8.5 Two New Ideas
8.5 Two New Ideas
8-5 Two ideas leading to a new quantum
mechanics
What about matter?
Louis de Broglie (1892–1989) French
Central idea:
Einstein’s relativity
E=mc2
Louis de Broglie
Matter & energy
are related
Werner Heisenberg
Louis de Broglie
8.5 Two New Ideas
de Broglie started with Einstein’s eqn.
Then he used Planck’s relationship
E = hν
E = mc 2
2
mc = hν
Recall linear momentum: p = mu
p = mc =
8.5 Two New Ideas
Next he used the eqn. c = λν
hν
c
hν
p = mc =
λν
p = mc =
hν
c
8.5 Two New Ideas
de Broglie arrived at the following eqn.
p = mc =
h
h
or λ =
mc
λ
This is valid for light…
What about matter?
Note: Photons have zero “rest” mass but will
have a relativistic mass and momentum
8.5 Two New Ideas
8.5 Two New Ideas
de Broglie equation predicts that matter
What is the wavelength of an e- traveling at
should have waves
1.00 x 107 m.s-1
h
h
p = mu =
or λ =
mu
λ
λ=
h
mu
λ=
6.626x10 -34 J s
= 7.27x10-11 m or 72.7 pm
9.109x10 -31 kg ⋅1.00x10 7 m s -1
[Note: 1.0 J = 1.0 kg.m2.s-2]
de Broglie’s equation
Einstein helped him get his Ph.D. thesis
accepted!
8.5 Two New Ideas
8.5 Two New Ideas
What is the wavelength of a baseball
What is the wavelength of a baseball
traveling at 44 m/s (mass = 0.145 kg)
traveling at 44 m/s (mass = 0.145 kg)
λ=
h
mu
h
[Note: 1.0 J = 1.0 kg.m2.s-2]
mu
6.626x10 -34 J s
λ=
= 1.04x10 -34 m
0.145 kg ⋅ 44.0 m s -1
λ=
8.5 Two New Ideas
8.5 Two New Ideas
The Uncertainty Principle
Δx ⋅ Δp ≥
Uncertainty
in position
The Uncertainty Principle: Implications
h
4π
Uncertainty
in momentum
h = Planck’s constant
Uncertainties are standard deviations
Δx ⋅ Δp ≥
h
4π
Limits to what we can know
Causality replaced with indeterminacy
Einstein was deeply bothered by this
as was Wien!!!!
8.5 Two New Ideas
8.5 Two New Ideas
Heisenberg’s γ-Ray Microscope
Heisenberg’s γ-Ray Microscope
Thought experiment: Gedanken
Thought experiment: Gedanken
Microscope resolution
is limited by λ of light
To measure position
of an electron…Need
very short wavelength
light, i.e., γ-rays
-
Amoeba
8.5 Two New Ideas
Electron
position?
8.5 Two New Ideas
Heisenberg’s γ-Ray Microscope
Heisenberg’s γ-Ray Microscope
Thought experiment: Gedanken
Thought experiment: Gedanken
γ-ray ν = 1022 s-1
Eγ = hν = 6.626 x 10-34 J s .1022 s-1
Eγ = 6.626 x 10-12 J
-
Electron
position?
8.5 Two New Ideas
But…easily ionize the eEIE = 2.179 x 10-18 J
Eγ = 6.626 x 10-12 J
-
Electron
position?
8.5 Two New Ideas
Heisenberg’s γ-Ray Microscope
Heisenberg’s γ-Ray Microscope
Thought experiment: Gedanken
Thought experiment: Gedanken
But…easily ionize the eEIE = 2.179 x 10-18 J
Eγ = 6.626 x 10-12 J
- Excess energy
goes into kinetic energy
Changes the momentum
Electron takes off!
-
8.5 Two New Ideas
Let’s do an uncertainty calculation
What is the uncertainty in the position of a
baseball (m = 0.145 kg), if its velocity is
measured with an uncertainty of 0.11 m.s-1?
