Electromagnetic Radiation, Cont…. Lecture 4

Energy States of Chemical Species The postulates of quantum theory as introduced by Max Planck in 1900, intended to explain emission by heated bodies, include the following: 1. Atoms, ions, and molecules can exist in certain discrete energy states only. When these species absorb or emit energy exactly equal to energy difference between two states; they transfer to the new state. Only certain energy states are allowed (energy is quantized).

2. The energy required for an atom, ion, or a molecule to transfer from a one energy state to another is related to the frequency of radiation absorbed or emitted by the relation: Efinal – Einitial = hn Therefore, we can generally state that: DE = hn

Types of Energy States Three types of energy states are usually identified and used for the explanation of atomic and molecular spectra: 1. Electronic Energy States: These are present in all chemical species as a consequence of rotation of electrons, in certain orbits, around the positively charged nucleus of each atom or ion. Atoms and ions exhibit this type of energy levels only.

2. Vibrational Energy Levels: These are associated with molecular species only and are a consequence of interatomic vibrations. Vibrational energies are also quantized, that is, only certain vibrations are allowed. 3. Rotational Energy Levels: These are associated with the rotations of molecules around their center of gravities and are quantized. Only molecules have vibrational and rotational energy levels.

The solid black lines represent electronic energy levels The solid black lines represent electronic energy levels. Arrows pointing up represent electronic absorption and arrows pointing down represent electronic emission. Dotted arrows represent relaxation from higher excited levels to lower electronic levels. The figure to left represents atomic energy levels while that to the right represents molecular energy levels.

Line Versus Band Spectra Since atoms have electronic energy levels, absorption or emission involves transitions between discrete states with no other possibilities. Such transitions will only result in line spectra. However, since molecular species contain vibrational and rotational energy levels associated with electronic levels, transitions can occur from and to any of these levels. These unlimited numbers of transitions will give an absorption or emission continuum, which is called a band spectrum. Therefore, atoms and ions always give line spectra while molecular species give band spectra.

Black Body Radiation When solids are heated to incandescence, a continuum of radiation called black body radiation is obtained. It is noteworthy to indicate that the produced emission continuum is: 1. Dependent on the temperature where as temperature of the emitting solid is increased, the wavelength maximum is decreased. 2. The maximum wavelength emitted is independent on the material from which the surface is made.

The Uncertainty Principle Werner Heisenberg, in 1927, introduced the uncertainty principle, which states that: Nature imposes limits on the precision with which certain pairs of physical measurements can be made. This principle has some important implications in the field of instrumental analysis and will be referred to in several situations throughout the course.

The Uncertainty Principle says that the product of the unceratinty Δx of the location of a particle and the uncertainty of the momentum Δpx can be no smaller than h/2p, where h is Planck's constant; i.e., Δx·Δpx ≥ (h/2p) It is also true that the product of the uncertainty in the energy ΔE of a particle and the uncertainty concering time Δt must be no smaller than h/2p. Thus ΔE·Δt ≥ h/2p

To understand the meaning of this principle, the easiest way is to assume that an unknown frequency is to be determined by comparison with a known frequency. Now let both interfere to give a beat. The shortest time that can be allowed for the interaction is the time of formation of one single beat, which is Pb. Therefore, we can write:

Example: The mean lifetime of the excited state when irradiating mercury vapor with a pulse of 253.7 nm radiation is 2*10-8 s. Calculate the value of the width of the emission line. ٍSolution: