Chapter 9: Intermolecular Attractions and the Properties of Liquids and Solids

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CHEMISTRY The Molecular Nature of Matter and
Change 3rd Edition
Chapter 7 Lecture Notes Quantum Theory and
Atomic Structure Chem 150 - Ken Marr - Winter
2006
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Welcome to Chem 150!! Below are a few due dates
and other useful information

1. Do the Prelab Preparation for tomorrow's lab
   activity, Atomic Spectrum of Hydrogen. Turn in
   the prelab questions at the start of lab and
   complete in your lab notebook the following
   sections of the report for this lab exercise
   Title, Introduction, Materials/Methods and Data
   Tables. 
2. The completed report for lab 1 is due on Monday
   January 9, 2005.
3. Due Friday January 6, 2006 ALE 1

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Quantum Theory and Atomic Structure
7.1 The Nature of Light
7.2 Atomic Spectra
7.3 The Wave-Particle Duality of Matter and
Energy
7.4 The Quantum-Mechanical Model of the Atom
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Section 7.1 The Nature of Light (Electromagnetic
Radiation)

• Light consists of waves with electrical and
  magnetic components
• Waves have a specific Frequency and Wavelength
• Symbol and Units of Each?
• c n l 3.00 X 108 m/s
• C 2.99792 X 108 m/s

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Figure 7.1
Frequency and Wavelength
c l n
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Amplitude (Intensity) of a Wave
Figure 7.2
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Figure 7.3
Regions of the Electromagnetic Spectrum
Increasing Wavelength
Increasing Frequency, S-1
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Practice Problems Interconverting Frequency
and Wavelength

• Calculate the frequency in hertz of green light
  with a wavelength of 550 nm.
• Calculate the broadcast wavelength in meters of
  an FM radio station that broadcasts at 104.3 MHz.
• Answers
• 5.4 x 1014 hertz
• 2.876 m

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Wave-Particle Duality of Light in some cases
light behaves as waves, in other times as photons
(particles)

• Evidence for Wave Behavior of light
• Refraction of light
• Diffraction of light
• Evidence for Particle Behavior of light
• Blackbody Radiation
• Photoelectric Effect

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Fig. 7.4 Different Behaviors of Waves and
Particles
Refraction of Light
Speed changes when pebble enters H2O
Diffraction of Light
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Evidence for the wave nature of light Diffraction
of Light
Diffraction of Light
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Blackbody Radiation Evidence for the Particle
Behavior of Light
Ephoton hn
1000 K ? emits a soft red glow
1500 K ? brighter more orange
2000 K ? brighter white in color
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Blackbody RadiationEvidence for Particle
Behavior of Light

• Only specific colors of light are emitted when
  blackbodies (heated solids) are heated
• 1000 K ? emits a soft red glow
• 1500 K ? brighter and more orange
• 2000 K ? brighter and white in color
• Max Plancks (1900) Atoms can only absorb or
  give off specific packets or quanta of light
  energy.
• These packet of energy are called photons.

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Particle Nature of Light

• Max Planck (1900)
• EMR is emitted as weightless packets of energy
  called photons
• Each photon has its own energy and frequency, n
• Ephoton hn
• h Plancks constant 6.626 x 10-34 J.s

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• Photoelectric Effect
• Evidence for Particle Behavior of Light
• Light of a certain minimum frequency (color) is
  needed to dislodge electrons from a metal plate.
• Wave theory predicts a wave of a minimum
  amplitude.

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Einsteins Explanation of the Photoelectric
Effect (1905)

• Light intensity is due to the number of photons
  striking the metal per second, not the amplitude
• A photon of some minimum energy must be absorbed
  by the metal
• E photon hn

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Relationship between Energy of Light and
Wavelength

• Derive an equation that relates E and l from the
  following equations c l n and E hn
• Use this equation to Answer the following
  questions.....
• Microwave ovens emit light of l 3.00 mm.
  Calculate the energy of each photon emitted from
  a microwave oven.
• Ans. 6.63 x 10-23 J/photon
• How many photons of light are needed for a
  microwave oven to raise the temperature of a cup
  of water (236 g) from 20.0 oC to 100.0 oC?
• Ans. 1.19 x 1027 photons

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Section 7.2 Atomic Spectra

• Continuous Spectrum
• Sunlight or from object heated to a very high
  temperature (e.g. light filament)
• Atomic Spectrum
• Also called line, bright line or emission
  spectrum
• Due to an atoms electron(s) excited by
  electricity or heat falling from a higher to a
  lower energy levelmore about this later!!

