Lucas Paquin CHEM 166A April 30 th , 2018 High Resolution Fourier Transform-Infrared Spectroscopy Introduction Spectroscopy probes transitions between different energy levels, or states, using light. Light in the infrared region of the EM spectrum can be used to probe vibrational and rotational transitions. The specific rotational and vibrational states are a result of the interactions between the different atoms in the molecule and, since each molecule has a unique arrangement of atoms, it has a unique IR spectrum almost like a fingerprint. In this lab, the spectra of HCl and DCl were obtained and analyzed. More specifically, the energy levels that are involved in the transitions that lead to each line of the spectrum were evaluated. The simplest model that considers rotational states is the rigid rotor (RR). This model considers two atoms at a fixed distance that rotate as a unit. The quantized energy levels of the rigid rotor are given in the following equation: h ¯ ¿ 2 2 I J ( J + 1 ) E J = ¿ (1) where J is the rotational quantum number that spans integers from 0 to ∞. The degeneracy of the J th quantum level is 2J+1. I is the moment of inertia, which is given by: I = μr 2 (2) where r is the distance between two atoms, and μ is the reduced mass, which is given by: μ = m a m b m a + m b (3) The simplest model for vibrations is the harmonic oscillator (HO). The vibrational levels for the harmonic oscillator are given by the following equation: E v = ( υ + 1 2 ) hv (4) where υ spans integers from 0 to ∞ and ν is the frequency of vibration. Transitions where Δυ=+1 and ΔJ=+1 are called the “R branch”, those where Δυ=+1 and ΔJ=−1 are called the “P branch”, and those where Δυ=+1 and ΔJ=0 are the “Q branch”. For
diatomic molecules the Q branch is a forbidden transition (rotation about the bond axis has no effect on the dipole moment) and is not observed in a spectrum (1) . As you count away from the center of the spectrum the intensity of individual lines increases, goes through a maximum and then falls off in the wings. This pattern arises from a combination of two effects, the population of molecules in a quantum state and the number of quantum states at a particular energy. The population in state J is given by the following equation: N ( J ) = N 0 ( 2 J + 1 ) e − B 0 J ( J + 1 ) kT (5)
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