9.5 Two New Ideas
8.5 Two New Ideas
Δx = ? Δu = 0.11 m.s-1 m = 0.145 kg
h
h
Δx ⋅ Δp ≥
so Δx ≥
4π
4πΔp
Heisenberg: Led Nazi effort to build A-bomb
p = mu so Δp = mΔu = 0.145kg ⋅ 0.11 m s -1
Δp = 0.016 kg m s -1
Δx ≥
h
6.626x10-34 Js
=
= 3.3x10 -33 m
4πΔp 4π ⋅ 0.016 kg m s -1
Uncertainty:
The Life & Science of
Werner Heisenberg
by David C. Cassidy
Very low uncertainty
Werner Heisenberg and Niel Bohr
Moe Berg
8.5 Two New Ideas
Copenhagen: A play…Bohr & Heisenberg
Copenhagen
by Michael Frayn
8.5 Two New Ideas
8.5 Two New Ideas
Need Measurement to know position
Need Measurement to know position
But act of measurement Changes System
But act of measurement Changes System
Fundamental quantum uncertainty
Fundamental quantum uncertainty
Can no longer talk about defined orbits
Can no longer talk about defined orbits
8.5 Two New Ideas
8.5 Two New Ideas
Copenhagen Interpretation Quantum Mech.
Bohr: Danish
Probabilities and the act of measurement
Founded Niels Bohr Institute
University of Copenhagen
Bohr Institute
8.5 Two New Ideas
8.5 Two New Ideas
Bohr mentored many scientists
Einstein & Bohr debated QM
Copenhagen interpretation of QM
Einstein: deterministic. Bohr: probability
Bohr
Heisenberg
Pauli
Bohr Institute
8.5 Two New Ideas
Philosophical Battle Decades Long
"Not often in life has a man given me so much
happiness by his mere presence as you have
done," Einstein wrote to Bohr
8.5 Two New Ideas
Nice book on current state of affairs
"God does not play dice," Einstein
"The Lord is subtle
but not malicious.“ Einstein
At one point Bohr retorted…
"Einstein, stop telling God
what to do!"
8-6 Wave Mechanics
8-6 Wave Mechanics
Taming the Atom
by
Han Christian von Baeyer
8-6 Wave Mechanics
Classical Waves
Describe by wave equation: Ψ(r,t)
Function of space & time
Solution to a type of differential eqn.
Standing waves in a string
8-6 Wave Mechanics
8-6 Wave Mechanics
1D Wave Equation
1D Wave Equation
Amplitude
Amplitude
ψ(x, t ) = A e
i ( kx - 2πν t )
ψ(x, t ) = A e
i = −1
2π
k=
λ
i = −1
2π
k=
λ
8-6 Wave Mechanics
8-6 Wave Mechanics
1D Wave Equation
Amplitude
Spatial
i ( kx - 2πν t )
1D Wave Equation
Spatial
Temporal
i ( kx - 2πν t )
Amplitude
Spatial
Temporal
i ( kx - 2πν t )
ψ(x, t ) = A e
ψ(x, t ) = A e
i = −1
2π
k=
λ
i = −1
2π
k=
λ
Wave vector
Standing Waves
Wave equation
completely specifies
a classical wave
You don’t have to
memorize this equation!
Standing Waves
Standing Waves
Standing Waves
For some interesting video clips on standing
waves take a look at the following website:
http://video.google.ca/videosearch?hl=en&q=
Standing%20waves&um=1&ie=UTF-8&sa
=N&tab=wv#
8-6 Wave Mechanics
8-6 Wave Mechanics
Standing Waves on a String
Standing Waves on a String
L
L
λ/2
n=1
2λ/2
n=2
Oscillating
sections
3λ/2
n=3
Constructive interference if L=nλ/2
8-6 Wave Mechanics
Standing Waves on a String
8-6 Wave Mechanics
Standing Waves on a String
L
Nodes
No oscillations
#Nodes=n+1
L
n=2
3 Nodes
#Nodes=n+1
8-6 Wave Mechanics
8-6 Wave Mechanics
Standing Waves: String Instruments
Standing Waves on a String
e- as a standing wave
L=nλ/2
constructive
interference
n=1,2,3,…
Violin
n not integer
destructive
interference
2D standing waves
on guitar body
8-6 Wave Mechanics
8-6 Wave Mechanics
de Broglie equation: matter a wave
de Broglie equation: matter as a wave
Problem: Devise a wave equation for
Problem: Devise a wave equation for
electron
electron
Erwin Schrödinger solved it
Erwin Schrödinger solved it: Multi-tasker!
