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General Chemistry
Principles and Modern Applications
Petrucci • Harwood • Herring
9th Edition
Chapter 8: Electrons in Atoms
Dr. Chris Kozak
Memorial University of Newfoundland, Canada
General Chemistry: Chapter 8
Slide 1
What is Quantum Theory?
Quantum Theory’s Explanation of Chemistry in 60 seconds
Electron
Earth
Classical
Quantum Mechanics
Mechanics
Nucleus
Sun
General Chemistry: Chapter 8
Slide 2
Quantum Numbers
In classical physics, all orientations are possible
In quantum physics, only certain orientations are possible.
They are quantized
…with quantum number j
j = 0, 1, 2, 3, 4, …
General Chemistry: Chapter 8
Slide 3
Quantum Numbers
For j = 1,
There are three orientations
Y
X
Z
General Chemistry: Chapter 8
Slide 4
Quantum Numbers
In general,
2j + 1
Orientations
j
2j + 1
0
1
1
3
2
5
etc.
General Chemistry: Chapter 8
Slide 5
Quantum Numbers
1
3
5
General Chemistry: Chapter 8
Slide 6
Quantum Numbers
General Chemistry: Chapter 8
Slide 7
Quantum Numbers
General Chemistry: Chapter 8
Slide 8
Quantum Numbers
The Periodic Table!
It explains all of chemistry,
all of biology and biochemistry,
and all the interesting parts of physics…
mostly.
General Chemistry: Chapter 8
Slide 9
Contents
8-1
8-2
8-3
8-4
8-5
8-6
8-7
Electromagnetic Radiation
Atomic Spectra
Quantum Theory
The Bohr Atom
Two Ideas Leading to a New Quantum
Mechanics
Wave Mechanics
Quantum Numbers and Electron Orbitals
General Chemistry: Chapter 8
Slide 10
Contents
8-8
8-9
Quantum Numbers
Interpreting and Representing Orbitals of
the Hydrogen Atom
8-9 Electron Spin
8-10 Multi-electron Atoms
8-11 Electron Configurations
8-12 Electron Configurations and the Periodic
Table
General Chemistry: Chapter 8
Slide 11
8-1 Electromagnetic Radiation
• Electric and magnetic
fields propagate as waves
through empty space or
through a medium.
• A wave transmits energy.
General Chemistry: Chapter 8
Slide 12
EM Radiation
Low ν
High ν
General Chemistry: Chapter 8
Slide 13
Frequency, Wavelength and Velocity
• Frequency (ν) in Hertz—Hz or s-1.
• Wavelength (λ) in meters—m.
µm
nm
D
• cm
pm
(10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m)
• Velocity (c)—2.997925 H 108 m s-1.
c = λν
λ = c/ν
General Chemistry: Chapter 8
ν= c/λ
Slide 14
Electromagnetic Spectrum
General Chemistry: Chapter 8
Slide 15
ROYGBIV
Red
Orange
Yellow
700 nm
Green
Blue
450 nm
Indigo
Violet
General Chemistry: Chapter 8
Slide 16
Constructive and Destructive Interference
General Chemistry: Chapter 8
Slide 17
Water and Light Wave Interference
General Chemistry: Chapter 8
Slide 18
Refraction of Light
General Chemistry: Chapter 8
Slide 19
8-2 Atomic Spectra
General Chemistry: Chapter 8
Slide 20
Atomic Spectra
General Chemistry: Chapter 8
Slide 21
Blackbody Radiation
1000 K
Embers
in a fire
1500 K
Stove heating
Element
General Chemistry: Chapter 8
2000 K
Lightbulb
Filament
Slide 22
8-3 Quantum Theory
Blackbody Radiation:
Max Planck, 1900:
Energy, like matter, is discontinuous.
E = nhν
General Chemistry: Chapter 8
Slide 23
The Photoelectric Effect
• Light striking the surface of certain metals causes
ejection of electrons
• Wave properties of light is unable to explain
some observations
• ν > νo
• ne- % I
• Ek % ν
threshold frequency
# of e- depends on intensity
kinetic energy depends on frequency
General Chemistry: Chapter 8
Slide 24
The Photoelectric Effect
General Chemistry: Chapter 8
Slide 25
The Photoelectric Effect
• At the stopping voltage the kinetic energy of
the ejected electron has been converted to
potential.
1
mu2 = e-Vs
2
• At frequencies greater than νo:
Vs = k (ν - νo)
General Chemistry: Chapter 8
Slide 26
The Photoelectric Effect
Ek = eVs
Eo = hνo
νo =
eVo
h
eVo, and therefore νo, are characteristic of the metal.
Conservation of energy requires that:
Ephoton = Ek + Ebinding
Ek = Ephoton - Ebinding
1
mu2 + eVo
2
1
eVs =
mu2 = hν - eVo
2
hν =
General Chemistry: Chapter 8
Slide 27
Photoelectron Spectroscopy
General Chemistry: Chapter 8
Slide 28
8-4 The Bohr Atom
E=
-RH
n2
RH = 2.179 H 10-18 J
General Chemistry: Chapter 8
Slide 29
Energy-Level Diagram
∆E = Ef – Ei =
= RH (
-RH
-RH
–
nf2
ni2
1
1
–
) = hν = hc/λ
ni2 nf2
General Chemistry: Chapter 8
Slide 30
Ionization Energy of Hydrogen
∆E = RH (
1
1
–
) = hν
ni2 nf2
As nf goes to infinity for hydrogen starting in the ground state:
hν = RH (
1
) = RH
ni2
This also works for hydrogen-like species such as He+ and Li2+.
hν = -Z2 RH
General Chemistry: Chapter 8
Slide 31
Great, but what do we really need to
know?
