Lecture36Notes(Spectroscopy)

Lecture36Notes(Spectroscopy) - Chem 120A Spectroscopy...

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Unformatted text preview: Chem 120A Spectroscopy 04.26.06 Spring 2006 Lecture 36 Reading: Engel: Ch 8, 11.4 and 15.4-15.8; McQuarrie and Simon: Ch 5, Ch 13.1 to 13.7 and 13.11 to 13.14 1 Introduction to spectroscopy Spectroscopy involves the interaction of light with matter. To study this interaction we can often treat light classically and matter using quantum mechanics. Electromagnetic radiation is customarily divided into different regions reflecting different types of molecular processes that can be caused by such radiation (see Figure 1). The absorption of microwave radiation generally causes transitions between rotational energy levels in molecules. Infrared radiation leads to vibrational excitations (as well as rotational). The absorption of visible and ultraviolet radiation causes transitions between electronic energy levels (and will also cause vibrational and rotational transitions). The frequency of radiation that can be absorbed or emitted leading to transitions between these various levels is given by Δ E = E e- E g = h ν (1) where E e and E g are the energies of the upper (excited) and lower (ground) states, respectively. Figure 1: The electromagnetic spectrum Chem 120A, Spring 2006, Lecture 36 1 Figure 2: An electromagnetic wave Let’s start with a monochromatic (single wavelength) beam of radiation. Classically we describe the beam of radiation by its wavevector, ~ k which gives both its direction and wavelength as ~ k = 2 π λ . We can obtain the frequency of radiation by λν = c or equivalently ω | ~ k | = c where ω = 2 πν and c is the speed of light. Secondly we need the polarization of the light. Remember that light consists of oscillating electric and magnetic fields perpendicular to eachother and to the direction of propagation (see Figure 2). The polarziation of light refers to the vector direction of its electric field. In a completely polarized beam of light all the electric fields are pointing in the same direction. In a completely depolarized beam of light the direction of the electric field is completely random. Any polarization can be described by the complex superposition of the vectors ~ ε 1 and ~ ε 2 which are perpendicular to eachother and also to ~ k (see Figure 3). The properties of these vecors can be summarized as ~ ε 1 · ~ ε 1 = 1 (2) ~ ε 2 · ~ ε 2 = 1 (3) ~ ε 1 · ~ ε 2 = (4) ~ ε 1 · ~ k = (5) ~ ε 2 · ~ k = (6) Figure 3: Polarization vectors for radiation of wavevector ~ k . So the polarization of any electromagnetic wave can be given by c 1 ~ ε 1 + c 2 ~ ε 2 (7) Chem 120A, Spring 2006, Lecture 36 2 For linearly polarized light either c 1 or c 2 is zero. Circular polarization of electromagnetic radiation is a polarization such that the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. The name is derived from this fact....
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This note was uploaded on 09/29/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.

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Lecture36Notes(Spectroscopy) - Chem 120A Spectroscopy...

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