Erwin Schrödinger
Austrian
1887-1961
Nobel Prize Physics 1933
8-6 Wave Mechanics
Erwin Schrödinger
Austrian
1887-1961
Nobel Prize Physics 1933
8-6 Wave Mechanics
Schrödinger Wave Equation
Schrödinger Wave Equation
Wave function of e-
HΨ = EΨ
Hamiltonian
Energy
HΨ = EΨ
Hamiltonian: Kinetic energy part &
potential energy part
8-6 Wave Mechanics
It gets really complicated
HΨ = EΨ
∂Ψ Time-dependent equation
HΨ = ih
∂t
Time-independent equation
8-6 Wave Mechanics
It gets really complicated
Hamiltonian for H atom
e2
h2 2
∇ H=2m e
4πε o r
⎧ ∂2
∂2
∂2 ⎫
where ∇ = ⎨ 2 + 2 + 2 ⎬
∂y
∂z ⎭
⎩ ∂x
2
Are we responsible for the Schrödinger Eqn.?
No!
8-6 Wave Mechanics
Quotation from Richard P. Feynman
"Where did we get that [Schrödinger's equation]
from? It's not possible to derive it
from anything you know.
It came out of the mind of Schrödinger."
--Richard P. Feynman
8-6 Wave Mechanics
Wave functions are solutions to Eqn
Wave functions: radial & angular parts
z
Ψ(r,θ , φ )
θ
radial
variable
8-6 Wave Mechanics
The important point to remember…
Wavefunction squared = probability
angular
variables
(x,y,z)=(r,θ,φ)
r
φ
y
x
Spherical polar coordinates
8-6 Wave Mechanics
Max Born: Probability Concept
2
Ψ(r,θ , φ ) = e - Probability
2
Ψ(r,θ , φ ) = e - Probability
Probability of finding the electron in space
Determines “shapes” of electron orbitals
Max Born: Physics Nobel 1954
1882-1970
8-6 Wave Mechanics
8-6 Wave Mechanics
Electron Charge Density Probability
2
Ψ(r,θ , φ ) = e Probability
-
Can only solve Schrödinger eqn. for
special cases
“Particle in a box”
+
Bohr: Electron Orbits
Classical Trajectories
-
Hydrogen atom: H
Hydrogen molecule: H2
Electron orbital
3D space in which you
will find the electron with
a defined probability
8-6 Wave Mechanics
Can only solve Schrödinger eqn. for
special cases
“Particle in a box”
Hydrogen atom: H
Hydrogen molecule: H2
Hydrogen-like species, e.g., He+
8.7 Quantum Numbers
8.7 Quantum Numbers
8-7 Quantum Numbers & Electron Orbitals
Quantum Numbers
n
l
ml
ms
principal quantum number
angular momentum quantum number
magnetic quantum number
spin quantum number
8.7 Quantum Numbers
Goal: Determine Electronic Configurations
Principal Quantum Number: n
Need to Assign quantum numbers
n can be a non-zero positive integer
Specific rules for quantum numbers
n = Principal Quantum Number
n = 1, 2, 3, 4, ...
8.7 Quantum Numbers
8.7 Quantum Numbers
n is related to the energy level: principal shell
“orbital”
Higher n=5
n=4
Energy n=3
n=2
l Orbital Angular Momentum Quantum No.
l is zero or positive integer up to n-1
l = Angular Momentum Quantum No.