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Continuous Spectrum
Line Spectra
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Rydberg Equation Predicts the Hydrogen Spectrum

• Rydberg Equation
• Empirically derived to fit hydrogens atomic
  spectrum
• Predicts ls of invisible line spectra
• e.g. Hydrogens Ultraviolet line spectrum
  (nL 1)
• R 1.096776 x 107 m-1 n 1, 2, 3,
  4,

L
H
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Using the Rydberg Equation

• Practice Exercise
• Calculate the wavelength in nm and determine the
  color of the line in the visible spectrum of
  hydrogen for which nL 2 and nH 3.
• Ans. 656.4 nm Color????

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1st The Good News.Niels Bohr Planetary model of
the atom explains Hydrogen's Spectrum (1913)

• An atoms energy is quantized because electrons
  can only move in fixed orbits (energy levels)
  around the nucleus
• Orbits are quantized
• i.e. Each orbit can only have a certain radius
• An electron can only move to another energy level
  (orbit) when the energy absorbed or emitted
  equals the difference in energy between the two
  energy levels
• Line spectra result as electrons emit light as
  they fall from a higher to lower energy level

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Bohrs Explanation of the Three series of
Spectral Lines of the Hydrogen Spectrum
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Animation of Bohrs Planetary Model

1. Animation (Flash)
2. Animation (QuickTime)

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Bohrs Equation Derived from the Ideas of
Planck, Einstein Classical Physics

• DEelectron ELower - EHigher or DEelectron
  Efinal - Einitial
• DEelectron -2.18 x 10-19 J (1/n2Lower -
  1/n2higher)
• But DE hc/ l, substitution yields
• 1/l 1.10 x107 m-1 (1/n2Lower - 1/n2higher)
• Bohrs Constant is within 0.05 of the Rydberg
  Constant
• Equation provides a theoretical explanation of
  Hydrogens Atomic Spectrum

1/l 1.10 x107 m-1 (1/n2Lower - 1/n2higher)
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Bohrs Equation Accurately Predicts the
Ionization Energy of Hydrogen

• Use Bohrs equation to calculate the ionization
  energy for
• a.) one hydrogen atom
• b.) one mole of hydrogen atoms
• 1/l 1.10 x107 m-1 (1/n2Lower - 1/n2higher)
• Energy H (g) ? H(g) e-
• Answers a.) 2.18 x 10-18J/atom b.) 1.31 x
  103 kJ/mole

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Now the Bad NewsBohrs Model is Incorrect!!

• Closer inspection of spectral lines shows shows
  that they are not all single lines
• Bohrs model doesnt account for the extra lines
• Only works for atoms or ions with one electron
• Bohrs model doesnt account for presence of
  electron-electron repulsions and electron-nucleus
  attractions in atoms with more than one electron.
• Electrons do not orbit around the nucleus!!!
• A new model is needed
• Would you believe that electrons behave as waves
  and as particles????

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Section 7.3 The Wave-Particle Duality of
Matter Electron Diffraction Evidence that
electrons behave as waves!
Davisson Germer (1927) Electrons are diffracted
by solids just like X-rays! Hence, electrons
behave as waves!
X-Ray diffraction pattern of Aluminum
X-Ray tube Aluminum
Source of electrons
Aluminum
Electron diffraction pattern of Aluminum
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Wave- Particle Duality of Matter and Energy

• Matter behaves as if it moves like a wave!!
• Only small, fast objects (e.g. e-, p , n0) have
  a measurable l
• me 9.11x10-31 kg mp mn 1.67x10-27 kg
• Louis DeBroglie (1924) combined
• E mc2 and E hc / l to yield
• l matter h/mu m mass u velocity
• DeBroglie l too small to measure for heavy, slow
  objects

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Locating an Electron....an uncertain affair!!

