Absorption, Emission and Fluorescence Spectroscopies. R. Corn - Chem M3LC
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1 Absorption, Emission and Fluorescence Spectroscopies R. Corn - Chem M3LC
2 Light behaves like an electromagnetic wave x 10 8 meters/sec λ = the Greek letter lambda ν = the Greek letter nu velocity = wavelength x frequency meters/sec = (meters) x (sec) -1 The units (sec) -1 are called Hertz (Hz)! Heinrich Hertz
3 By the way, we use light to define time and space: The definition of one second: Light produced by the transition between the two hyperfine ground states* (F=3 and F=4) of Cesium is defined as having a frequency of exactly 9,192,631,770 Hz. The definition of one meter: The speed of light is defined as exactly 299,792,458 meters/second. Thus a meter is defined as the length of the path travelled by light in vacuum during a time interval of 1/(299,792,458) of a second (about 3.33 nanoseconds) *Cesium Ground State: [Xe]6s1 S=1/2 L=0 J= 1/2 ==> 2S1/2 (doublet S 1/2) Nuclear Spin I = 7/2; F = J + I = 4 or 3. These are the two hyperfine levels of the ground state of the Cesium atom. This is the basis of the atomic clock.
4 But light also behaves like a particle! We call the particles photons, each with a energy given by: E photon = hν = hc λ h = Planck's constant Joule sec Max Planck
5 Three Spectroscopic Processes: Absorption: M + hν M* Emission: M* M + hν Fluorescence: M + hν M* M + hν hν > hν
6 Atomic Absorption Spectrometry Atoms have quantized energy levels and can absorb and emit photons of energy equal to the difference in energy between two levels. ΔE = hν = hc λ Grotrian diagram for Hydrogen
7 Molecules also have quantized energy levels too, and can absorb and emit photons of energy equal to the difference in energy between two levels: LUMO Molecular Absorption Spectrometry hν ΔE = hν HOMO M + hν M* Ferrozine (Fz 2- )
8 The Fe(II)-Ferrozine complex absorbs light in the visible. Fe Fz 2 Fe(Fz) 4 3 Ferrozine (Fz 2- ) 3 Ferrozine for every Fe 2+. We can use absorption at a specific wavelength to measure Fe(II) in solution. "Colorimetry"
9 Absorption Spectroscopy measures the amount of light absorbed by a sample. Transmittance T = P P 0 Absorbance M + hν M* Beer s Law: A = ϵbc A = logt = log P 0 P ε = molar absorptivity (units of M -1 cm -1 ) b = pathlength (in cm) C = concentration (in M)
10 The Absorption Spectrum plots the amount of light absorbed by a sample as a function of photon wavelength. monochromator can come either before or after the sample Absorption spectrum: Absorbance vs. wavelength
11 The Absorption Spectrum plots the amount of light absorbed by a sample as a function of photon wavelength. monochromator can come either before or after the sample choose this λ Absorption spectrum: Absorbance vs. wavelength
12 We can measure the concentration of a species by measuring the Absorbance at a particular wavelength. Beer s Law: A = ϵbc A Concentration (nm) Linear Calibration Curve: y = mx y = Absorbance m = εb x = Concentration
13 Using the Standard Curve with Unknowns Just measure the Absorbance, and calculate the Concentration! Beer s Law: A = ϵbc Abs Concentration (nm) Concentration = Abs/εb = y/m = 1800 nm We need to have calculated m.
14 Equations for Fitting a Linear Calibration Curve (y = mx + b) from a set of N (x,y) data points: * m and b can be calculated from this set of summations *note: the intercept b is not the pathlength b!
15 We can also calculate the slope and intercept standard deviations from the set of summations: sr is used to calculate sm and sb
16 We also can calculate 95% confidence intervals for the slope and intercept from the standard deviations: Note that the d.o.f. is N-2 (we calculate slope and intercept)
17 Finally, here are the (somewhat complex) equations for calculating the standard deviation and confidence interval when using the calibration curve.