l = 0, 1, 2, 3,..., n - 1
E
Lower
Energy
n=1
8.7 Quantum Numbers
l is related to the sublevel or subshell (“orbital”)
8.7 Quantum Numbers
l is related to the sublevel or subshell
l=0
l =1
l=2
l=3
8.7 Quantum Numbers
ml Magnetic Quantum Number
s subshell
p subshell
d subshell
f subshell
8.7 Quantum Numbers
ml determines the no. of electronic orbitals
ml is an integer from -l to +l
m l = Magnetic Quantum Number
m l = - l, - l + 1, - l + 2,..., 0, 1, 2, ..., l - 1, l
2l + 1 values of ml
l =0
ml = 0
s orbital
One s orbital
8.7 Quantum Numbers
8.7 Quantum Numbers
ml determines the no. of electronic orbitals
p orbital
l =1
Three p orbitals
m l = - 1, 0,+1
8.7 Quantum Numbers
d orbital
l =2
m l = - 2,-1, 0,+1,+2
8.7 Quantum Numbers
ml determines the no. of electronic orbitals
d orbital
l =2
m l = - 2,-1, 0,+1,+2
ml determines the no. of electronic orbitals
Five d orbitals
8.7 Quantum Numbers
ml determines the no. of electronic orbitals
l = 3 f orbital
m l = - 3,-2,-1, 0,+1,+2,+3
Seven f orbitals
8.7 Quantum Numbers
Orbitals have well defined shapes
Shapes of
the probability
clouds for the
electrons
ms Spin Quantum Number for an electron
ms = +
1
1
or 2
2
Spin Up or Spin Down
8.7 Quantum Numbers
8.7 Quantum Numbers
H atom: orbitals of the same n have same E
Can an orbital have the following quantum
“Degenerate” orbitals (have identical energy)
Degenerate Orbitals for Hydrogen
numbers: n=3, l=0, ml=0?
Same
energy
Note! This is only
true for H atom
Not true for
multi e- atoms
Fig 8.23
8.7 Quantum Numbers
What type of orbital corresponds to the
quantum numbers n=3, l=1, ml=1?
n and l
Determine the
Orbital type
l = 1 → p orbital
3p orbital
n
Orbital type
8.9 Pauli Exclusion Principle
No two electrons can have exactly the same
set of four quantum numbers (Pauli)
n = 3 Positive integer...OK
l = 0 l can range from 0 to n - 1...OK
m l = 0 m l can range from - l to l...OK
These are valid quantum nos. for an orbital
8.9 Electron Spin: 4th Quantum Number
ms Spin Quantum Number for an electron
Important
point…
This means
two e- in one
orbital must
have different
ms values
ms = +
1
1
or 2
2
Spin Up or Spin Down
Maximum of two electrons per orbital
Their spins must be opposite: “paired”
8.9 Electron Spin: 4th Quantum Number
Spinning electron generates magnetic field
Spin Up
If n, l, and ml are the same, then ms must
differ
ms can be +1/2 or -1/2…so maximum two
electrons per orbital
Note: If n, l, and ml are the same, then the
electrons are in the same orbital and must
differ in ms value
Spin Down
8.9 Electron Spin: 4th Quantum Number
Spinning electron generates magnetic field
8.9 Electron Spin: 4th Quantum Number
Spinning Electron generates Magnetic Field
Spin Up
Spin Up
Spin Down
Spin Down
For “paired” electrons in an orbital…
magnetic fields cancel
For “unpaired” single electron
In an orbital…Net mag. field
8.9 Electron Spin: 4th Quantum Number
SternStern-Gerlach Experiment…
Experiment…more details
Can detect magnetic field from unpaired
or
Beam of neutral (not charged) Ag atoms from a vaporized Ag source is directed
through an external magnetic field (not an electrical field)
electron spins
The effect is observed due to the magnetic field of the lone unpaired electron
spin in the neutral silver atoms as they pass through the external magnetic field
The lone unpaired electron in each individual silver atom can be either spin up or
N
spin down which accounts for the observation of two spots deflected either up or
down where the silver atoms strike the detector
S
Note this is not a charge effect…it is due entirely to the electron spin and the
presence of the external magnetic field
Stern-Gerlach Expt., Univ. of Frankfurt, 1922
