Modern Theory of the Atom: Quantum Mechanical Model

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Modern Theory of the AtomQuantum Mechanical
Model
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Recap of Bohr Model

• electrons
• particles moving in circular orbits with specific
  speed, position, energy
• quantization of energy levels is imposed
• electrons can move between energy levels
• higher energy levels farther from nucleus
• moving up to higher E level electron absorbs
  energy
• moving down to lower E level electron emits
  light energy
• Ground state
• electrons located in lowest possible energy
  levels
• closest can be to nucleus

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1924 De Broglie

• Proposed this Idea
• if light can show both particle and wave
  behavior, maybe matter can too

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2 kinds of waves

• Traveling wave
• wave not confined to given space
• travels from one location to another
• interrupted by hitting
• boundary or another
• wave

• Standing wave
• confined to given space (ends are pinned)
• interference between incident reflected waves
• at certain frequencies
• certain points seem to be standing still
• other points - displacement changes in regular way

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• Traveling Wave

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• Standing wave

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DeBroglie Electron-Wave
wavelength describing electron depends on energy
of electron at certain energies, electron waves
make standing waves in atom wave does not
represent path of electron
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Modern Theory

• electron treated as wave
• cannot specify both position speed of electron
• can determine probability of electrons location
  in given region of space
• Quantized energy levels arise naturally out of
  wave treatment

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Bohr Model vs. Modern Theory

• electron particle
• e- path is orbit
• holds 2n2 electrons
• circular path
• each orbit has specific energy
• can find exact position/ speed

• electron wave
• e path is orbital
• holds 2 electrons
• not necessarily circular
• each orbit has specific energy
• probable location

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Heisenberg uncertainty principle

• Fundamentally impossible to know velocity
  position of particle at same time
• Impossible to make observation without
  influencing system

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What can orbitals do for us?

• Physical structure of orbitals explain
• Bonding
• Magnetism
• Size of atoms
• Structure of crystals

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Orbital Modern Theory

• orbital term describes region where e- might be
  found
• each orbital
• specific energy specific shape
• described by 4 parameters of wave function (like
  an address)
• quantum numbers n, l, m, s

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n principal quantum number

• specifies atoms principal energy levels
• whole number values 1, 2, 3, 4,
• maximum electrons in any principal energy level
  2n2

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l Describes sublevels

• principal energy levels have sublevels
• sublevels depends on principal energy level
• 1st principal energy level has 1 sublevel
• 2nd
  2
• 3rd 3
  
• 4Th 4
  , etc.

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Naming sublevels

• Sublevels are labeled by shapes
• s, p, d, f
• s orbitals spherical
• p orbitals dumbbell shaped
• d f orbitals more complex shapes

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m 3rd quantum number

• sublevels made up of orbitals
• each sublevel has specific of orbitals

sublevel of orbitals
s 1
p 3
d 5
f 7
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s orbital shapes
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p orbital shapes
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d orbital shapes
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f orbital shapes
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4th quantum number s

• e- spin 2 possible values
• clockwise and counter clockwise

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Address for each electron

• 4 quantum numbers
• no 2 e- can
• occupy the same space in atom
• can have same 4 quantum numbers
• therefore only 2 electrons per orbital
• (Pauli exclusion principle)

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principle energy level sublevels orbitals total e-
1 s 1 2
2 s 1 2
p 3 6
3 s 1 2
p 3 6
d 5 10
4 s 1 2
p 3 6
d 5 10
f 7 14
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3rd principal energy level, 3 sublevels
2nd principal energy level, 2 sublevels s p
1st principal energy level, 1 sublevel s
Each box represents an orbital and holds 2
electrons
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Order of fill Aufbau Principle

• each electron occupies lowest energy orbital
  available
• learn sequence of orbitals from lowest to highest
  energy
• some overlap between sublevels of different
  principal energy levels

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Aufbau Principle

• Follow arrows
• sequence of orbitals
• 1s, 2s, 2p, 3s, 3p, 4s,
  
• 3d, 4p, 5s, 4d,
• exceptions do occur
  - half-filled orbitals
  
• have extra stability
• - magic is 8

• 1s
• 2s 2p
• 3s 3p 3d
• 4s 4p 4d 4f
• 5s 5p 5d 5f
• 6s 6p 6d 6f
• 7s 7p

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Electron Configurations
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Compare Bohr Schrodinger
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Frequencies in Chemistry
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Electron Configuration PT
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