18 Metal-Ligand Complexation Equilibria Fe Fz 2 Fe(Fz) 4 3 Kf = Kf = formation constant Three Ferrozine will form a metal-ligand complex with Fe 2+ Ferrozine (Fz 2- ) is a metal ligand
19 Metal-Ligand Complexation Equilibria Fe Fz 2 Fe(Fz) 4 3 Kf = Kf = formation constant K f = [Fe(Fz)4 3 ] [Fe 2+ ][Fz 2 ] 3 C tot Fe(II) = [Fe2+ ] + [Fe(Fz) 4 3 ] C tot Fe(II) = Total Fe(II) in solution
20 Alpha Fractions - Chemical Speciation in Solution Fe Fz 2 Fe(Fz) 4 3 Kf = C tot Fe(II) = [Fe2+ ] + [Fe(Fz) 4 3 ] Alpha fractions: α Fe 2+ + α Fe(Fz) 4 3 = 1 α Fe 2+ = [Fe2+ ] C tot Fe(II) α Fe(Fz) 4 3 ] CFe(II) tot 3 = [Fe(Fz)4 C tot Fe(II) = Total Fe(II) in solution
21 Let s calculate the alpha fraction for Fe 2+ : Fe Fz 2 Fe(Fz) 4 3 Kf = only depends on Kf and [Fz 2- ]!
22 Let s calculate the alpha fraction for Fe 2+ : Fe Fz 2 Fe(Fz) 4 3 Kf = For example: [Fz 2 ] = 10 3 M α Fe 2+ = 10 6 only depends on Kf and [Fz 2- ]!
23 Alpha plot for Iron-Ferrozine complex α Fe(Fz) 4 3 α Fe 2+ Kf = 10 15
24 Metal Complex Formation Constants Weak Metal Complex Formation Constants have similar values of K1 to Kn Therefore, many species co-exist in solution!
25
26 EDTA Metal Ion Complexation Equilibria Ethylene Diamine Tetra-acetic Acid (H4Y) EDTA - the world s best metal ion chelator Y 4- Chelate
27 Absorption versus Emission Absorption is the process that consumes a photon and puts the atom or molecule in an excited state. M + hν M* Emission is the process that creates a photon and takes the the atom or molecule in an excited state back to the ground state. M* M + hν
28 The Emission Spectra of H, He and Hg.
29 Fluorescence Spectroscopy Fluorescence is the process that first consumes a photon and puts the atom or molecule in an excited state... M + hν M* And then emits a photon of lower energy which takes the the atom or molecule back to the ground state. M* M + hν hν > hν
30 Fluorescence Spectroscopy Net reaction: M + hν M* M + hν hν > hν The emitted photon has less energy than the absorbed photon because the molecule loses some energy (by vibrating and rotating) in the excited state: M* hν M
31 The Fluorescence Spectrum plots the amount of light emitted by a sample as a function of photon wavelength. P0 P PF P0 = power of incident light beam (units: W) P = power of transmitted light beam. PF = power of emitted fluorescence.
32 Quantitative Fluorescence Spectroscopy The power of the emitted fluorescence is proportional to the absorbed power, P0-P: where ΦF, the quantum yield, is: Φ F = substituting from Beer s law: P F = Φ F (P 0 P) photons emitted photons absorbed P F = Φ F P ( 0 1 e εbc )
33 Quantitative Fluorescence Spectroscopy P F = Φ F P ( 0 1 e εbc ) the exponential here can be expanded as follows: % P F = Φ F P 0 εbc' 1 εbc 2! + (εbc)2 & 3!... (εbc)n ( * (n +1)! ) and just the first term here is significant for small εbc: P F = Φ F P 0 εbc PF is proportional to concentration at small εbc.
34 Fluorescence Spectroscopy The absorption and fluorescence spectra of riboflavin. riboflavin absorption fluorescence
35 Method of Standard Addition You can determine the concentration of an unknown solution C by fluorescence using the method of standard addition. 1. Make five solutions C + n where n= 0 to 4 2. Measure the fluorescence from these five solutions and record the values F0 to F4. This leads to five (x,y) data points: (C, F0), (C +, F1), (C + 2, F2), (C + 3, F3), (C + 4, F4). 3. Graph the following five (x,y) data points: Point # x y F0 F1 F2 F3 F4 (0, F0), (, F1), (2, F2), (3, F3), (4, F4). We will get a straight line that can be fit with the linear equation y = mx + b.
36 Method of Standard Addition This line is the same line as a standard calibration curve, but shifted to the left by an amount equal to C. To get the value of C, we set y=0 and calculate the value for the x intercept x0 = x at y=0: x0 = b/m = -C therefore: C = b/m in units of. From Wikipedia.
37 Hydroxyquinoline: a metal chelator that fluoresces upon binding! Mg 2+ 8-hydroxyquinoline-5-sulfonic Acid Fluorometric Detection of Mg 2+ in Seawater
38 Hydroxyquinoline: a metal chelator that fluoresces upon binding! 8-hydroxyquinoline Trivalent Cations Mg Divalent Cations
39 EDTA Metal Ion Complexation Equilibria Ethylene Diamine Tetra-acetic Acid (H4Y) EDTA - the world s best metal ion chelator Y 4- Chelate
40 EDTA titrations for metal ions pca pca or pmg can be used to determine the titration endpoint.
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