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Spectra of Diatomic Molecules, a Summary Molecular Physics, Wolfgang Demtroder Questions regarding this topic are in red belowโฆ. 1. Between which pairs of molecular states can transitions take place by absorption or emission of electromagnetic radiation? 2. What is the transition probability and what are the factors by which it is determined? 3. What are the spectral profiles of emission or absorption lines for such a transition? Einstein Coefficients Absorption: The Probability Stimulated Emission Spontaneous Emission ๐๐๐๐ ๐๐ก ๐๐๐๐ ๐๐ก ๐๐๐๐ ๐๐ก = ๐ต๐๐ ๐(๐ฃ ๐๐๐ ๐ต๐๐ = ๐ต๐๐ ๐(๐ฃ ๐ ๐ก๐๐ = ๐ด๐๐ ๐ด๐๐ ๐๐ = ๐ต ๐๐ ๐๐ 8๐โ๐ 3 = ๐ต๐๐ ๐3 ๐ ๐๐๐ Note: ๐๐๐๐ ๐๐ก Indicates probability per unit time can be larger than one! ๐ด๐๐ (3๐ โ 3๐ ) โ 108 ๐ โ1 For sodium Average Power Dipole Moment Classical: Quantum Mechanical: ๐ = ๐ ๐ = ๐0 si n( ๐๐ก) โ ๐ = ๐ ๐ = ๐ ๐น๐ ๐ ๐น๐ ๐๐ dipole moment of a stationary state 2 ๐2 ๐4 ๐= 3 4๐๐0 ๐ 3 โ ๐ท๐๐ = ๐ ๐น๐ ๐ ๐น๐ ๐๐ ๐๐๐ With ๐2 = 1 2 ๐ 2 0 4 ๐๐๐ 4 = ๐ท 3 4๐๐0 ๐ 3 ๐๐ power emitted For a transitionAverage both states must in the transition contribute = transition dipole moment We replace the classical average ๐ 2 by the quantum mechanical expression 1 ๐ท๐๐ + ๐ท๐๐ 2 = 2 ๐ท๐๐ 2 2 โข Although the fluorescence intensity of a single molecular โข dipole has an angular distribution I(theta)a sin(theta), where theta is the angle between the dipole axis and the direction of observation, the total emission from N molecules with random orientations in space is isotropic. Electric Dipole Transition for N atoms atoms radiate Vibration-Rotation Transitions Selection Rule: 1 Vibrational Bands R-band P-band During a transition between different vibrational states the internucleus distance changes and thus also the rotational constant Difference of vibrational levels without rotation Electronic Transitions,Franck-Condon Factors Example โข For R-branch with โข For P-branch with Frank-Condon Factors Spectral Line Shapes Classical Model Doppler Shift Gaussian Profile Voigt Profile Collisional Broadening Effects of Elastic and Inelastic Collisions Two-Photon Transitions Multi Photon Transitions Inelastic scattering: Raman Scattering