Silver (Ag) atoms with unpaired e- of different
spin state were deflected in opposite
directions by magnetic field
Otto Stern
Walther Gerlach
Ag atom with unpaired
eAg
Ag
Ag
Beam of Ag atoms (neutral charge)
Ag
Ag
Ag
Ag
Ag
N
Ag
Ag
Ag
S
8.9 Electron Spin: 4th Quantum Number
Electronic structure: must specify all four
quantum numbers
http://www.aip.org/pt/vol-56/iss-12/p53.html
Ag
Particle
Detector
8.9 Electron Spin: 4th Quantum Number
8.9 Electron Spin: 4th Quantum Number
Electronic structure: must specify all four
Electronic structure: must specify all four
quantum numbers
quantum numbers
e.g. n=3, l=1,ml=0, ms=1/2
e.g. n=3, l=1,ml=0, ms=1/2
The
Chemist’s
notation
8.9 Electron Spin: 4th Quantum Number
l = 1 → p orbital
3p1
8.8 Orbitals of the Hydrogen Atom
Electronic structure: must specify all four
8-8 Orbitals of the Hydrogen Atom
quantum numbers
e.g. n=4, l=2, ml =-1, ms=1/2
And n=4, l=2, ml =-2, ms=1/2
The
Chemist’s
notation
l = 2 → d orbital
4d 2
Two electrons
n
Orbital type
Note: This notation gives the electron
configuration for the orbital
8.8 Orbitals of the Hydrogen Atom
8.8 Orbitals of the Hydrogen Atom
You don’t need to know Orbital Functions
l: Angular Momentum Quantum No. & Orbital
Lectures will cover what you need to know
Type (e.g. s, p, d, f orbital)
1 ⎛Z⎞
⎜ ⎟
R(2s) =
2 2 ⎜⎝ a o ⎟⎠
3/ 2
(2 - σ )e
Orbitals have different shapes of e- σ2
Probability clouds: Where am I likely to find
1/ 2
⎛ 3 ⎞
Y(p x ) = ⎜ ⎟
⎝ 4π ⎠
probability clouds
sin θcos φ
the electron within the atom?
8.8 Orbitals of the Hydrogen Atom
l =0
ml = 0
s orbital
8.8 Orbitals of the Hydrogen Atom
s orbital
One s orbital
2
Ψ(r,θ , φ ) = e Probability
-
Ψ(r)2 e- probability at distance r from the nucleus
s Oobital
Ψ(r)2 e- probability at distance r from the nucleus
Ψ2 1s orbital
r
Distance from
nucleus
Ψ2 3s
orbital
Ψ2 2s orbital
r
r
Nodes
Zero probability
of finding e-
Nodes
8.8 Orbitals of the Hydrogen Atom
8.8 Orbitals of the Hydrogen Atom
s orbitals are spherical in shape
s orbitals are spherical in shape
n>1, s orbital will have nodes (e.g. 3s orbital)
Note: Orbital Size is proportional to n
More likely to find 1s e- close to nucleus
n>1, s orbital will have nodes (e.g. 3s orbital)
Note: Orbital Size is proportional to n
More likely to find 1s e- close to nucleus
2s
1s
3s
2s
1s
Nodes
3s
Node: Ψ changes sign…n-1 nodes for s orbital
8.8 Orbitals of the Hydrogen Atom (End)
p orbitals
p orbital
l =1
Three p orbitals
m l = - 1, 0,+1
8.8 Orbitals of the Hydrogen Atom
p orbitals
p orbital
l =1
Three p orbitals
m l = - 1, 0,+1
Nodal planes
Ψ(r)2 2p orbital
r
Distance from
nucleus
“Dumbbell” shape for p orbitals
px orbital
py orbital
pz orbital
p orbital shape depends on radial & angular
Number of nodal planes =
l
8.8 Orbitals of the Hydrogen Atom
8.8 Orbitals of the Hydrogen Atom
d orbitals
d orbital
l =2
m l = - 2,-1, 0,+1,+2
dxy
dxz
dyz
Five d orbitals
dx2 -y2
dz 2
Nodes : ψ = 0 so ψ changes sign
Radial nodes = n – l – 1
Nodal planes or angular nodes = l
3p orbital: n=3 and l =1
3-1-1 = 1 Radial node 1 Nodal plane
r
Number of nodal planes=
Nodal planes
l
8.8 Orbitals of the Hydrogen Atom
Different electron orbitals can overlap
Each electron “obeys” its own ψ
3p orbital
3p orbital e- density
8.8 Orbitals of the Hydrogen Atom
f orbitals
l = 3 f orbital
m l = - 3,-2,-1, 0,+1,+2,+3
3s orbital &
3p orbital
http://itl.chem.ufl.edu/ao_pict/ao_pict.html
8.8 Orbitals of the Hydrogen Atom
s orbitals, shape from radial only
p, d, & f orbitals, shape from radial & angular
2
Ψ(r,θ , φ ) = e - Probability
radial
variable
angular
Orbital “shape”
variables
plays an important role
in bonding between atoms
…covered later in the course
8.10 Multielectron Atoms
8-10 Multielectron Atoms
