The Absorption of Light

The absorption of light energy can result in the increase in energy of the atom or molecule in a number of different ways. If the light is in the UV/Visible region it can produce an electronic change whereby an electron is moved to an orbit of higher energy. If the light is in the infrared range then it can result in an increase in vibrational or rotational energy. It is not intended here to deal extensively with the wave theory of light but some basic concepts must be introduced to understand the basic mechanics of UV spectrometry.From equation (1) and (2)he energy (E) in a quantum of light of frequency(ν) is given by,

⁽³⁾

where (c) is the velocity of light, (λ) is the wavelength of the light,

and (h) is Planks constant = 6.62 x 10^-27 ergs/sec.
The size of a single quantum of light energy is inconveniently small and so the energy associated with the transition of (N) quanta is used (where (N) is Avogadro’s number 6.02 x 10²³, the number of molecules in a gram molecule of the substance). The energy associated with the transition of a gram molecule is called an einstein. Thus, the number of einsteins required to effect a given transition will vary with the frequency of the radiation. Consider first the Bohr atom, which is depicted in figure 6 as a hydrogen atom.

Figure 6. The Bohr Atom

Although now considered obsolete, the Bohr atom serves as a useful introduction to the phenomena of light absorption and light emission and, thus, will briefly be discussed. Bohr depicted the hydrogen atom as a central positively charged nucleus (in the case of hydrogen , a single proton) orbited by a negatively charged electron held in equilibrium by the balanced outward centrifugal force and the inward electrical attractive force. This likens the electron and atom to a planet revolving round a star. The electron could spin round a number of different orbits having different energies in each, the actual energy increasing as the orbit becomes larger. Three such orbits are depicted in figure 6, labelled (n=1), (n=2), and (n=3). The innermost orbit has the lowest energy (n=1).
If light of 656 nm wavelength strikes a hydrogen atom and is absorbed (E= hν) and this can result in an electron in the orbit where n=2 being transferred to the orbit where n=3. In a similar manner if an electron in orbit n=3 falls back to the obit where n=2 then light of 656 nm will be emitted. Thus, the basic mechanics of UV/visible light absorption and fluorescent emission can be accounted for. However, although the energy difference of the electrons between orbits could be understood, an explanation of the factors that control the value of (n) requires a more sophisticated model to be considered. The star-planet model must be significantly modified.
In 1924 the concept was introduced that all electromagnetic radiation could be considered as either waves or particles and furthermore very small particles (i.e. electrons) travelling at high speed could also exhibit wave properties. This was confirmed by experiments that demonstrated the diffraction of electrons (in the manner of light) and ultimately the development of the electron microscope.
In 1924, Broglie produced equations that reconcile, in a relatively simply way, this particle-wave nature as follows.
If(λ) is the wavelength of the wave and (p) the momentum of the particle,
()And for an electron, mass (m_e) traveling in a straight line at a velocity (v)

Then (5)
The wave nature of the electron easily explains the restricted nature of the different orbits. The electron can only exist in orbits in which the wave is a standing wave.
Such a condition is depicted in figure 7. It follows that if the orbit radius is (r), for a standing wave the circumference of the orbit.
And for an electron, mass (me) travelling in a straight line at a velocity (v)
(6)
The integer (n) is known as the principal quantum number introduced by Bohr and can take values of 1.2.3………n

Figure 7. An Electron in Orbit Presented as a Standing Wave

The orbital depicted in figure 7 is for n =12.
The behaviour of an electron as a wave rather than as a particle provoked a quite different approach to the theory called Quantum Mechanics or Wave mechanics. The subject of wave mechanics is outside the scope of this book and for those readers who wish to study the subject further they are recommended to read Basic Atomic and Molecular Spectroscopy by J. Michael Hollas published by the Royal Society of Chemistry.