Download Chapter 6

Chp 6: Atomic Structure
1. Electromagnetic Radiation
2. Light Energy
3. Line Spectra & the Bohr Model
4. Electron & Wave-Particle Duality
5. Quantum Chemistry & Wave Mechanics
6. Atomic Orbitals
1. Absorption - An Electron Absorbs the
Light, Acquiring It’s Energy and Entering
an “Excited State”
2. Emission - An Electron “Relaxes” to a
Overview
Chemical Reactions are a Result of
Electron Interactions Between Various
Elements
Elemental Behavior Is the Result of the
Element’s Electronic Structure
Periodic Table is Based on an Elements
Electronic Structure
1. Light Travels Through Space
2. Light has Color
3. Light has Energy
Lower Energy State While Emitting Light
4. Light Energy is
Quantized
Name Some Characteristics
of Light
6.1 Electromagnetic Radiation
Wavelength (l) - Distance Between
two Peaks
Frequency (u) - How Often Waves
Goes Through a Complete
Cycle (1/sec = hertz)
Speed (c) - How Fast Wave
Propagates
So What Is Light?
Spectrum
l
c
u
u
c
l
c = 3 X 108 m/sec
c=lu
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6.2 Nature of Matter: WaveParticle Duality
Electromagnetic Radiation & Energy
Planks Constant relates the Energy of
a photon of light to it’s frequency.
Light exhibits both wave
and particle behavior.
E=hu
Photon - “Particle of Light”
(Einstein)
E = nhn, where n = # of photons
Einstein’s Photoelectric Effect
h=Planck’s Constant
h= 6.63X10-34J.sec
How do we relate the Energy of light
to it’s wavelength?
from c  lu
Eh
c
l
Electromagnetic Radiation & Energy
Small Wavelength
High Frequency
High Energy
Large Wavelength
Low Frequency
Low Energy
E=hu
Light Intensity
I = nhu
(n = moles of photons)
Think about the video on Einstein’s
photoelectric effect and the difference between
“intense” red light and “weak” blue light
Wavelength (meters)
Photon Energy Problem
How many photons of microwave radiation
(l=125mm) are required to heat 1 L of water
from 20.0oC to the boiling point?
ELight = q
-Use s for specific heat capacity
as c is the speed of light
nhu = msDT
Sodium Line Spectra
Sodium gives off yellow light of a specific
wavelength of 589.0 nm.
What is the frequency of the yellow line
spectra of sodium?
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Sodium Line Spectra
Sodium gives off yellow light of a specific wavelength
of 589.0 nm.
1. Determine E for a photon of sodium yellow light
Bohr Model of Hydrogen Atom
Correctly Described the Hydrogen
Spectrum
Used Concept of Orbits (Wrong)
Used Concept of Quantized
Energy Levels (Right)
2. Determine E for a mole of photons of sodium yellow light
Bohr Equation for Hydrogen
Energy of the nth level:
RH= Rydberg constant
RH=Rhc
1
E n   RH ( 2 )
n
Bohr Model of Hydrogen Atom
nf= 1
for UV
light
nf= 2
for
visible
light
RH= 2.18x10-18 J
Energy for transition ni --> nf:
DEni n f  En f  Eni  hu   Rh (
DE ni n f  hu  Rh (
1
1
 )
n 2f ni2
nf= 3
for IR
light
1
1
 )
ni2 n 2f
Bohr Problem:
What Is the Energy Level of the Excited
State Which Is Responsible for the Blue
Green Emission Line at 486.1 nm?
That is, what is the initial quantum state; ni?
