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Unformatted text preview: 5.61 Physical Chemistry Lecture #34 1 SPECTROSCOPY: PROBING MOLECULES WITH LIGHT In practice, even for systems that are very complex and poorly characterized, we would like to be able to probe molecules and find out as much about the system as we can so that we can understand reactivity, structure, bonding, etc. One of the most powerful tools for interrogating molecules is spectroscopy. Here, we tickle the system with electromagnetic radiation (i.e. light) and see how the molecules respond. The motivation for this is that different molecules respond to light in different ways. Thus, if we are creative in the ways that we probe the system with light, we can hope to find a unique spectral fingerprint that will differentiate one molecule from all other possibilities. Thus, in order to understand how spectroscopy works, we need to answer the question: how do electromagnetic waves interact with matter? The Dipole Approximation An electromagnetic wave of wavelength λ , produces an electric field, E(r, t ) , and a magnetic field, B(r, t ) , of the form: E(r, t )=E 0 cos( k·r – ω t) B(r, t )=B 0 cos( k·r – ω t) Where ω=2πν is the angular frequency of the wave, the wavevector k has a magnitude 2π/λ and k (the direction the wave propagates) is perpendicular to E 0 and B . Further, the electric and magnetic fields are related: E · B =0 E = c B  Thus, the electric and magnetic fields are orthogonal and the magnetic field is a factor of c (the speed of light, which is 1/137 in atomic units) smaller than the electric field. Thus we obtain a picture like the one at right, where the electric and magnetic fields oscillate transverse to the direction of propagation. Now, in chemistry we typically deal with the part of the spectrum from ultraviolet ( λ ≈ 100 nm ) to radio waves ( λ ≈ 10 m ) 1 . Meanwhile, a typical molecule There are a few examples of spectroscopic measurements in the XRay region. In these cases, the wavelength can be very small and the dipole approximation is not valid. http://www.monos.leidenuniv.nl 1 2 5.61 Physical Chemistry Lecture #34 is about 1 nm in size. Let us assume that the molecule is sitting at the origin. Then, in the 1 nm 3 volume occupied by the molecule we have: k·r ≈ k r ≈ 2p/(100 nm) 1 nm = .06 Where we have assumed UV radiation (longer wavelengths would lead to even smaller values for k·r ). Thus, k·r is a small number and we can expand the electric and magnetic fields in a power series in k·r : E(r, t ) ≈ E [ cos( k·0 ω t)+O( k·r) ] ≈ E cos( ω t) B(r, t ) ≈ B [ cos( k·0 ω t)+O( k·r) ] ≈ B cos( ω t) Where we are neglecting terms of order at most a few percent. Thus, in most chemical situations, we can think of light as applying two time dependent fields: an oscillating, uniform electric field (top) and a uniform, oscillating magnetic field (bottom) . This approximation is called the Dipole approximation – specifically when applied to the electric (magnetic) field it is called...
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 Spring '08
 greenwood
 Calculus, Physical chemistry, Photon, Magnetic Field

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