Seven f orbitals
8.10 Multielectron Atoms
Hydrogen Atom: Single Electron
8.10 Multielectron Atoms
Hydrogen Atom: Single Electron
1
H
1.0094
Z=1
Z=p
p=eH has
one
electron
8.10 Multielectron Atoms
All other atoms have more than one electron
8.10 Multielectron Atoms
Must consider several new effects for
multielectron atoms
Greater nuclear charge Z>1…more protons
Repulsion between negatively charged
electrons in orbitals
“Screening” of outer shell e- from the full
attraction of the nucleus by inner shell e-
8.10 Multielectron Atoms
8.10 Multielectron Atoms
H atom orbitals same n…same Energy
Multi e- same n…different energies
Degenerate Orbitals for Hydrogen
Due to charge attraction & repulsion
Same
energy
Note! This is only
true for H atom
e-
e-
Repulsion between electrons
e-
p+
Attraction between electrons & protons
8.10 Multielectron Atoms
8.10 Multielectron Atoms
We must consider the location of
e-
relative
We must consider the location of e- relative
to the nucleus and nuclear charge (Z)
to the nucleus and nuclear charge (Z)
Recall that electron orbitals differ in size (n)
Recall that electron orbitals differ in shape
(s,p,d,f orbitals)
3s
2s
1s
Orbital size &
shape will affect
“screening” abilities
of its electrons
“Screening”…how well inner eblock outer e- from attractive force of nucleus
90% probability cloud
8.10 Multielectron Atoms
8.10 Multielectron Atoms
Electron screening
Wave Function: Radial & Angular Functions
e-
Outer
experience
a lower
effective
nuclear
charge
Inner shell (orbital)
electrons
screen
outer efrom full
attraction of
the nucleus
Ψ(r, θ, φ) = R(r) Y(θ, φ)
Wave function
Radial function
Angular function
Zeff < Z
8.10 Multielectron Atoms
8.10 Multielectron Atoms
Ψ2 is the probability of finding e- at a single
P(r)…the radial distribution function
point in space
P(r) is the total integrated probability for a
2
Ψ(r, θ, φ) = e Probability at (r, θ, φ)
-
spherical shell at distance r from the nucleus
r
(r,θ,φ)
Ψ2
= probability at one point
P(r) = 4πr 2 ⋅ R 2 (r )
Radial wave function
Note: P(r) = 0 for r = 0
8.10 Multielectron Atoms
8.10 Multielectron Atoms
Plots of P(r) vs. r/ao
Most probable radius ao = 52.9 pm “Bohr Radius”
2s
1s
2p
s orbitals are better at screening than p & d
Screening s orbitals > p orbitals > d orbitals
Strength
s Zeff > p Zeff > d Zeff
(for same n)
Orbital energy depends on n and Zeff
3p
3s
3d
s orbitals have greater penetration
Note: e- in s orbitals can get closer to nucleus
8.10 Multielectron Atoms
2
Z eff
En ∝ - 2
n
In general, for the same value of n
s orbitals lie at more negative E than p, than d
8.11 Electron Configurations
Note: for multielectron atoms, orbitals with
the same n are not degenerate
8-11 Electron Configurations
Less negative…higher energy
E
3p
3d
3s
More negative…lower energy
8.11 Electron Configurations
8.11 Electron Configurations
Chemical Properties: Electron Configurations
Rules: Building up e- configurations for Z>1
Valence (outer) Electrons are most Important
1. Electrons occupy orbitals in a way that
Goal: Determine
e-
configurations for atoms
Important to understanding chemical bonding
minimizes the energy of the atom
2. No two e- in an atom can have the same
set of four quantum numbers (Pauli
Exclusion Principle)
8.11 Electron Configurations
Rules: Building up
e-
8.11 Electron Configurations
Rules: Building up e- configurations for Z>1
configurations for Z>1
3. Electrons will occupy orbitals of the same
3. Electrons will occupy orbitals of the same
in
energy singly (i.e. unpaired). The single e- in
these degenerate orbitals will have the same
these degenerate orbitals will have the same
spin state (Hund’s Rule)
spin state (Hund’s Rule).
