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142 Basic physical chemi.5try

7 .3 Quantum yields
Although each photon absorbed by a molecule activates that molecule
in the initial step of a photochemical process , it can be seen from
Reactions (7 .5) and (7. 7) to (7 1 3) that this does not necessarily result
.
in a chemical change . For example , the energy may be reradiated
[Reaction (7 . 1 0)] or it may be transferred to another molecule [Reac­
.
tion (7 1 3 )] . This "inefficiency" factor in photochemistry is taken into
account quantitatively by defining quantum yields.
i
The overall quantum yield of a stable product A s defined as
Number of moles of A formed
= (7 1 4)
.
<l>A Number of einsteins absorbed
We can also define the quantum yield for a particular primary pathway
(e.g . , dissociation or reaction). Thus , the quantum yield for the i1h
primary pathway or process is

Number of excited moles that proceed via pathway i
-
<P ; - Number of einsteins absorbed (7. 1 5)
The probability of an excited molecule absorbing more than one pho­
ton during its short lifetime is very small for low to moderate light
intensities (including all those in the atmosphere). Therefore ,
.
(7 1 6)
where the summation includes all photochemical and photophysi­
s
.
cal primary pathway . Equation (7 1 6) is known as the Stark-Einstein
law . Although </J; � 1 , the overall quantum yield for a product (<I> A)
c
can be very mu h greater than unity, as illustrated in the following ex ­
ercise.
Exercise 7. . One of the very early photochemical reactions to be
3
recognized was that involving hydrogen, Hz(g), and chlorine, Clz(g).
Hydrogen and chlorine can be mixed together without reacting; but if
the mixture i s exposed to light the two substances react explosively to
form hydrochloric acid, HCl(g). The reaction sequence is

C l 2(g) + v � 2Cl(g) (7. 1 7 a)
h
Cl(g) + H (g)� HCl(g) + H(g) (7. 1 7b)
2
H(g) + l (g)� HCl(g) + Cl(g) (7. 1 7 c)
C
z