Download Modern Theory of the Atom

Modern Theory of the Atom
Quantum Mechanical Model
Or
Wave Mechanical Model
Or
Schrodinger’s Model
source
Recap of Bohr Model
• Electrons treated as particles moving in circular
orbits. Specify speed, position, energy.
• Quantization of energy levels is imposed.
• Ground state: electrons close to nucleus
• Electron transitions between energy levels can
occur. Higher energy levels are farther from
nucleus.
– Moving up, electron absorbs energy
– Moving down, electron emits light energy
• Wavelengths of light in H spectrum can be
predicted. Depend on energy difference of 2
levels involved in transition.
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1924: De Broglie
• Proposed that if light can show both
particle and wave behavior, maybe matter
can too.
Every wavelength of light has its
own unique frequency and its own
unique energy.
2 kinds of waves
Traveling wave
• Wave is not confined
to a given space
• Travels from one
location to another
• Interrupted by a
boundary or another
wave
Standing wave
• Confined to a given
space. (Ends pinned.)
• Interference between
incident & reflected
waves.
• At certain frequencies,
certain points seem to
be standing still.
• Other points,
displacement changes
in a regular way.
Traveling Wave #1
• Traveling Wave #2
Guitar string
• Standing wave #1
DeBroglie Electron-Wave
The wavelength
describing an electron
depends on the energy of
the electron.
At certain energies,
electron waves make
standing waves in the
atom.
The wave does not
represent electron path.
Guitar vs. Electron
• In the guitar string, only multiples of halfwavelengths are allowed.
• For an orbiting electron, only whole numbers of
wavelengths allowed.
 = h/mv
Where h=Planck’s constant, m=mass, v=velocity
Modern Theory
• Electron is treated as a wave.
• Cannot specify both position & speed of
electron.
• Can determine probability of locating the
electron in a given region of space.
• Quantized energy levels arise naturally out
of wave treatment.
Heisenberg uncertainty principle
• Fundamentally impossible to know the
velocity and position of a particle at the
same time.
• Impossible to make an observation without
influencing the system.
Bohr Model vs. Modern Theory
•
•
•
•
•
Electron = particle
Orbit
Holds 2n2 electrons
Circular
Each orbit has a
specific energy
• Can find position,
speed
•
•
•
•
Electron = Wave
Orbital
Holds 2 electrons
Not necessarily
circular
• Each orbital has a
specific energy
• Probable location
Orbital – Modern Theory
• Orbital = term used to describe region
where an electron might be.
• Each orbital has a specific energy and a
specific shape. Each holds 2 electrons.
• Described by 4 parameters in the wave
function – quantum numbers = n, l, m, s –
like an address
s orbitals
p orbitals
d orbitals
What can orbitals do for us?
• Physical structure of orbitals explains
– Bonding
– Magnetism
– Size of atoms
– Structure of crystals
Quantum Numbers
• Each electron in an atom has a set of 4
quantum numbers – like an address.
• No two electrons can have all 4 quantum
numbers the same.
– n = principal energy level, n = 1,2,3,4,. . .
– l = type of orbital, l= 0,1,2,3,n-1
– ml = orientation of orbital, ml = -l, …, 0, … +l
– s or ms = electron spin = +1/2 or -1/2
Energy Level Diagram
n: principal quantum number
• Specifies atom’s major (principal) energy
levels
• Has whole number values: 1, 2, 3, 4, …
• Maximum # of electrons in any principal
energy level = 2n2
l = Describes sublevels
• Principal energy levels have energy
sublevels or fine structure or splitting.
• The number of sublevels depends on the
principal energy level.
–
–
–
–
1st principal energy level has 1 sublevel
2nd “
“
“
“ 2“
3rd “
“
“
“ 3“
4th “
“
“
“ 4 “, etc.
Naming sublevels
• Sublevels are labeled s, p, d, or f by
shape
• s orbitals – spherical
• p orbitals – dumbbell shaped
• d & f orbitals have more complex
shapes
m = 3rd quantum number
• Sublevels are
made up of orbitals
• Each kind of
sublevel has a
specific # of
orbitals
Sublevel
# of orbitals
s
1
p
3
d
5
f
7
4th quantum number = s
• Electron spin - 2 possible values
• 4 quantum numbers = address for
each electron.
• No 2 electrons in an atom can have
the same 4 quantum numbers. Thus,
only 2 electrons per orbital.
• Pauli exclusion principle.
Prin.En.Lev Sublevels
1
s
2
s
p
3
s
p
4
d
s
p
d
f
# orbitals/sl Total # elec
1
2
1
2
3
6
1
2
3
6
5
1
3
5
7
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 the lowest
orbital available
• Learn sequence of orbitals from
lowest to highest energy
• Is 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
4f
5f
6f
Sequence of
orbitals:
1s, 2s, 2p, 3s,
3p, 4s, 3d, 4p,
5s, 4d, …
Follow the arrows
Exceptions do
occur: half-filled
orbitals have
extra stability.
Hund’s Rule
• Distribution of electrons in equal energy
orbitals: Spread them out as much as
possible!
Electron Configurations
Compare Bohr & Schrodinger
Frequencies in Chemistry
Electron Configuration & P.T.
Principle
Energy
Levels

n = 1,2,3,4
Holds 2n2
Electrons
max

Hold 2
Sublevels  Orbitals 
Electrons
Max
1st energy level has 1 sublevel : s
2nd “
“ “ 2 sublevels : s and p
3rd “
“ “ 3
“ : s, p, and d
4th “
“ “ 4
“ : s, p, d, and f
s sublevel holds 1 orbital
p sublevel holds 3 orbitals
d sublevel holds 5 orbital
f sublevel holds 7 orbitals