Homework Help
Homework Help
View Details
Assignment Help
Assignment Help
View Details
Online Tutoring
Online Tutoring
View Details
Home » Chemistry Homework Help » Physical Chemistry » Einstein Coefficient
Einstein Coefficient
The absorption and emission of radiation are related through the Einstein coefficients.

A molecule of a liquid, like the 2-butanone molecules that produce the absorption band is involved in nearly continuous energy exchanging processes with neighboring molecules. The energy that a molecule gains from the incident radiation is quickly degraded into the thermal energy of the solution.

The consequences of the absorption into the thermal energy can be studied if we imagine the absorbing molecules to be noninteracting gas phase species in a radiation environment. To investigate this situation, we first describe the radiation environment in a nearly enclosed oven, or cavity.

A cavity acts as a blackbody, a term that implies that no frequency regions have particular tendencies to absorb or emit radiation, and tendencies that would lead to a particular colour. The nature of the radiation emitted from such a cavity was deduced to a particular colour. The nature of the radiation was deduced by Max Planck in the early stages of the development of quantum mechanics. The idea that the cavity radiation is in equilibrium with the particles led Planck to express the density of radiation in the cavity as
 
pv = 8∏hv3/c3/ehv/(kT) – 1

This equation leads to an expression for the distribution of energy in the radiation that emerges from a cavity that is in complete agreement with experimentally obtained blackbody radiation is completely specified by the temperature. An example of the radiation emitted from a cavity at 6000 K, the approximate temperature of the surface of the sun, is illustrated.

Einstein coefficients: now we investigate, as Einstein did, the affairs of a molecule that is in, and is affected only by, the radiation of the cavity treated above. The particles with which we deal are in equilibrium with the radiation and, like the wall particles, are distributed throughout their allowed states according to the Boltzmann distribution. The population of the l and m states is given by:

Nm/ Nt = e – hv/m/kT Where hvtm is the energy separation between these states.
 
The population of the higher energy m state will be less than that of the lower energy l state.

Assume that the molecules within the cavity can absorb radiation and are thereby brought from the l quantum state. Einstein recognized that the equilibrium reached by the molecules in the cavity can be described on the basis of the three processes. The rtes of the processes are expressed in terms of Einstein coefficients. The Einstein coefficients for induced absorption and for included emission are represented by B, that for spontaneous emission by A. the coefficients for the induced transitions depend, as the two quantum states and on a transition operator that is not dependent on the direction of the radiation.

The Einstein coefficients determine the rate of the various transition processes by the expressions. If the three processes are the only effective processes, at equilibrium the rate of l = m transitions must equal the rate of m l transitions. We can write with Bml = Blm,

Blm Ni p (vlm) = Blm Nm p (vlm) + Aml Nm

Rearrangements lead to:

Nm/Ni = Blm p(vlm)/Blm p(vlm) + Aml

Relative rates of spontaneous and induced transitions for molecules in a cavity at 6000 K:
   
  Rotational Transitions
(vlm = 1010 Hz)
Electronic transitions
(vlm = 1015 Hz)
Aml//Blm 6.2 × 10-28 6.2 × 10-13
P(vlm) 7.7 × 10-24 2.1 × 10-16
Aml/[p(vlm)Blm] 8.0 × 10-5 3.0 × 103

Services:- Einstein Coefficient Homework | Einstein Coefficient Homework Help | Einstein Coefficient Homework Help Services | Live Einstein Coefficient Homework Help | Einstein Coefficient Homework Tutors | Online Einstein Coefficient Homework Help | Einstein Coefficient Tutors | Online Einstein Coefficient Tutors | Einstein Coefficient Homework Services | Einstein Coefficient


   



       
       
       



