Modern Spectroscopy

J. Michael Hollas

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118681602
• Edition: 4
• Topic: Physical Sciences
• Subtopic: Spectroscopy & Spectrum Analysis

The latest edition of this highly acclaimed title introduces the reader to a wide range of spectroscopies, and includes both the background theory and applications to structure determination and chemical analysis. It covers rotational, vibrational, electronic, photoelectron and Auger spectroscopy, as well as EXAFs and the theory of lasers and laser spectroscopy.
* A revised and updated edition of a successful, clearly written book
* Includes the latest developments in modern laser techniques, such as cavity ring-down spectroscopy and femtosecond lasers
* Provides numerous worked examples, calculations and questions at the end of chapters

1

Some Important Results in Quantum Mechanics

1.1 Spectroscopy and quantum mechanics

Spectroscopy is basically an experimental subject and is concerned with the absorption, emission or scattering of electromagnetic radiation by atoms or molecules. As we shall see in Chapter 3, electromagnetic radiation covers a wide wavelength range, from radio waves to γ-rays, and the atoms or molecules may be in the gas, liquid or solid phase or, of great importance in surface chemistry,adsorbed on a solid surface.

Quantum mechanics, in contrast, is a theoretical subject relating to many aspects of chemistry and physics, but particularly to spectroscopy.

Experimental methods of spectroscopy began in the more accessible visible region of the electromagnetic spectrum where the eye could be used as the detector. In 1665 Newton had started his famous experiments on the dispersion of white light into a range of colours using a triangular glass prism. However, it was not until about 1860 that Bunsen and Kirchhoff began to develop the prism spectroscope as an integrated unit for use as an analytical instrument. Early applications were the observation of the emission spectra of various samples in a flame, the origin of flame tests for various elements, and of the sun.

The visible spectrum of atomic hydrogen had been observed both in the solar spectrum and in an electrical discharge in molecular hydrogen many years earlier, but it was not until 1885 that Balmer fitted the resulting series of lines to a mathematical formula. In this way began the close relationship between experiment and theory in spectroscopy, the experiments providing the results and the relevant theory attempting to explain them and to predict results in related experiments. However, theory ran increasingly into trouble as it was based on classical newtonian mechanics until, from 1926 onwards, Schrödinger developed quantum mechanics. Even after this breakthrough, the importance of which cannot be overstressed, it is not, I think, unfair to say that theory tended to limp along behind experiment. Data from spectroscopic experiments, except for those on the simplest atoms and molecules, were easily able to outstrip the predictions of theory, which was almost always limited by the approximations that had to be made in order that the calculations be manageable. It was only from about 1960 onwards that the situation changed as a result of the availability of large, fast computers requiring many fewer approximations to be made. Nowadays it is not uncommon for predictions to be made of spectroscopic and structural properties of fairly small molecules that are comparable in accuracy to those obtainable from experiment.

Although spectroscopy and quantum mechanics are closely interrelated it is nevertheless the case that there is still a tendency to teach the subjects separately while drawing attention to the obvious overlap areas. This is the attitude I shall adopt in this book, which is concerned primarily with the techniques of spectroscopy and the interpretation of the data that accrue. References to texts on quantum mechanics are given in the bibliography at the end of this chapter.

1.2 The evolution of quantum theory

During the late nineteenth century evidence began to accumulate that classical newtonian mechanics, which was completely successful on a macroscopic scale, was unsuccessful when applied to problems on an atomic scale.

In 1885 Balmer was able to fit the discrete wavelengths λ of part of the emission spectrum of the hydrogen atom, now called the Balmer series and illustrated in Figure 1.1, to the empirical formula

(1.1)

where G is a constant and n′ = 3, 4, 5,…. In this figure the wavenumber¹

and the wavelength λ are used: the two are related by

(1.2)

Using the relationship

(1.3)

where v is the frequency and c the speed of light in a vacuum, Equation (1.1) becomes

(1.4)

in which R_H is the Rydberg constant for hydrogen. This equation, and even the fact that the spectrum is discrete rather than continuous, is completely at variance with classical mechanics.

Another phenomenon that was inexplicable in classical terms was the photoelectric effect discovered by Hertz in 1887. When ultraviolet light falls on an alkali metal surface, electrons are ejected from the surface only when the frequency of the radiation reaches the threshold frequency ν_t for the metal. As the frequency is increased, the kinetic energy of t...