energy singly (i.e., unpaired). The single
e-
4. Once orbitals of the same energy are filled
singly, additional electrons can be added
with the opposite spin.
8.11 Electron Configurations
8.11 Electron Configurations
Notations for Electron Configurations: e.g., C
C Z=6 so 6e- to fill
spdf notation (condensed)
C 1s 2 2s 2 2p 2
n
spdf notation (expanded)
Orbital diagram
Orbital
type
No. of
electrons
C 1s 2 2s 2 2p1x 2p1y
Rule 1. Minimize the overall Energy
Fill lower Energy orbitals first
Order for
filling eorbitals
2s
l=0 l=1 l=2 l=3
Arrows indicate filling order
You must
know this
table
6
7
2p
8.11 Electron Configurations
1
2
3
4
5
C
1s
n
8.11 Electron Configurations
Rule 2. Pauli Exclusion Principle
Rule 3. Fill degenerate orbitals singly first
Implication: Orbital can contain a maximum
This minimizes electron-electron repulsion
of two electrons (they must be paired…i.e.
have opposite spins)
Austrian
1900-1958
Physics Nobel
1945
Wolfgang Pauli
Pauli was
a walking
lab disaster!
E
2p
2s
8.11 Electron Configurations
8.11 Electron Configurations
Rule 3. Fill degenerate orbitals singly first
Rule 3. Fill degenerate orbitals singly first
This minimizes electron-electron repulsion
This minimizes electron-electron repulsion
E
E
2p
2s
2p
2s
8.11 Electron Configurations
8.11 Electron Configurations
Rule 3. Fill degenerate orbitals singly first
Rule 4. Once degenerate orbitals are filled
This minimizes electron-electron repulsion
singly, we can then begin to add a second eto each orbital (this fills the orbital)
E
E
2p
2s
2p
2s
8.11 Electron Configurations
8.11 Electron Configurations
Rule 4. Once degenerate orbitals are filled
singly, we can then begin to add a second
Rule 4. Once degenerate orbitals are filled
e-
to each orbital (this fills the orbital)
singly, we can then begin to add a second eto each orbital (this fills the orbital)
In Nature, we would actually have
a distribution of all spin up & all
spin down…
E
2p
2s
2p
2s
Chemists typically only use the up arrows!
E
2p
2s
8.11 Electron Configurations
8.11 Electron Configurations
Rule 4. Once degenerate orbitals are filled
Rule 4. Once degenerate orbitals are filled
singly, we can then begin to add a second e-
singly, we can then begin to add a second e-
to each orbital (this fills the orbital)
to each orbital (this fills the orbital)
E
2p
2s
8.11 Electron Configurations
Building up e-: “Aufbau process” (German)
E
2p
2s
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of e-
Ground state electron configurations (lowest
energy)
8.11 Electron Configurations
Determine Z from Periodic Table e. g. K Z=?
8.11 Electron Configurations
Determine Z from Periodic Table e. g. K Z=?
