## Rotational Selection Rules

A selection rule is a statement about which transitions are allowed (and thus which lines may be observed in a spectrum). The classical idea is that for a molecule to interact with the electromagnetic field and absorb or emit a photon of frequency ν, it must possess, even if only momentarily, a dipole oscillating at that frequency. A gross selection … Read more

## Centrifugal Distortion

In our calculations so far, we have been treating molecules as rigid rotors – assuming that they do not distort under the stress associated with rotation. However, the forces that act on the atoms in rotating molecules are sufficient to cause some distortion of the molecular geometry, which in turn will alter the moment of inertia of … Read more

## Linear and Asymmetric Rotors

Linear rotors are linear molecules, for example CO2, C2H2 (ethyne) and all diatomic molecules. The moment of inertia of a linear molecule about an axis that lies along the molecular axis is necessarily zero, as the atoms all lie on this axis and so are at zero distance from it. The component of angular momentum about this axis … Read more

## Symmetric Rotors

In a symmetric rotor, two of the moments of inertia are equal, but different from the third. Molecules belonging to this category include ammonia (NH3), benzene (C6H6), and chloromethane(CH3Cl). eg The unique axis of the molecule (the one about which the moment of inertia is different from the other two) is called its principle axis. In the molecule … Read more

## Spherical Rotors

A spherical rotor is one for which the three moments of inertia (about mutually perpendicular axes) are equal. This implies that the molecule must be highly symmetric. (In fact, molecules that are spherical rotors must belong to a cubic or icosahedral point group – see the symmetry section, here, for a further explanation.) Examples of spherical rotors are tetrahedral molecules … Read more

## Introduction to Rigid Rotors

In a discussion of rotational energy levels, a very important property is the moment of inertia, I, of the molecule about any particular rotational axis. The moment of inertia of a molecule is generated by taking the mass of each atom in the molecule, multiplying it by the square of its perpendicular distance from the rotational axis, and summing these … Read more

## Intensities of Spectral Lines

The intensity of a spectral line at a given frequency is related to the net rate of absorption (or emission) at that frequency. Thus no lines are observed at frequencies that do not correspond to a transition between two energy states – since no absorption can occur at these frequencies, the intensity of a spectral line at this frequency … Read more

## An Introduction to Spectroscopy

Spectroscopy is, in general terms, the study of the interaction of electromagnetic radiation with matter. Since the energy of individual particles is quantised (restricted to discrete values), it follows that the energies of the molecules which make up matter are also quantised. This means that there must be fixed separations between the energy levels of … Read more

## Liquid-liquid phase diagrams

These diagrams are temperature composition diagrams for systems of two partially miscible liquids (that is, liquids which do not mix in all proportions at all temperatures). The interpretation of these diagrams is in principle precisely the same as that of liquid-vapour diagrams. A typical example of such a diagram looks like this (note the x axis is … Read more

## Temperature Composition Diagrams

These are phase diagrams which show the composition of two phases in equilibrium at a given pressure, and how these compositions change with temperature (as opposed to the pressure composition diagrams which showed the pressure dependence of the composition at a fixed temperature). For an ideal mixture, in which A is more volatile than B, the vapour-composition diagram has the following … Read more