6
1 Introduction to Photochemistry
I ph =
I
hν
=
cε 0 E
2
0
2hν
.
(1.19)
When necessary to avoid ambiguity, the previously defined energy flux density is
tagged as “energy” irradiance.
By dividing the average momentum density (1.7) by ρ ph , we obtain the momentum
of one photon, P ph = hν/c. In the same way, we get the component of its angular
momentum along the k-axis, J ph = ±h/2π = ±. The photon is a boson, since its
angular momentum is an integer in units, with the peculiarity that the projection of
J ph on the k-axis cannot be null. A beam of linearly polarized or unpolarized light
is made of equal numbers of photons with opposite angular momenta.
Turning to nonmonochromatic light, we can define the spectral photon irradiance
as:
I ph,ω (ω) =
I ω (ω)
ω
=
cε 0 E
2
ω (ω)
2ω
.
(1.20)
For the equivalent quantities I ph,ν (ν) and I ph,λ (λ) Eqs. (1.14) and (1.15) are valid.
The total photon flux density or total irradiance is obtained by integrating the spectral
quantities:
I ph,tot =
∞
0
I ph,ω (ω) dω =
∞
0
I ph,ν (ν) dν =
∞
0
I ph,λ (λ) dλ .
(1.21)
Notice that there is no direct relationship between I ph,tot and I tot , except in the case
of monochromatic light.
1.3 Photochemistry Versus Thermal Chemistry
The electronic excitations that trigger photochemical and photophysical events
require energies roughly in the interval 100–1000 kJ/mol (1–10 eV, or
24–240 kcal/mol). These energies are of the right order of magnitude to break bonds
or cause other major molecular rearrangements: in fact, the excitation often consists
in bringing an electron from a bonding or nonbonding orbital to an antibonding one.
The corresponding wavelengths go from 1200 to 120 nm, encompassing all the visible spectrum (λ ∈ [400, 750] nm), a large part of the ultraviolet (UV, λ ∈ [10, 400]
nm) and the near-infrared (NIR, λ ∈ [750, 1500] nm).
The flux of light (or any other form of energy) going through a material system
puts it in a state of nonequilibrium. A (normally small) fraction of molecules will
populate excited states with energies much higher than the average. To quantify such
a departure from equilibrium we must take into account the average time spent by a
molecule in one of the excited states normally accessed through light absorption. A
reasonable value for such “lifetime” is τ = 10
−9 s. Suppose we irradiate compound
A during a given time, say one hour, in order to convert it to B. If nearly all molecules
1 Introduction to Photochemistry
I ph =
I
hν
=
cε 0 E
2
0
2hν
.
(1.19)
When necessary to avoid ambiguity, the previously defined energy flux density is
tagged as “energy” irradiance.
By dividing the average momentum density (1.7) by ρ ph , we obtain the momentum
of one photon, P ph = hν/c. In the same way, we get the component of its angular
momentum along the k-axis, J ph = ±h/2π = ±. The photon is a boson, since its
angular momentum is an integer in units, with the peculiarity that the projection of
J ph on the k-axis cannot be null. A beam of linearly polarized or unpolarized light
is made of equal numbers of photons with opposite angular momenta.
Turning to nonmonochromatic light, we can define the spectral photon irradiance
as:
I ph,ω (ω) =
I ω (ω)
ω
=
cε 0 E
2
ω (ω)
2ω
.
(1.20)
For the equivalent quantities I ph,ν (ν) and I ph,λ (λ) Eqs. (1.14) and (1.15) are valid.
The total photon flux density or total irradiance is obtained by integrating the spectral
quantities:
I ph,tot =
∞
0
I ph,ω (ω) dω =
∞
0
I ph,ν (ν) dν =
∞
0
I ph,λ (λ) dλ .
(1.21)
Notice that there is no direct relationship between I ph,tot and I tot , except in the case
of monochromatic light.
1.3 Photochemistry Versus Thermal Chemistry
The electronic excitations that trigger photochemical and photophysical events
require energies roughly in the interval 100–1000 kJ/mol (1–10 eV, or
24–240 kcal/mol). These energies are of the right order of magnitude to break bonds
or cause other major molecular rearrangements: in fact, the excitation often consists
in bringing an electron from a bonding or nonbonding orbital to an antibonding one.
The corresponding wavelengths go from 1200 to 120 nm, encompassing all the visible spectrum (λ ∈ [400, 750] nm), a large part of the ultraviolet (UV, λ ∈ [10, 400]
nm) and the near-infrared (NIR, λ ∈ [750, 1500] nm).
The flux of light (or any other form of energy) going through a material system
puts it in a state of nonequilibrium. A (normally small) fraction of molecules will
populate excited states with energies much higher than the average. To quantify such
a departure from equilibrium we must take into account the average time spent by a
molecule in one of the excited states normally accessed through light absorption. A
reasonable value for such “lifetime” is τ = 10
−9 s. Suppose we irradiate compound
A during a given time, say one hour, in order to convert it to B. If nearly all molecules