Submit Your Query ???
Topics
Covalent Radii Crystal Shapes, Point Groups Diffraction Pattern Assignments Electron Diffraction Ionic Radii Lattice Energies Diffraction Lattices, Unit Cells Neutron Diffraction Waals Radii X-ray Diffraction Bond Moments Electric Capacitor Atoms, Molecules Properties Paramagnetism Electrolytic Dissociation Solution Ionic Strength Solvent Dielectric Effect Electrolysis Solutions Ionic Mobilities Electrolytes In Solutions Solutions Molar Conductance Solutions Specific Conductance Electrochemical Cell EMF Electrodes Ion Selective Electrodes Junction Potentials Cells Electromotive Force Standard Electrode Potentials Collision Theory Gas Viscosity Theory Elementary Reactions Lasers Molecule-Molecule Collisions Electrochemical Cell Photochemical Quenching Surface Decompositions Atomic Molecular Energies Molecular Energies Particle-in-a-box Particle-on-a-line Rotational Energies Schrodinger Wave Equation De Broglie Wave Length Vibrational Energies Waves And Particles Boltzmann Distribution Gas Heat Capacities Metals Heat Capacities Molecules Collection Energies One Dimensional Motion Partition Function Rotational Motions Thermal Energy Three Dimensional Motion Vibrational Motions Aqueous Ion Energies Bond Energies Chemical Systems Energy Enthalpy, Chemical Reactions Chemical System Enthalpy Thermodynamics First Law Heat Capacities Thermodynamics Molecular Thermal Energy Standard Enthalpy Substance Carnot Cycle Absolute Zero Entropies Entropy Thermodynamics Laws Entropy Molecular Basis Third Law Molecular Basis Rotational Energy Thermodynamics Second Law Thermodynamics Third Law Vapourization Entropy Vibrational Entropy Equilibria And Distributions Real Gases Equilibria Free Energy Equilibrium Constant Free Energy And Pressure Free Energy, Temperature Free Energy Function Free Energy Real Gases Free Energy Fugacity Non-ideal Gases Fugacity Thermodynamic Properties Chemical Equilibria Boyle Gas Pressure Continuity Of States Critical Point Gas Mixtures Kinetic Molecular Theory Gases-Properties, Theories Molecular Energies, Speed Molecular Interactions Real Gas PVT Temperature Volume Waals Gases Behaviour Waals Critical Point Molecular Diameters Virial Equation Diffusion Coefficient Diffusion Molecular View Donnan Membrane Equilibria Electrophoresis Macromolecular Dynamics Average Mass Range Solution Viscosity Sedimentation And Velocity Colloids Macromolecules Micelles Adsorption Isotherm Adsorption Of Gases Boiling Point Diagrams Pressure Temperature Relation Distillation Eutectic Formation Immiscible Liquids Phase Equilibria Liquid Surfaces Phase Rule Pressure Phase Diagrams Solid Compound Foundation Surface Tension Vapour Pressure Three Component System Vapour Pressure Composition Atomic States Bohr Atom Electron Spin Angular Momentum Hydrogen Hydrogen Atom Spectra Hydrogen Radical Factor Quantum Atomic Structure Quantum Mechanical Operators Variation Theorem Enzymes Catalyzed Reactions First Order Rate Equations Flash Photolysis Chemical Reactions Mechanism Enzyme Reactions Mechanism Reactions Mechanisms Photochemical Reactions Rate Equation Second Order Rate Equations Temperatures And Rates Unimolecular Gas Reactions Absorption Coefficient Einstein Coefficient Electromagnetic Induction Electronic Spectra Electron Spin Spectroscopy Infrared Adsorption Spectroscopy Microwave Absorption Nuclear Spin States Nuclear Magnetic Resonance Photoelectron Spectroscopy Polyatomic Vibrational Spectra Rotational Vibrational Spectra Conjugated Systems Spectra Transition Moment Character Tables Symmetry Group Theory Molecular Symmetry Types Orbital Symmetries Point Groups Reducible Representation Symmetry Elements, Operations Molecular Properties Symmetry Transformation Matrices Diatomic Molecule Orbitals Electronegativity Hybridization Hydrogen Molecule Ion Ionic Bond Molecular Orbitals Orbitals Pie Electrons Two Electron Bond Virial Theorem Partial Molal Properties Solute Free Energy Ideal Mixtures Solution Thermodynamic Property Liquid Vapour Free Energies Osmotic Pressure Partial Molal Quantities Solvent Free Energy Vapour Pressure Lowering