Order Basic Optical Principles Assignment

Order Basic Optical Principles Assignment
1.1 Orbitals have regions in which they have negative and positive signs.
Explain the physical background of the signs and how this relates to the
probability of finding electrons at a certain place.
1.2 Spectroscopists often describe energies that are necessary to excite certain
electronic states by the wave number of the corresponding photons in
units of cm1
. Why is this more advantageous than describing the corresponding energies in units of the photons wavelength?
1.3 Try to estimate the shape of the possible molecular π-orbitals of the molecule hexatriene (CH2ˆCH-CHˆCH-CHˆCH2). How many nodal
planes does each orbital have? What is the energetic order of these orbitals? Which orbitals are the HOMO and LUMO orbitals?
1.4 What are important prerequisites before a photon can be absorbed by a
molecule?
1.5 Figure 1.6 shows schematically four π-wave functions of the molecule
anthracene. Sketch the transition density for a transition between the
states f and g. In what direction relative to the molecular axis is the transition dipole moment orientated?
1.6 Figure 1.5 shows schematically the π-wave functions of the molecule
butadiene. Which of the following transitions of butadiene are dipole
allowed:
a) The π1®π4* transition?
b) The π1®π3* transition?
c) The π2®π3* transition?
1.7 Describe in general the important factors that govern the shape of
absorption and fluorescence spectra of molecules in a liquid environment.
1.8 The probabilities of finding nuclei at certain positions can be calculated
from vibrational wave functions (1.6) in the same way as the probabilities
of finding electrons at certain positions can be calculated from electronic
wave functions. Figure 1.10 shows schematically the probabilities of finding nuclei at certain positions relative to their equilibrium position for
Order Basic Optical Principles Assignment
v´ =0, 1, 2. Try to guess what the corresponding vibrational wave functions look like.
1.9 Describe in general the factors that determine the probabilities for fluorescence, internal conversion and intersystem crossing of molecules in a
liquid environment.
1.10 Below are given corresponding wave numbers and time constants for several transitions between various states of a fluorescent molecule:
S0® S1: 18 000 cm1
S0® S2: 22 000 cm1
T1® S0: 15 000 cm1
Radiative S1® S0 transition (fluorescence): τrad
Fl =5 ns
Nonradiative S1Î S0 transition (internal conversion): τS
IC ˆ 25ns
S1Î T1 intersystem crossing: τISC ˆ 100ns
Radiative T1® S0 transition (phosphorescence): τPh ˆ 2s
Nonradiative T1Î S0 transition (intersystem crossing): τT!S
ISC ˆ 20 μs
Sketch the Jablonski diagram using the given data. Mark the radiative
and nonradiative transitions on the diagram. Which wavelengths are
needed to excite the molecule into S1 and S2? Calculate for this fluorescent molecule (a) the lifetime of the first excited singlet state, τS1 . (b) The
fluorescence quantum yield ΦFL. (c) The triplet quantum yield ΦTriplet.
(d) The triplet-state lifetime τTriplet. (e) The phosphorescence quantum
yield after excitation into S1.
1.11 Fluorescent molecules with larger conjugated π-systems often absorb and
emit at longer wavelengths and have larger transition dipole moments
than molecules with smaller conjugated π-systems. Try to explain why