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
energy levels possess specific quantum of energy

• electrons can move between energy levels
• higher energy levels farther from nucleus
• e- moving up to higher E level electron absorbs
  energy
• e- 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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DeBroglie Electron-Wave
Proposed this Idea if light can show both
particle and wave behavior, maybe
matter can too
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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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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Transverse (ocean)
Longitudinal (compressed/sound)
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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
• cannot specify both position speed of electron
• can only determine probability of electrons
  location in given region of space

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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
• structure of orbitals explain
• bonding, magnetism, atom size, crystal structure

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n principal quantum number

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

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l describes sublevels

• sublevels are labelled by shape
• s, p, d, f

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• s orbitals
• spherical

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• p orbitals dumbbell shaped

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d orbitals complex shapes
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f orbitals complex shapes too
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Sublevels
1st principal energy level
s (1 sublevel) 2nd level
s,p (2 sublevels) 3rd
level
s,p,d (3 sublevels) 4th level
s,p,d,f (4
sublevels)
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m 3rd quantum number (orbitals)

• each sublevel contains 1 or more orbitals
• each orbital holds a max of 2 electrons

• s has 1 orbital
• p has 3 orbitals
• d has 5 orbitals
• f has 7 orbitals

1st PEL s (1 sublevel) 1 orbital (__
electrons) 2nd PEL s,p (2 sublevels) 4
orbitals (__ e-) 3rd PEL s,p,d (3 sublevels)
9 orbitals (___ e-) 4th PEL s,p,d,f (4
sublevels) 16 orbitals (___ e-)
2
8
18
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4th quantum number s

• e- spin 2 possible values
• clockwise and counter clockwise
• Illustrated by arrows with opposite directions

?
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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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Memorize

• s p d f
• 1 3 5 7
• 2e- 6e- 10e- 14e-

sublevels
of orbitals
max of electrons
each orbital holds 2 e-
s
p
d
f
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electron configurations

• add e- to atoms so that e- are in lowest energy
  levels most stable or ground state
  configuration
• start with 1s, then work upward in order of
  increasing energy
• use Aufbau rule.

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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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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 7d 7f

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• 1s2
• 2s2 2p6
• 3s2 3p6 3d10
• 4s2 4p6 4d10 4f14
• 5s2 5p6 5d10 5f14
• 6s2 6p6 6d10
• 7s2 7p6 7d10

He C Mg Zn

• 1s2

1s22s22p2

• 1s22s22p63s2

1s22s22p63s23p6 4s23d10
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from these modern configurations, we can figure
out Bohr Configurations All you have to do is add
up the electrons in each shell (energy level)
He C Mg Zn

• 1s2

1 2 2
1s22s22p2
1 2 2 22 2 4

• 1s22s22p63s2

1 2 2 26 3 2 2 8 2
1s22s22p63s23p64s23d10
1 2 2 26 3 2610 42 2 8 18
2
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Hunds Rule

• most e- with same spin, so if more than one same
  orbital
• e- fill orbitals one at time before pairing up

• 1s2 2s2 2p4

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Which element? How many unpaired e-? How many
principal energy levels occupied? How many
principal energy levels are fully occupied? How
many sublevels contain e-? How many sublevels
full? How many orbitals contain e-?
Boron
1
2
1
3
2
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