• Orbital
• Region in space where an electron wave is most
  likely to be found
• Exact location of an electron cant be determined
• Can only determine the probability of finding an
  electron....why?
• Electrons behave as waves!!
• In order to see the position of an electron we
  must probe it with radiation which changes its
  position and/or velocity

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Section 7.4Quantum Mechanical Model of the Atom
Electron Waves in Atoms

• Electrons are standing waves
• Peaks and troughs only move up and down
• Similar to how guitar strings move
• Orbitals
• Are areas in space where electron waves are most
  likely to be found
• Orbitals are made of electron waves

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Quantum Mechanics and Atomic Orbitals

• Erin Schrodinger (1926) developed a mathematical
  equation called a wave function to describe the
  energy of electrons
• The square of the wave function gives the
  probability of finding an electron at any point
  in space, thus producing a map of an orbital

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Atomic Orbital An area in space where an
electron wave is most likely to be found outside
of the nucleus
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Orbitals are Identified by 3 Quantum Numbers

• Principle Quantum Number, n (n 1,2,3)
• Determines the orbitals size and energy (I.e.
  which energy level the electron occupies)
• Relates to the average distance of the e- to the
  nucleus
• Secondary Quantum Number, l
• Determines the orbitals shape or sublevel s,
  p, d or f
• l 0 to n-1
• Orbitals with the same values for n and l are
  called sublevels

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Orbitals are Identified by 3 Quantum Numbers

• Magnetic Quantum Number, ml
• Determines the orbitals orientation in space
• ml -l, , 0 , l
• ml represents the orbital within the sublevel.
• S - sublevel has 1 orbital
• p - sublevel has 3 orbitals
• d - sublevel has 5 orbitals
• F - sublevel has 7 orbitals

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n Principal quantum Number (size and energy of
orbital)
l Angular momentum Q.N. (shape of orbital)
ml magnetic Q.N. (orientation of orbital)
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Relationship between Angular momentum Q.N. , l,
and sublevel names s, p, d and f

• Value of l Sublevel
• 0
  s
• 1
  p
• 2
  d
• 3
  f f
• 4
  g
• 5
  h

Sublevels only used by electrons in the excited
state
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Summary of Relationships Between n, l and ml
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Practice Makes Perfect?

• What is the subshell (e.g. 1s, 2s, 2p, etc.)
  corresponding to the following values for n and
  l?
• n 2, l 1
• n 4, l 0
• n 3, l 2
• n 5, l 3
• n 3, l 3

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Practice Makes Perfect?

• Which of the following sets of quantum numbers
  are not possible?
• n 2, l 1, m l 0
• n 2, l 2, m l 1
• n 2, l 1, m l -2
• n 3, l 2, m l -2
• n 0, l 0, m l 0

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The Relationship between the 4 Quantum Numbers,
Energy Levels, Sublevels and Orbitals

• See figure 6.15, page 239 in Brady (Transp.)

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Practice Makes Perfect?

• What subshells are found in the 4th shell?
• Which subshell is higher in energy?
• 3s or 3p
• 4p or 4d
• 3p or 4p

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1s orbital 2s orbital
3s orbital
Shapes of orbitals As the value for n
increases, the electron is more likely to be
found further from the nucleus
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Fig. 7.18 Shapes of the three orbitals in the 2p
sublevel 2px 2py 2pz Note that the three
orbitals are mutually perpendicular to each other
(fig. D), thus contributing to an atoms overall
spherical shape
An accurate representation of the 2pz orbital
Stylized shape of 2pz used in most texts
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Fig. 7.19 c-g Shapes of the five orbitals in
the 3d sublevel Note that the relative positions
of the five orbitals in the 3d sublevel
contribute to the overall spherical shape of an
atom (fig. H)
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Fig. 7.20 One of the possible seven orbitals of
the 4f sublevel Since only the s, p, and d
sublevels are commonly involved with bonding, we
will not be concerned with the shapes of the
orbitals of the f-sublevel