Emission is an exothermic process
Absorption is an endothermic process
6.4 Wave-Particle Duality
De Broglie’s Hypothesis:
All Matter has a Characteristic Wavelength
hc
E  mc2  hv 
l
l
h
mv
v=velocity & mv = momentum
Note the inverse relationship between the
mass and the wavelength
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DeBroglie Wavelength of Electron
Calculate the DeBroglie Wavelength of an
Electron moving at 1.00% the speed of light
c = 3x108m/s, m=9.11x10-31kg
E = mc2
mc2 = hu
E = hu
uc
c=lu
l
DeBroglie Wavelength of Electron
Calculate the DeBroglie Wavelength of an
Electron moving at 1.00% the speed of light
c = 3x108m/s, m=9.11x10-31kg
mc2 = hc
l
mv = h
mc = h
l
l
Wave-Particle Duality – Electron
Diffraction
lelec = 2.4 x 10-10m and is
diffracted by a crystal like NaCl
Wave-Particle Duality Uncertainty
The characteristic wavelength of an
electron in a hydrogen atom is 240pm
The size of an isolated H atom is
about 240 pm
This leads to an uncertainty in the
location of the electron
Heisenberg’s Uncertainty Principle
You can not simultaneously know both the
position and momentum of an electron
To measure the position of an electron,
you need a wavelength smaller than it’s
characteristic wavelength, which is of
such a high energy that it alters the
electron’s position during the
measurement process
Physical Meanings of Wave Functions
Bohr Model Uses Orbits
Quantum Mechanics Uses Orbitals
(Y2)
Y2 - Probability Distribution Function,
Describes the probability of finding an
electron in a specific location for a given
energy state
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Quantum Numbers
Physical Meanings of Wave Functions
Bohr Model Uses Orbits
Quantum Mechanics Uses Orbitals
(Y2)
Orbitals are Probability Distribution Functions - They
Represent the Probability of Finding an Electron at a
Certain Space in Time
Different Orbitals Are Defined by Their
Shapes and Distance From the Nucleus
Quantum Numbers
Bohr Orbits Can Be Described by One Quantum
Number, N, the Principle Quantum Number
Quantum Mechanics Uses 4 Quantum Numbers
n l ml ms -
Principle Quantum Number
Azimuthal Quantum Number
Magnetic Quantum Number
Spin Quantum Number (Dirac)
n - Principle Quantum Number
n has integral values; n = 1,2,3...
Each Orbital Can Be Described
by It’s Set of Quantum Numbers
n correlates to the “shells” and the periods
of the periodic table
There are n2 orbitals in each shell
No Two Electrons Can Have the
Same Set of Quantum Numbers
l - Azmuthal Quantum Number
Describes the shape of the orbital
Use letters to designate values of l
s: l=0
d: l=2
p: l=1
f: l=3
l has values of 0 to n-1 for each principle level
-The 1st Principle Level has l = 0
- the 2nd has l = 0,1
- the 3rd has l = 0,1,2
- the 4th has l = 0,1,2,3
- all the rest have 4 or less
1s
2s, 2p
3s, 3p, 3d
4s, 4p, 4d, 4f
The Larger the Value of n, the Greater
the Average Distance From the Nucleus
& the Greater the Orbital’s Energy
ml - Magnetic Quantum Number
Describes Orientation in Space
There are 2l+1 values of ml for each
type of azmuthal quantum number with
values ranging form l to -l
1 type of s (l = 0) orbital
3 types of p (l = 1) orbitals
5 types of d (l = 2) orbitals
7 types of f (l=3) orbitals
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Each Orbital can be identified by it’s
Quantum numbers
n
6.6 Orbital Shapes &
Energies: S Orbitals
(l=0)
Spherical in Nature
l, use letters s,p,d & f
Example, 2px
“Balloon Diagram” shows region of
90% probability of finding electron
ml, describes orientation
All Periods Have S Orbitals
1s
2s
3s
“Onion Skin” layers
of 1st 3 S orbitals
s orbital radial probability
functions
P Orbitals (l=1)
There are 3 types of P orbitals
2nd Period & Greater Have P Orbitals
Y2
Y2
1s
r
Y2
2s
3s
node
nodes
r
r
d Orbitals (l=2)
5 types of d orbitals
f orbitals
3rd Period & Greater Have
d Orbitals
7 types of f orbitals
4th Period & Greater Have f Orbitals
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