Absorption, Emission and Fluorescence Spectroscopies Chem M3LC. R. Corn
Review: Light behaves like an electromagnetic wave... 2.998 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 1857-1894
Review: But light also behaves like a particle! We call the particles photons, each with a energy given by: h = Planck's constant 6.626 10 34 Joule sec Max Planck 1858-1947
Review: Atoms have quantized energy levels and can absorb and emit photons of energy equal to the difference in energy between two levels E = hν Grotrian diagram for Hydrogen
Review: 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 hν E = hν HOMO M + hν M*
Absorption Spectroscopy measures the amount of light absorbed by a sample by this process. M + hν M* Transmittance: Absorbance: T = P/P0 A = log(p0/p) Absorbance is proportional to Concentration For atoms: Atomic Absorption Spectroscopy For molecules: Molecular Absorption Spectroscopy
The Fe(II)-Ferrozine complex absorbs light in the visible. Ferrozine (Fz 2- ) Fe 2+ + 3 Fz 2- => Fe(Fz)3 4- We can use the absorption band to measure Fe(II) in solution.
The Absorption Spectrum plots the amount of light absorbed by a sample as a function of photon wavelength. Absorption spectrum
Beer s Law relates the amount of light absorbed by a sample to the concentration of the absorbing species. Absorbance A = log(p0/p) Beer s Law: A = εbc b = pathlength (in cm) c = concentration (in M) ε = molar absorptivity (units of M -1 cm -1 )
Thus, we can measure the concentration of a species by measuring the Absorbance at a particular wavelength. Beer s Law: A = εbc Abs Concentration (nm) Linear Calibration Curve: y = mx y = Absorbance m = εb x = Concentration
Just measure the Absorbance, and calculate the Concentration! Beer s Law: A = εbc Abs Text Concentration (nm) Concentration = Abs/εb = y/m = 1800 nm We need to calculate m.
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!
We can also calculate the slope and intercept standard deviations from the set of summations: sr is used to calculate sm and sb
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)
Finally, here are the (somewhat complex) equations for calculating the standard deviation and confidence interval when using the calibration curve.
Metal-Ligand Complexation Equilibria Fe 2+ + 3 Fz 2- => Fe(Fz)3 4- Kf Chem M3LC R. Corn Kf = formation constant Ferrozine (Fz 2- ) is a metal ligand Three Ferrozine will form a metal-ligand complex with Fe 2+
Ba 2+ forms a complex with methylthymol blue (MTB 5- ): MTB 5- MTB: abs. max @ 460 nm Ba-MTB complex: abs. max @ 610 nm
Barium-MTB Complexation Equilibrium: Kf is the Ba-MTB Formation Constant C tot is the total Barium Concentration
Alpha Fractions for free and complexed Ba2+
Alpha plot for Barium-MTB complex
Metal-Ligand Complexation Equilibria Fe 2+ + 3 Fz 2- => Fe(Fz)3 4- Let s calculate the alpha fraction for Fe 2+ : Kf Kf = formation constant
Metal-Ligand Complexation Equilibria Fe 2+ + 3 Fz 2- => Fe(Fz)3 4- Let s calculate the alpha fraction for Fe 2+ : Kf Kf = formation constant
Alpha plot for Iron-Ferrozine complex
Metal Complex Formation Constants Weak Metal Complex Formation Constants have similar values of K1 to Kn Therefore, many species co-exist in solution!
EDTA Metal Ion Complexation Equilibria Ethylene Diamine Tetra-acetic Acid (H4Y) EDTA - the world s best metal ion chelator Y 4- Chelate
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
The Emission Spectra of H, He and Hg.
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
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
The Fluorescence Spectrum plots the amount of light absorbed 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.
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 )
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... (εbc)n ( ' * & 3! (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.
Fluorescence Spectroscopy The absorption and fluorescence spectra of riboflavin. riboflavin absorption fluorescence
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 # 1 2 3 4 5 x 0 1 2 3 4 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.
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.
Hydroxyquinoline: a metal chelator that fluoresces upon binding! Mg 2+ 8-hydroxyquinoline-5-sulfonic Acid Fluorometric Detection of Mg 2+ in Seawater
Hydroxyquinoline: a metal chelator that fluoresces upon binding! 8-hydroxyquinoline Trivalent Cations Mg Divalent Cations
EDTA Metal Ion Complexation Equilibria Ethylene Diamine Tetra-acetic Acid (H4Y) EDTA - the world s best metal ion chelator Y 4- Chelate
EDTA titrations for metal ions pca pca or pmg can be used to determine the titration endpoint.