IMT Chapter 3 Energy Levels in Real Chemical Systems

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IMT Chapter 3 Energy Levels in Real Chemical
Systems

• Particle-in-a-Box
• T R V E
• Chemical Reactions and Equilibrium
• Applications

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I. Particle-in-a-Box

• Two important equations from the early 20th
  century
• DeBroglie All particles have a wave-like
  nature
• Imagine a particle of mass, m, confined to a
  1-dimensional box of length, d.
• The particle must fit in the box, so only
  certain wavelengths will be allowed
• Energy level spacings are governed by two
  variables

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II. T R V E

• Electronic
• Hydrogen atom is the only solvable system
• Vibrational
• What types of vibrations are possible?
• Model for vibrations of diatomic molecule 2
  balls connected by a spring
• start with spring attached to wall
• move to real bond 2 balls connected by
  spring. Some alterations neeed
• mass (m) replaced by reduced mass (µ)
• atoms get close together, nuclei repel
• atoms get too far apart, bond breaks

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• Rotational
• Model Rigid Rotor
• Translational
• movement of gaseous atoms and molecules in a
  straight line
• Model Particle in a 3-D box
• LOTS of degeneracy!
• Maxwell-Boltzmann curves (Kotz Chap 12)
• Combine

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III. Chemical Reactions and Equilibrium

• KEYS
• For any competing sets of energy levels,
  Boltzmann still applies
• Equilibrium is established by a competition
  between different set of energy levels
• What about dissimilar systems?

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Energy
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Competition between sets of energy levels is
determined by

• relative energies of the lowest levels of each
  set
• relative spacings of the sets
• temperature
• General Rules
• Low T lower lying energy levels are favored
• High T more closely spaced energy levels are
  favored

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IV. Applications
A. Absorbance
Absorption spectrum of chlorophyll
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B. Fluorescence
Fluorescence band much more narrow than
absorption band