19
K
39.098
Z=19
Need to
fill 19 e-
8.11 Electron Configurations
Start filling up
e-
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of e-
as we increase Z
Increasing Z
H (Z=1): 1s1
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of
8.11 Electron Configurations
e-
H (Z=1): 1s1
He (Z=2): 1s2
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of eH (Z=1): 1s1
He (Z=2): 1s2
Li (Z=3): 1s22s1
Be (Z=4): 1s22s2
Atom: Determine Z…then fill equal no. of eH (Z=1): 1s1
He (Z=2): 1s2
Li (Z=3): 1s22s1
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of eH (Z=1): 1s1
He (Z=2): 1s2
Li (Z=3): 1s22s1
Be (Z=4): 1s22s2
B (Z=5): 1s22s22p1
8.11 Electron Configurations
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of
e-
B (Z=5): 1s22s22p1
Atom: Determine Z…then fill equal no. of eB (Z=5): 1s22s22p1
C (Z=6)
C (Z=6)
1s 2s
2p
N (Z=7)
1s 2s
8.11 Electron Configurations
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of
e-
Atom: Determine Z…then fill equal no. of e-
B (Z=5): 1s22s22p1
B (Z=5): 1s22s22p1
C (Z=6)
C (Z=6)
N (Z=7)
N (Z=7)
O (Z=8)
O (Z=8)
1s 2s
2p
2p
F (Z=9)
1s 2s
8.11 Electron Configurations
2p
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of eB (Z=5): 1s22s22p1
We have filled across the Table to Ne
Ne
Noble
gas
C (Z=6)
N (Z=7)
O (Z=8)
Noble
gases
F (Z=9)
Ne (Z=10)
1s 2s
2p
8.11 Electron Configurations
8.11 Electron Configurations
We have filled across the Table to Ne
Noble Gas Electron Configuration
Filled octet: 8eNe
Noble
gas
Noble
gases
Stable
electron
configs.
8.11 Electron Configurations
Ne (Z=10)
1s 2s
2p
Inner
Valence electrons
shell
(orbitals with highest n)
eNoble gases are unusually stable because
they have completely filled orbitals
They don’t want to gain or lose e-
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of e-
Noble Gas Electron Configuration
Ne (Z=10)
Ne (Z=10)
1s 2s
1s 2s
2p
2p
Na (Z=11) [Ne]
3s
To simplify the notation, chemists use the
following notation to represent filled inner
shells: [Noble Gas Chemical Symbol]
3p
[Ne] stands for 1s22s22p6
8.11 Electron Configurations
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of eNe (Z=10)
Atom: Determine Z…then fill equal no. of eNe (Z=10)
1s 2s
2p
1s 2s
Na (Z=11) [Ne]
Na (Z=11) [Ne]
Mg (Z=12) [Ne]
Mg (Z=12) [Ne]
3s
3p
2p
Al (Z=13) [Ne]
3s
3p
8.11 Electron Configurations
8.11 Electron Configurations
Atom: Determine Z…then fill equal no. of
e-
Atom: Determine Z…then fill equal no. of e-
Ne (Z=10)
Ne (Z=10)
1s 2s
2p
1s 2s
Na (Z=11) [Ne]
Na (Z=11) [Ne]
Mg (Z=12) [Ne]
Mg (Z=12) [Ne]
Al (Z=13) [Ne]
Al (Z=13) [Ne]
3s
3p
3s
Complete
inner shells
Complete
Inner shells
8.11 Electron Configurations
8.11 Electron Configurations
Configuration Notation Convention
Note: 4s fills But we choose to write:
lower n to the left
before 3d
Sc (Z=21) [Ar] 3d14s2
e.g. Sc+ [Ar] 3d14s1
Instead of filling order:
[Ar] 4s23d1
Why? Because ionized eare usually pulled from the
orbital with the higher n
(which may not be the last
one filled as in this case)
8.11 Electron Configurations
The exceptions
We expect:
Cr (Z=24) [Ar]
3d
4s
[Ar] 3d44s2
Actual:
Cr (Z=24) [Ar]
[Ar] 3d54s1
We expect:
Cu (Z=29) [Ar]
[Ar] 3d94s2
Actual:
Cu (Z=29) [Ar]
[Ar] 3d104s1
Reason: Extra stability for filled and half-filled
d orbitals
2p
3p
Valence e-
Fill d orbitals in
Same way…
Cr & Cu exceptions*
3d
4s