Page 247 - Essentials of physical chemistry

Basic Spectroscopy 209

the lowest energy part of a broad electronic transition starts at the red edge. At the time this
calculation was presented, it was sensational and it eventually led many researchers to continue to
improve the Xa idea to what is now modern density functional theory (DFT). This type of
calculation, although an approximation, encouraged further development of the idea that the
electron–electron exchange can be parameterized with more refined functions. Today, the majority
of modern quantum chemistry invokes some form of a parametric calculation for electron–electron
exchange within a DFT program, although there are competing models that try to avoid any
parameters. In Chapter 17, we discuss the fact that even the best DFT exchange potentials still
use some form of analytical ‘‘Hartree–Fock exchange.’’ The problem of how to represent electron–
electron exchange between indistinguishable particles is not fully solved as of 2010 and research
continues to search for exact formulas.

GENERAL PRINCIPLES OF SPECTROSCOPY

We hope a few points were made regarding spectroscopy in this brief treatment. This has been a
‘‘broad brush’’ view of spectroscopy using mostly the simple mathematics of the Bohr H atom, so
that we can consider several types of spectroscopy in what may be the only opportunity if this is a
one-semester treatment. Spectroscopic topics in the latter chapters of this text will be more precise
but require a foundation of more detailed mathematics.

1. Spectroscopy involves measurement of electromagnetic radiation as absorbed or emitted
from atoms and molecules between definite energy levels and can be characterized by
wavelength or frequency. Light energy is proportional to frequency, e ¼ hn, and angular
momentum is quantized as well (mvr ¼ n h).
2. The Bohr model of the H atom was derived to obtain two key formulas:

2
Z
(13:6057 eV)
n
E(n, Z) ¼
and
2

n
(0:5291772 A ˚ )
Z
r(n, Z) ¼
3. The electron volt unit of energy and the wave number quantity were encountered in this
brief introduction to spectroscopy. A survey of units used in spectroscopy was presented as
12,398
was derived.
a preparation for further studies. The valuable formula DE (eV) ¼
l (A ˚ )
4. We noted some details of basic electronic circuits and diffraction of electromagnetic
radiation. LiF was mentioned as a crystal for use as an x-ray diffraction device.
5. Examples were shown here based mainly on applications of the Bohr model of the atom for
the H-atom spectrum and XRF. The Bohr model only applies to systems with a single
electron orbiting a single positive ion. The model can be used for systems with more than
one electron to treat an outer electron shell as orbiting a spherical inner ion with a
noninteger effective nuclear charge. It was necessary to define the molar absorption
coefficient e(l) to understand molecular electronic spectra and the Beer–Lambert law
was illustrated for aqueous KMnO 4 .
6. Concepts like excitation, emission, quantum numbers, and electron volts have all been
introduced in a framework of simple algebra, so in later chapters we can focus on the
quantum phenomena with familiarity of concepts and units already in hand.