1. Transition dipole moment

Transcription

1 1. Transition dipole moment You have measured absorption spectra of aqueous (n=1.33) solutions of two different chromophores (A and B). The concentrations of the solutions were the same. The absorption spectra have similar shape but the spectrum of A is 1.2 times broader than the spectrum of B. Maximum optical density A is 1.67 times larger than that of B. The absorption reaches is maximum at ν max = cm -1. Fluorescence lifetime τ fl (A) = 1 ns; fluorescence yield Φ fl (A) =Φ fl (B)= 0.3; a) Calculate the transition dipole moment of A in Debye (µ A =?) b) Calculate the transition dipole moment of B in Debye (µ B =?) c) Calculate fluorescence lifetime of B (τ fl (B) =?) 2. Jablonski diagram/sms Jablonski diagram of a dye molecule is given at the figure. The rates are: k IC = 0.5 ns -1 k fl = 0.5 ns -1 k ISC = 0.25 ns -1 k T = 0.1 ms -1 a) Calculate Φ fl ; Φ ISC ; Φ IC b) Fluorescence intensity of a single molecule of this dye is monitored by a fluorescence microscope. Fluorescence blinking is observed. What is the characteristic time the molecule stays in dark, non-fluorescent states? 3. Fluorescence decay Fluorescence decay of a sample without quencher (Φ fl =1) is shown at the figure. a) What is the fluorescence radiative lifetime of the chromophores? b) A dynamic quencher was added to the initial sample so that Φ fl =0.33; Draw the fluorescence decay at the same graph c) A static quencher was added to the initial sample. 50% of all dye molecules form complexes with the quenchers. Draw the fluorescence decay at the same graph d) To the solution obtained in (c) a dynamic quencher was added so that the fluorescence lifetime become 1 ns. Draw the fluorescence decay at the same graph e) Calculate fluorescence quantum yield for the case d)

2 4. Electron transfer Molecules of a dye are attached to TiO 2 nanoparticles via a spacer. Changing the spacer allows to change the distance r between the dye and the particle. When the dye is close to the nanoparticle an electron transfer reaction occurs. The distance parameter of electron transfer β=10 nm -1. For r=0.2 nm the electron transfer rate k ET = s -1. The free dye in solution has fluorescence lifetime τ fl = 1 ns and fluorescence quantum yield Φ fl = 0.5. a) Calculate Φ fl and τ fl for r = 0.2 nm b) Calculate k EL, Φ fl and τ fl for r = 1 nm 5. Förster energy transfer Donor (D) and acceptor (A) chromophores are separated by distance r= 4.24 nm. The orientation of the transition dipole moments of the molecules are shown at the figure where α=45 o. Molecules of D without A has fluorescence yield Φ D =1 and fluorescence lifetime τ D =4 ns Molecules of A without D has fluorescence yield Φ A =1 Förster radius for energy transfer from D to A for random orientations of the molecules is R 0 Random =5 nm For the pair of molecules shown at the figure calculate: a) Förster radius R 0 b) Efficiency of energy transfer from D to A c) Fluorescence lifetime of the donor 6. Fluorescence anisotropy Your sample (a frozen solution of a chromophore) has two strong absorption bands (see the figure). The one at 350 nm corresponds to absorption to S 2 state; the other at 550 nm is absorption to S 1 state. So, you can excite fluorescence by excitation via 350 band or 550 nm band. You know, that the transition dipole moment of optical transition between S 0 and S 1 is perpendicular to the dipole moment of optical transition between S 0 and S 2. a) What will be the fluorescence anisotropy when excited at 550 nm? b) What will be the fluorescence anisotropy when excited at 350 nm? c) You increase the temperature and the solvent become liquid. Fluorescence lifetime is 4 ns; rotation correlation time of the molecules is 1 ns at these conditions. Calculate fluorescence anisotropy for 550 and 350 nm excitation wavelengths.

3 7. Practical Spectroscopy You have 2 spectra of a sample obtained with different excitations (λ ex1 and λ ex2 ) with a grating spectrometer (see the figure). The excitation light is a narrow laser line (linewidth < 0.1 nm). The resolution of the spectrometer is 0.1 nm. a) Identify the features in the spectrum (second order of light diffraction on the grating; Raman scattering, fluorescence) b) Determine λ ex1 and λ ex2 c) Calculate the frequency (in cm -1 ) of the molecular vibration giving the Raman line observed in the spectra d) Draw how the spectrum A would look like if the both slits of the spectrometer are increases up to 5 mm. Liner dispersion is dx/dλ=1 mm/1nm. Draw the spectrum at the same graph where the spectrum A is shown. 8. Lasers What should be the output mirror reflectivity to reach critical inversion of 2*10 17 cm -3 for a 9 cm long laser media with the cross-section of 4*10-19 cm 2 and a regular highly reflecting mirror (R=0.999)? 9. Coherent techniques Consider three Gaussian Fourier-transform limited pulses. The spectrum of one pulse is centered at 500 nm with FWHM of 35 nm, the second is centered at 700 nm with FWHM of 75 nm and the third is centered at 900 nm with FWHM of 110 nm. Which pulse is the shortest and which is the longest? 10. Quantum mechanics We have a coherent state: α = exp n 1 2 α ( α ) n 2 n n! Explain the physical meaning of the parameter α. Explain why in most of the laser experiments one can describe the laser generated electric field classically. Calculate the probability of finding n photons in the single-mode coherent state. 11. Surface science and spectroscopy The conventional three dimensional FCC (face centered cubic) unit cell of copper has a lattice constant of 3.61 Å (length of the cube). Draw a two dimensional surface unit cell for the (100), (110) and (111) surfaces and determine the size of the unit cell.

4 To problem 1 ε A B 2000 ν To problem 2 k ISC S 1 T 1 k IC k 0 fl k T S 0 To problem 5 D α A α r To problem 6 Absorptio Fluorescenc λ

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