2p2, 2p3, 2p4, 2p5, 2p6, .

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Spin

• The fourth quantum number is termed spin.
• Spin really defines the symmetry of objects.
  Electrons have spin 1/2 that means that if one
  rotates an electron 180, it looks the same.
• It turns out that all material particles have
  spin that is 1/2n (where n is an integer).
• Light turns out to have 1n spin (turn through
  360 or multiples to look the same).

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Pauli Exclusion Principle
Important

• In order to make a true quantum mechanical model
  of the atom, we need a set of rules to explain
  the model.
• The Bohr Atom had a set of rules governing
  electron placement that explains much chemistry.
• The four quantum numbers play the same role.
• One additional rule was added by Pauli - no two
  electrons with the same four quantum numbers can
  exist in the same atom.
• This became known as the Pauli Exclusion
  Principle.

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Matrix/Wave Mechanics

• Matrix mechanics and wave mechanics are two
  equivalent mathematical representations of
  Quantum Mechanics.
• They explain wave/particle duality and placement
  of electrons in atoms.
• Both calculate momentum (p) and position (q) for
  particles using the following equation pq-qphi
  (h is Planks constant and i is an imaginary
  number (square root of -1) that indicates
  wavelike characteristics)

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Heisenbergs Uncertainty Principle
Important

• The equation qp-pqhi has some odd implications.
• Mathematical calculations involving matrices (or
  vectors) depend on the order of calculations.
• The above equation suggests that one cannot
  define both position and momentum at the same
  time. Depending on which one is measured first,
  Plancks constant defines a limit of inherent
  uncertainty in any observation.
• This has been termed Heisenbergs Uncertainty
  Principle.
• This destroys deterministic certainty about
  reality - it says that at some level of
  measurement, we can NEVER be certain about the
  exact reality of any measurable occurrence.

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Inside the Nucleus

• Wave/particle duality also extends into the
  nucleus.
• It requires that there be two more fundamental
  forces (with gravity and electromagnetism) to
  hold the protons and neutrons together.
• We call these the strong and weak forces.

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The Copenhagen Interpretation

• Bohr argued in 1927 that quantum mechanics has
  certain intrinsic characteristics
• Heisenburg Uncertainty Principle
• Pauli Exclusion Principle
• actions governed by probability theory
• Wave / Particle duality -
  Complementarity
• This is the current view of QM

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The Newest Paradigm

• A paradigm shift is in progress that we may
  summarize in our last lecture.
• It involves the fundamental makeup of everything
  in the universe.
• We now know of more than 100 types of subatomic
  particles - all have mass and 1/2n spin. We call
  these Fermions.
• Examples include, electrons, protons, neutrons,
  anti-particles, neutrinos,..
• There are also several types of particles with
  no rest mass and 1n spin. We call these Bosons.
• Examples include, photons, gluons,..
• We think the Fermions are made up of quarks.
• Quantum Chromodyamics and the Electroweak force,
  together with Quantum Mechanics, make up the
  current Standard Model for matter.

Important