• Calculate the energy, frequency and wavelength for any
hydrogen atom transition
• Identify the wavelengths of the electromagnetic spectrum
as being in the UV, visible or IR regions.
• You should be able to do Examples 8-1 to 8-4 (and the
practice examples)
General Chemistry: Chapter 8
Slide 32
8-5 Two Ideas Leading to a New
Quantum Mechanics
• Wave-Particle Duality.
– Einstein suggested particle-like properties of light
could explain the photoelectric effect.
– But diffraction patterns suggest photons are wavelike.
• de Broglie, 1924
– Small particles of matter may at times display
wavelike properties.
General Chemistry: Chapter 8
Slide 33
deBroglie and Matter Waves
E = mc2
hν = mc2
hν/c = mc = p
p = h/λ
λ = h/p = h/mu
General Chemistry: Chapter 8
Slide 34
X-Ray Diffraction
Structure 1
Structure 2
General Chemistry: Chapter 8
Slide 35
The Uncertainty Principle
• Werner Heisenberg
∆x ∆p ≥
h
4π
General Chemistry: Chapter 8
Slide 36
Sample Problems
1.
Some Diamonds appear yellow because they contain nitrogen compounds that
absorb purple light with a frequency of 7.23 x 1014 Hz. Calculate the
wavelength in nm of absorbed light.
2.
Calculate the E of one photon of UV (λ = 1 x 10-8 m), visible (λ = 5 x 10-7 m)
and IR (λ = 1 x 10-4 m) light. What do the answers indicate about the
relationship between λ and E?
3.
Calculate the Energy required to remove an electron from a hydrogen atom in
its ground state.
4.
Calculate the wavelength of the transition from n = 4 to n = 1 in Hydrogen (one
of the Lyman series of transitions).
5.
Calculate the de Broglie wavelengths of a 50 kg mass travelling at ¼ the speed
of light and for a proton (m = 1.673 x 10-27 kg) travelling at this speed. What do
these wavelengths say about the wave properties of matter in relation to their
size?
General Chemistry: Chapter 8
Slide 37
8-6 Wave Mechanics
• Standing waves.
– Nodes do not undergo displacement.
λ=
2L
, n = 1, 2, 3…
n
General Chemistry: Chapter 8
Slide 38
Wave Functions
• ψ, psi, the wave function.
– Should correspond to a
standing wave within the
boundary of the system
being described.
• Particle in a box.
ψ =
General Chemistry: Chapter 8
2
 nπ x 
sin 

L
 L 
Slide 39
Probability of Finding an Electron
General Chemistry: Chapter 8
Slide 40
Wave Functions for Hydrogen
• Schrödinger, 1927
Eψ = Hψ
– H (x,y,z) or H (r,θ,φ)
ψ(r,θ,φ) = R(r) Y(θ,φ)
R(r) is the radial wave function.
Y(θ,φ) is the angular wave function.
General Chemistry: Chapter 8
Slide 41
Principle Shells and Subshells
• Principle electronic shell, n = 1, 2, 3…
• Angular momentum quantum number,
l = 0, 1, 2…(n-1)
I = 0, s
l = 1, p
l = 2, d
l = 3, f
• Magnetic quantum
number,
• ml= - l…-2, -1, 0, 1, 2…+l
General Chemistry: Chapter 8
Slide 42
Orbital Energies
General Chemistry: Chapter 8
Slide 43
9-8 Interpreting and Representing the
Orbitals of the Hydrogen Atom.
General Chemistry: Chapter 8
Slide 44
s orbitals
General Chemistry: Chapter 8
Slide 45
p Orbitals
General Chemistry: Chapter 8
Slide 46
p Orbitals
General Chemistry: Chapter 8
Slide 47
d Orbitals
General Chemistry: Chapter 8
Slide 48
8-9 Electron Spin: A Fourth Quantum
Number
General Chemistry: Chapter 8
Slide 49
Electronic Structure of the H atom
We have 3 quantum numbers for H
n=1
1s orbital
l=0
ml = 0
ms
Only one type of orbital
orientation/symmetry
Only one electron (can be
either +1/2 or -1/2)
Ground State Configuration:
General Chemistry: Chapter 8
1s1
Slide 50
8-10 Multi-electron Atoms
• Schrödinger equation was for only one e-.
• Electron-electron repulsion in multi-electron
atoms.
• Assume they have Hydrogen-like orbitals
(by approximation).
General Chemistry: Chapter 8
Slide 51
8-11 Electron Configurations
Three Main Principles
• Aufbau process.
– Build up and minimize energy.
• Pauli exclusion principle.
– No two electrons can have all four
quantum numbers alike.
• Hund’s rule.
– Degenerate orbitals are occupied singly
first.
General Chemistry: Chapter 8
Slide 52
Orbital Energies
General Chemistry: Chapter 8
Slide 53
Orbital Filling
General Chemistry: Chapter 8
Slide 54
Aufbau Process and Hund’s Rule
spdf notation: C (carbon) 1s22s22p2
Expanded notation:
1s22s22px1py1
General Chemistry: Chapter 8
Slide 55
Filling p Orbitals (Electrons in Boxes)
General Chemistry: Chapter 8
Slide 56
Filling the d Orbitals
General Chemistry: Chapter 8
Slide 57
8-12 Electron Configurations and the Periodic Table
General Chemistry: Chapter 8
Slide 58