Mie vs Rayleigh Sun
Chemists Probe Various Energy Levels of Molecules With Appropiate Energy Radiation It is convenient (and accurate enough for our purposes) to treat a molecule or system of molecules as a sum of component energies. Etotal = Etranslational + Erotation + Etranslational + Evibration + Eelectronic + Ee-Spin + Enuclear + Eother Energy associated with any one of the above have certain allowed energies that are quantized and can be associated, perturbed and probed by specific frequencies of EM radiation (energy).
Radiation-Induced Transitions (Absorptive (near resonance transitions) in molecules) Absorption Stimulated emission Spontaneous emission Rapid (10-15 s) Non-radiative process Absorption: A transition from a lower electronic state to a higher energy electronic state with transfer of energy from the radiation field to an atom or molecule(s). Emission: A transition from a higher level to a lower level with transfer of energy from the emitter to the radiation field. If no radiation is emitted, the transition from higher to lower energy levels is called nonradiative decay.
UV-Vis Transitions Occur Between Electronic States Sub-levels numbers represent vibrational levels within an electronic state. Discrete roto-vibronic modes within the electronic transition are smeared out due to collisions giving the appearance of a band.
Boltzman Distribution Determines the Population of the Energy Levels The relative population of molecules in either state is described by the Boltzmann equation. n upper = exp( E n lower k T ) E is the energy in Joules, k is Boltzman constant = 1.38 x 10-21 J K -1 and T is the temperature in Kelvin. E 4 E 2 E 0 1. ΔE << kt (populated upper states) 2. ΔE >> kt (most in ground state) Increasing T
Transition Energies Vs 1/2 kt at 300K Quantum mechanics yields the expressions for the electronic, vibrational, rotational and nuclear energy levels in molecules: The energies associated with various spectroscopic transitions can be summarized: Spectral Transition Electronic Vibrational Rotational 1/2 kt cm -1 20,000 2,000 10 100 kcal/mol 60 6 0.029 0.3 This tells us about the spacing of transitions and the populations
1. UV-Visible Spectroscopy (190-800 nm) Transitions between electronic states or molecular orbitals of molecules where distribution of electrons is altered. Useful to think of excited electronic state as an electronic isomer of the ground state. electrons are redistributed around stationary nucleui certain selection rules derived from quantum mechanics and molecular orbital theory allow and disallow electronic transitions in molecules. incident light must be near-resonance transition ground to excited states are coupled only by permanent or induced-dipole moment by E. the path connecting the ground and excited states (dipole moment integral) can be not be zero.
I 0 The Beer-Lambert Law of Absorption --Consider monochromatic light of intensity I0 passing through a sample (width = l) that absorbs light. Let I be the intensity of light a any arbitrary point z along a line parallel to the incident light beam. As the light passes through a slice dz it is found experimentally that the fractional change in intensity light (di /I ) is proportional to a constant (α) times the concentration of absorbing material and the length of the sample the beam passes through. di = α C dz Slice = dz I t log form It I I 0 di I = z = l z=0 ln I t I 0 = α C l α C dz Sample width = 1 exponential form I t = I 0 e α C l We normally re-cast this in base-10 log form
Beer-Lambert Law Change of base rule ln I t I 0 = α C l log a x = log b x log b a log e T = log T log e = log T 0.43429 = α C l I0 It log T = A = ɛ C l A = absorbance = log(i o /I) = -log(t) I 0 = intensity of incident light I = intensity of transmitted light ε = molar absorptivity coefficient in cm -1 M -1 (= 0.43429 α) C = concentration in M l l = path length of absorbing solution in cm -1 http://www.hellma-worldwide.de/en/default.asp
Transmittance and Absorbance Linear and Convenient Concentration Concentration An absorbance of 1 is 10 x reduction in transmittance