Download Modern Theory of the Atom: Quantum Mechanical Model

Modern Theory of the Atom:
Quantum Mechanical Model
Recap of Bohr Model
• Electrons are particles moving in circular orbits
– Specific speed, position, energy
• Quantization of energy levels is imposed
• Ground state: electrons closest to nucleus
• 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
1924: De Broglie
• Proposed:
– if light can show both particle and wave behavior,
maybe matter can too
2 kinds of waves
Traveling wave
Standing wave
• Wave not confined to • Confined to given space
given space
(ends are pinned)
• Travels from one
location to another
• Interference between
incident & reflected
waves
• Interrupted by
boundary or another
wave
• At certain frequencies:
– certain points seem to be
standing still
– Other points - displacement
changes in regular way
Traveling Wave #1
• Traveling Wave #2
Guitar string
• Standing wave #1
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
electron path
Modern Theory
• Electron treated as wave
– Cannot specify both position & speed of electron
– Can determine probability of locating electron in
given region of space
• Quantized energy levels arise naturally out of
wave treatment
Bohr Model vs. Modern Theory
•
•
•
•
•
Electron = particle
Orbit
Holds 2n2 electrons
Circular
Each orbit has
specific energy
• Can find exact
position/ speed
•
•
•
•
•
Electron = Wave
Orbital
Holds 2 electrons
Not necessarily circular
Each orbit has specific
energy
• Probable location
Orbital – Modern Theory
• Orbital = term used to describe region
where electron might be
• Each orbital has specific energy and
specific shape
• Described by 4 parameters of wave
function (like an address):
– quantum numbers = n, l, m, s
What can orbitals do for us?
• Physical structure of orbitals explain:
– Bonding
– Magnetism
– Size of atoms
– Structure of crystals
Heisenberg uncertainty principle
• Fundamentally impossible to know
velocity and position of particle at same
time
• Impossible to make observation without
influencing system
n: principal quantum number
• Specifies atom’s principal energy levels
• whole number values: 1, 2, 3, 4, …
• Maximum # electrons in any principal
energy level = 2n2
l = Describes sublevels
• Principal energy levels have sublevels
• # sublevels depends on principal energy
level
–
–
–
–
1st principal energy level has
2nd “
“
“
“
3rd “
“
“
“
4Th “
“
“
“
1 sublevel
2
“
3
“
4
“ , etc.
Naming sublevels
• Sublevels are labeled by shapes:
– s, p, d, f
• s orbitals: spherical
• p orbitals: dumbbell shaped
• d & f orbitals: more complex shapes
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
s orbitals
p orbitals
d orbitals
4th quantum number = s
• Electron spin: 2 possible values
• 4 quantum numbers = address for each
electron
• No 2 electrons in atom can have same 4
quantum numbers
– only 2 electrons per orbital
= Pauli exclusion principle
Prin.E Level Sublevels
1
s
2
s
p
3
s
p
d
4
s
p
d
f
# orbitals
1
1
3
1
3
5
1
3
5
7
Total # elec
2
2
6
2
6
10
2
6
10
14
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
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
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
Sequence of orbitals:
1s, 2s, 2p, 3s, 3p, 4s, 3d,
4p, 5s, 4d, …
4f
5f
6f
Follow arrows
Exceptions do occur:
- half-filled orbitals
have extra stability
Electron Configurations
Compare Bohr & Schrodinger
Frequencies in Chemistry
Electron Configuration & PT
Principle
Energy
Levels


n = 1,2,3,4
Sublevels

hold 2
Orbitals  electrons max
1st E level has 1 sublevel :
2nd “
“ 2 sublevels :
3rd “
“ 3
“
:
4th “
“ 4
“
:
holds 2n2
electrons max
s sublevel holds 1 orbital
p sublevel holds 3 orbitals
d sublevel holds 5 orbital
f sublevel holds 7 orbitals
s
s and p
s, p, and d
s, p, d, and f