Chemistry Reference
In-Depth Information
The relationship between the amount of light or the number of photons absorbed and the number of
molecules, that, as a result, undergo a reaction, is defined as the quantum yield. It is defined as the
number of molecules involved in a particular reaction divided by the number of quanta absorbed in
the process [
1
,
3
].
Another fundamental law of photochemistry was formulated by Grotthus and Draaper [
82
,
83
]. It
states that only the light that is absorbed by a molecule can be effective in producing photochemical
changes in that molecule. There is also a fundamental law of photochemistry that states that the
absorption of light by a molecule is a one-quantum process, so that the sum of the primary processes,
the quantum yield, must be unity [
82
,
83
]. Also, the law of conservation of energy requires that the sum
of the primary quantum yields of all processes be equal to unity. Mathematically this can be expressed as:
X
F
total
¼
F
i
¼
1
i
where
is the quantum yield. The quantum yield of photochemical reactions is important because it
sheds light on the mechanisms of the reactions. The number of molecules involved in a particular
photoreaction can be established by an analytical kinetic process and the number of quanta absorbed
can be measured with the aid of an actinometer. The quantum yield can also be expressed in general
kinetic terms [
1
]:
F
X
'
i
ES
'
j
R
P
i
F
i
¼ '
ES
'
R
P
i
or
F
i
¼
i
The above equations signify that a quantum yield of a particular photo process is the product of
two or three distinct probabilities. These are:
'
ES
is the probability that the excited state will undergo
the primary photoreaction necessary for the process. The probability that any metastable ground state
intermediate will proceed to stable products is
P
i
and the probability that the excited state will
undergo the primary photoreaction necessary of the process is
'
R
.
The concept that matter can only acquire energy in discrete units (quanta) was introduced in 1900
by Max Planck [
83
]. The corollary of the quantization of energy is that matter itself must be
quantized, i.e., constructed of discrete levels having different potential energies. Occupying these
particular levels are electrons that obviously possess the energy of the level which they occupy. In a
molecule, the intramolecular motions of the electrons and the associated molecular electronic levels
must be taken into account. There are, in addition to electronic levels, modes of vibration and rotation
that are also quantized. In other words, the absorption of a photon of light by any molecule is a
reaction that must promote transitions between quantum states. This requires two conditions. These
are: (1) for a molecular state
E
n
, so that
hu ¼ E
n
E
m
; (2) there must be specific interaction between the radiation and the light-absorbing
portion of the molecule that results in a change in the dipole moment of the molecule during the
transition. If we designate the wave functions of the states
m
with energy
E
m
, there must be a state
n
of higher energy,
m
and
n
as
c
m
and
c
n
respectively, then the
transition moment integral that may not equal to zero is:
R
mn
¼ðC
m
=PC
n
Þ
P ¼ e
P
r
i
, where
P
e
where
is the electric dipole operator. It has the form of
is the electronic charge
r
i
i
and
.
The increase in the energy of a molecule as a result of absorbing a quantum of radiation can be
expressed in the relationship [
85
]:
is the vector that corresponds to the dipole moment operator of an electron
DE ¼ hC=l
