Spectroscopy Lecture 1 PDF
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Uploaded by AstoundingGlockenspiel
Ain Shams University
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Summary
This document is a lecture on molecular spectroscopy, covering the interaction of electromagnetic radiations with matter. It discusses different types of molecular spectroscopy, including pure rotational, vibrational, and electronic spectroscopy. The concepts of absorption and emission are also introduced. The lecture then focuses on rotational spectra, providing the essential conditions, quantum mechanical selection rule, and a detailed explanation on a diatomic molecule's rotational spectra.
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# Molecular Spectroscopy - The study of interaction of electromagnetic radiations with matter is called Molecular spectroscopy. ## Types of Molecular Spectroscopy: - Pure rotational (Microwave) spectra - Vibrational (Infrared) spectra - Electronic (UV) Spectra - Raman Spectra - Nuclear Magnetic...
# Molecular Spectroscopy - The study of interaction of electromagnetic radiations with matter is called Molecular spectroscopy. ## Types of Molecular Spectroscopy: - Pure rotational (Microwave) spectra - Vibrational (Infrared) spectra - Electronic (UV) Spectra - Raman Spectra - Nuclear Magnetic Resonance (NMR) spectra - Electron Spin Resonance (ESR) Spectra ## Two Components of EM Radiation - Electrical field (E): varies in magnitude in a direction perpendicular to the direction of propagation. - Magnetic field (M): at right angle to the electrical field, is propagated in phase with the electrical field. - Wavelength (λ): distance from one wave crest to another. - Frequency (v): No. of crests passing a fixed point/ given time. - Amplitude: height of each peak (watts/sq. meter). - The speed of EM energy “c” 300,000km/second, c = νλ where λ and v are inversely related. ## Interaction of Electromagnetic Waves with Matter - **Absorption:** - When a particle in a lower energy state absorbs a photon of energy (hν) and moves to a higher energy state. - The energy difference between the two states (ΔE) is equal to the energy of the absorbed photon (ΔE = hν ). - **Emission:** - When a particle in a high energy state emits a photon of energy (hν) and moves to a lower energy state. - The energy difference between the two states (ΔE) is equal to the energy of the emitted photon (ΔE = hν). ## Types of Molecular Spectra - **Pure Rotational Spectra:** These are related to the rotation of molecules - **Vibrational Rotational Spectra:** These are related to the vibration of molecules - **Electronic Band Spectra:** These are related to the electronic transitions in molecules ## Rotational Spectra - Microwaves are used to study rotational spectra. ### Molecular Energy Levels - High energy - Electronic levels - Vibrational levels - Rotational levels - Ground state (S<sub>O</sub>) - Low energy ## Rotational Spectra of a Diatomic Molecule - **Essential condition:** The molecule must have a permanent dipole moment. - **Quantum Mechanical Selection Rule:** Only those rotational transitions are allowed for which ΔJ = +1. All other transitions are forbidden. - **Explanation:** Consider a diatomic molecule rotating about its center of gravity (C.G) - r = the bond length - m<sub>1</sub>= the mass of one atom - m<sub>2</sub>= the mass of another atom - r<sub>1</sub>= the distance of the atom 1 from the C.G - r<sub>2</sub>= the distance of the atom 2 from the C.G - at center of gravity: m<sub>1</sub>r<sub>1</sub>= m<sub>2</sub>r<sub>2</sub> - The moment of inertia I of a molecule is I = μr² where µ = reduced mass of the molecule = m<sub>1</sub>m<sub>2</sub> / m<sub>1</sub>+m<sub>2</sub> - According to classical mechanics, the angular momentum (L) of a rotating molecule is L = Iω , where ω = angular velocities - According to quantum mechanics, L = √J(J+1)h/2π , where J = rotational quantum number = 0, 1, 2, 3..... - The energy of rotating molecule is E<sub>J</sub>= J(J+1)h<sup>2</sup>/8π<sup>2</sup>I - **Rotational spectra** is shown by: - Gaseous polar molecules (e.g. HCl, H<sub>2</sub>O, HBr, CO, NO) - Heteronuclear diatomic molecules - Microwave active - Non - Polar molecules (e.g. H<sub>2</sub>, Cl<sub>2</sub>, N<sub>2</sub>, O<sub>2</sub>) - Homonuclear diatomic molecules - Microwave inactive ## Selection Rules for Rotational Transitions - The molecule must have a permanent dipole moment. - Only those rotational transitions are allowed for which ΔJ = +1. - The frequency of rotation is higher for lighter molecules (lower moment of inertia) than for heavier molecules (higher moment of inertia). ## Rotational Spectra of Diatomic Molecule (Continued) - The rotational spectrum of a rigid diatomic molecule appears at the following rotational frequencies 2B, 4B, 6B, 8B, etc.. And each appears as lines in the detector. These lines are equally spaced by 2B. - The interspaceial distance of the spectral lines is 2B - Lines in a pure rotational spectrum are equally spaced by 2B. ## Rotational Spectra of Diatomic Molecule (Continued 2) **E<sub>J</sub> = BJ(J+1)** - J=0, E<sub>J</sub> = 0 - J=1, E<sub>J</sub> = B1(1+1)= 2B - J=2, E<sub>J</sub> = B2(2+1)= 6B - J=3, E<sub>J</sub> = B3(3+1)= 12B Spacing between adjacent lines = 2B. So, B can be obtained from the spacing between rotational lines.
