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Spectroscopy – study the interaction of matter and electromagnetic radiation.
• irradiate sample• measure scattering, absorption, or
emission in terms of measured parameters.
• interpret results.
= c/E = h
where h is Planck’s constant (6.63x10-34 J/s) and E is given as Joules. A mole of photons
therefore has an energy of ENA, where NA is Avagadro’s number (6.022x1023).
Visible light ~ 400-700 nmUV light ~ 200-400 nm
Quantum mechanics can be used to describe the spatial distribution of all matter (or at least for relatively simple systems like single electrons) in terms of discrete, quantized energy levels using solutions to the Schrödinger equation:
Hn = Enn
where (x, y, z) is a wave function that describes the position of a particle such as an electron as a distribution in space, H is the Hamiltonian operator that operates on the wave function to describe an observable property such as energy (E), and n is the quantum number that describes each of the quantized energy states for the system.
Quantum Mechanical Description of Matter
En hman
2 2
28
Soultions of the time-dependent Schrödinger equation can be used to describe the various energy levels of a system, i.e. for a particle in a one-dimensional box of width a, the energy levels can be described by
En (kcal/mol) = -(22e4)/((40)2h2n2) = -(1312)/n2
Quantum Mechanical Description of Matter
n = 1
n = 2
n = 3
While the energy levels of the hydrogen atom are more complex, they too can be described by quantum mechanics:
Note that each system is unique. The spacing of energy levels on the left is increasing as n increases, while the spacing decreases as n increases for the hydrogen atom above.
Etot = Etrans + Erot + Evib + Eelec + Ee-spin + Enuc
Energy levels of matter
Molecular Orbitals
nn
EkT
ex
gr
exp
Boltzmann Distribution
Describes the distribution of atoms among different energy states:
Selection Rules
• E = hv
• net displacement of charge
• e- spins stay opposite
s
p
AII
ct
log
10
0
Absorption of light – Beer-Lambert Law
z
y
x
d
d
cos
sin
sindd
sinsin
Photoselection
Anisotropy: Polarization:r = (I|| - I)/(I|| + 2I) P = (I|| - I)/(I|| + I) = 2P/(3 - P) = 3r/(2 + r)
For a single fluorophore:I|| cos2I sin2sin2 = ½sin2
Therefore, since cos2 + sin2 = 1r = ½(3cos2 - 1)
Fluorescence Polarization
Jablonski Diagram
Morse Diagram
Franck-Codon Principle
•Excitation vs. Emission Spectra
•Stoke’s Shift
•Invariance of emission spectra to excitation wavelength
Mirror Image Rule