QUANTUM MECHANICS

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QUANTUM MECHANICS

Predicting the most probable position of an
electron.
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BOHRs MODEL

• Cannot successfully predict line spectra for any
  other element besides hydrogen.
• Electrons must not be moving in circular orbits
  at set distances from the nucleus.

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BACK TO THE 3 ?s ABOUT e-

• How are the electrons moving?
• As waves
• NOT in orbits

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Where are they located?

• In ORBITALS
• Areas of high probability based on the wave
  motion and energy of an electron
• Every orbital has an address given by a set of
  4 QUANTUM NUMBERS.

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How much energy do they have?

• Determined by the n value (like Bohr).
• Higher n higher energy level more energy
  further from the nucleus.

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SCIENTISTS CONTRIBUTING to QUANTUM THEORY

• DeBROGLIE
• 1924
• French
• Proposed the particle wave duality to describe
  electron motion.

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HEISENBERG

• 1927
• Proposed the Heisenberg uncertainty principle.
• The more you know about the e- position, the less
  you know about its velocity.

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SCHRODINGER

• 1926
• Austrian
• Proposed a complex mathematical relationship to
  predict where an e- is located.

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SCHRODINGER EQUATION

• A calculus problem.
• We will deal only with the answers.
• 4 answers to the Schrodinger equation are known
  as QUANTUM NUMBERS.

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4 QUANTUM NUMBERS

• n
• l
• ml
• ms

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1. Prinicpal Quantum Number

• Symbol n
• Tells what energy level the electron is in.
• Possible values
• n 1 to infinity

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2. Orbital Quantum Number

• Symbol l (small cursive l)
• Tells about the shape of the orbital where the
  electron is housed.
• Possible values 0 to (n-1)

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Orbital Quantum Number and Shapes

• L 0 s orbital spherical
• L 1 p orbital peanut shaped
• L 2 d orbital daisy
  (cloverleaf)
• L 3 f orbital flower

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s orbital
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p orbitals
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d orbitals
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3. Magnetic Quantum Number

• Symbol ml
• Tells about the orientation of the orbital around
  the nucleus (around the axis).
• Possible values
• - l to l including 0

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Values of ml

• s orbital 1 orientation, 1 ml value (0)
• p orbital 3 orientations, 3 ml values (-1, 0,
  1)
• d orbital 5 orientations, 5 ml values
  (-2,-1,0,1,2)

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4. Spin quantum number

• Symbol ms
• Tells the direction of electron spin within an
  orbital.
• Possible values 1/2 or 1/2
• 1/2 clockwise spin
• - 1/2 counter clockwise spin

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RULES for QUANTUM NUMBERS and ELECTRONS

• Pauli Exclusion Principle
• Every electron in an atom must have a unique set
  of quantum numbers.
• Electrons in the same orbital must have opposite
  spins.

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ENERGY LEVEL DIAGRAM

• A way to keep track of electrons.
• Includes lines or boxes that represent orbitals.
• Also shows orbital types and energy levels.
• Once filled, it is possible to find the quantum
  number set for any electron in the atom.

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RULES FOR FILLING AN ENERGY LEVEL DIAGRAM

• AUFBAU PRINCIPLE
• Meaning Building up
• Electrons must be filled in from the lowest
  energy level to the highest.
• Do not move to the next sublevel until the one
  below has been completely filled.

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HUNDS RULE

• Electrons will fill an unoccupied orbital within
  a sublevel before pairing up with another
  electron in an orbital.
• This minimizes electron repulsion and leads to
  stability.

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OCTET RULE

• Atoms become stable when their outermost energy
  level contains 8 electrons.
• Noble gases have a full OCTET.
• The outermost electrons are called VALENCE
  ELECTRONS.