Origin of a Theory or Where did “near-dissociation theory” & the “Le Roy Radius” come from? In the beginning ... I was doing experiments studying rates of reaction and trying to understand the reaction mechanism. Question: How did we measure the amount of I 2 present at each instant as the reaction proceeded? Ans. Using spectroscopy: I 2 vapour absorbs light in the visible, and changes in the fraction of the incident light absorbed tell us about changes in the I 2 concentration. Question: How do we quantitatively relate the fraction of light absorbed to the amount of I 2 present? Ans. (a) By experiment, when possible. Ans. (b) Using quantum mechanical theory to calculate “absorption coefficients”, and how they vary with temperature ! However, this requires a knowledge of the forces (or interatomic potential energy functions) between the atoms in the molecule.
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Origin of a Theory or
Where did “near-dissociation theory” & the “Le Roy Radius”come from?
In the beginning ... I was doing experiments studying rates of reaction and trying tounderstand the reaction mechanism.
Question: How did we measure the amount of I2 present at each instant as thereaction proceeded?
Ans. Using spectroscopy: I2 vapour absorbs light in the visible, and changesin the fraction of the incident light absorbed tell us about changes in the I2
concentration.
Question: How do we quantitatively relate the fraction of light absorbed to theamount of I2 present?
Ans. (a) By experiment, when possible.
Ans. (b) Using quantum mechanical theory to calculate“absorption coefficients”, and how they vary with temperature !
However, this requires a knowledge of the forces (or interatomic potential energyfunctions) between the atoms in the molecule.
Aside: What is Spectroscopy?
Ans. It is the study of the patterns of energies and intensities of the particular“colours” (i.e., frequencies or wavelengths) of light absorbed or emitted by molecules.
What does it tell us?The discrete energies (Eν = h ν ) associated with the particular colours (frequencies)of light absorbed or emitted by molecules tell us:
• molecules can only have energies with a discrete particular values
• the energies associated with these discrete colours (frequencies) of light tell usthe spacings between the energy levels in molecules
• the pattern of level spacings associated with radial or vibrational motion tells usabout the forces between the particles
• recall your discussion of the H atom and of atomic orbital energies:
... and the level spacing pattern depends on the potential
energy function V (x) , or inter-particle forces ~F = − d V (x)
dx
What About the Spectroscopy of I2 ?
Our experimental study of the kinetics of the I + I + M −→ I2 + M recombinationreaction had left me interested in the spectroscopy of the I2 molecule, and led to thefollowing paper.
This work used a conventional technique for determining the molecular dissociationenergy from a plot of the vibrational level spacings ∆Gv+1/2 vs. the vibrationalquantum number v .
It turned out later that my result was wrong – but working on this led me to wonder:
What is the characteristic functional behaviour of vibrationalspacings for levels near a dissociation limit ?
or more generally
What is a better way of determining molecular bond dissociationenergy from the observed vibrational spacings ?
What Forces Hold Matter Together?
1. Covalent bonding: in “network solids” such as diamond & graphite
2. Polymeric solids: very long chain hydrocarbon molecules which are
all tangled up with one another, and sometimes also joined by hydrogen
bonding; e.g., plastics
3. Metals: a “sea” of electrons loosely distributed around a structured cage
of + ve charged ion cores
4. Ionic solids: closely packed regular arrays of + ve & − ve ions; e.g.,
NaCl, MgCl2 , MgO, ...
• strength of binding ∝ (+ ve charge)×(− ve charge)(ion separation distance) ∝ Z1 Z2 e