Solutions
Problems of Chap. 1
1.1 If λ
−1
= 1500 cm
−1
= 1.5 · 10
5 m
−1 , E = hc/λ = 2.9797 · 10
−20 J. For a
mole, and using kJ instead of J, E = 2.9797 · 10
−20
· N A /1000 = 17.94 kJ/mol.
More simply, use the conversion factor from cm
−1 to kJ/mol, 0.0119627 (see Appendix A).
A wavelength of 500 nm corresponds to λ
−1
= 10
9
/500 m
−1
= 10
7
/500 cm
−1
=
20000 cm
−1
= 20000 · 0.0119627 kJ/mol = 239.25 kJ/mol.
1.2 The He–Ne laser delivers 10
−3 W on a surface of π · 10
−6 m
2 , so the irradiance
is 10
−3
/(π · 10
−6
) = 318 W/m
2 .
The power of the tungsten lamp emitted in the visible spectrum is 2 W. At a distance
of 2 m it is spread on a spherical surface of 4π · 2
2
= 50.3 m
2 , so the irradiance is
2/50.3 = 0.0398 W/m
2 .
1.3 With ε = 1000 mol
−1 L cm
−1 , a thin layer of thickness l m, with a concentration
of 1 mol/L, absorbs a fraction ln(10) · 1000 · 100 · l = 2.3 · 10
5 l of the impinging
light. If the irradiance is 100 W/m
2 , a layer of area 1 m
2 absorbs 2.3 · 10
7 l W. Since
at λ = 500 nm one photon has the energy of 239.25 kJ/mol (see Problem 1.1), the
layer would absorb 2.3 · 10
7 l/239250 = 96.2 l mol of photons per second. In the
volume of the layer, l m
3 , there are 1000 l mol, so each molecule absorbs in the
average 96.2 l/(1000 l) = 0.0962 photons per second, i.e., a photon every 10.4 s.
1.4 If, to excite CCl 3 CF 3 , we need λ > 220 nm, the photon energy is hν >
10
7
/220 = 45450 cm
−1 . The C-Cl dissociation energy is 330 kJ/mol = 27600 cm
−1
(see the conversion factor in Appendix A). Then, the photon energy is well above
the bond dissociation energy and the limiting factor for the photodissociation is the
absorption spectrum.
1.5 The lifetime of T 1 of benzophenone is determined by the rates of ISC and
phosphorescence: τ T 1 = (1/0.06 + 1/0.007)
−1
= 0.0063 s. The rate of ISC starting
from S 1 is so much higher than the rate of any other process involving this state
© Springer International Publishing AG, part of Springer Nature 2018
M. Persico and G. Granucci, Photochemistry, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-89972-5
241
Problems of Chap. 1
1.1 If λ
−1
= 1500 cm
−1
= 1.5 · 10
5 m
−1 , E = hc/λ = 2.9797 · 10
−20 J. For a
mole, and using kJ instead of J, E = 2.9797 · 10
−20
· N A /1000 = 17.94 kJ/mol.
More simply, use the conversion factor from cm
−1 to kJ/mol, 0.0119627 (see Appendix A).
A wavelength of 500 nm corresponds to λ
−1
= 10
9
/500 m
−1
= 10
7
/500 cm
−1
=
20000 cm
−1
= 20000 · 0.0119627 kJ/mol = 239.25 kJ/mol.
1.2 The He–Ne laser delivers 10
−3 W on a surface of π · 10
−6 m
2 , so the irradiance
is 10
−3
/(π · 10
−6
) = 318 W/m
2 .
The power of the tungsten lamp emitted in the visible spectrum is 2 W. At a distance
of 2 m it is spread on a spherical surface of 4π · 2
2
= 50.3 m
2 , so the irradiance is
2/50.3 = 0.0398 W/m
2 .
1.3 With ε = 1000 mol
−1 L cm
−1 , a thin layer of thickness l m, with a concentration
of 1 mol/L, absorbs a fraction ln(10) · 1000 · 100 · l = 2.3 · 10
5 l of the impinging
light. If the irradiance is 100 W/m
2 , a layer of area 1 m
2 absorbs 2.3 · 10
7 l W. Since
at λ = 500 nm one photon has the energy of 239.25 kJ/mol (see Problem 1.1), the
layer would absorb 2.3 · 10
7 l/239250 = 96.2 l mol of photons per second. In the
volume of the layer, l m
3 , there are 1000 l mol, so each molecule absorbs in the
average 96.2 l/(1000 l) = 0.0962 photons per second, i.e., a photon every 10.4 s.
1.4 If, to excite CCl 3 CF 3 , we need λ > 220 nm, the photon energy is hν >
10
7
/220 = 45450 cm
−1 . The C-Cl dissociation energy is 330 kJ/mol = 27600 cm
−1
(see the conversion factor in Appendix A). Then, the photon energy is well above
the bond dissociation energy and the limiting factor for the photodissociation is the
absorption spectrum.
1.5 The lifetime of T 1 of benzophenone is determined by the rates of ISC and
phosphorescence: τ T 1 = (1/0.06 + 1/0.007)
−1
= 0.0063 s. The rate of ISC starting
from S 1 is so much higher than the rate of any other process involving this state
© Springer International Publishing AG, part of Springer Nature 2018
M. Persico and G. Granucci, Photochemistry, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-89972-5
241