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Einstein or photochemical equivalence law is applicable only to the primary photochemical process or in other words as a result of primary absorption of one quantum, only one molecule undergoes dissociation and the products enter no further reaction. It means the ratio of number of molecules excited and number of quanta absorbed is 1:1.
In actual practice in most of the cases an activated molecule initiates a series of thermal reactions called secondary reactions as in the cases of chain reactions like between H2 and Br2 and H2 and Cl2 etc. As a result in such reactions many reactant molecules may undergo chemical change by absorbing one quantum only and the ratio deviates from 1:1.
To describe the deviation from 1:1 the term quantum efficiency or quantum yield (ϕ) was introduced . This can be defined as follows:
“It is the number of molecules which undergo chemical change per quantum of absorbed energy” or in other words the ratio of the number of molecules reacting in a given time and the number of quanta absorbed in the same time is called quantum efficiency or quantum yield .

?= No. of molecules reacting in a given time
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No. of quanta or photons absorbed in the same time
or
?= No. of moles reacting in a given time
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No. of einsteins absorbed in the same time
or
?= Rate of chemical reaction
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No. of einsteins absorbed
or =
Rate of chemical reaction
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No. of einsteins of light
or
?= -d[A]/dt
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Energy of absorbed light

The concept of quantum yield can be extended to any physical or chemical reaction following light absorption. The quantum yield is dependent on the light intensity. The value of quantum yield vary from very low of 0.04 to very high value of the order of 106.

Experimental Determination of Quantum Yield or Efficiency

We have seen in the last section that quantum yield or efficiency is defined as
?=Rate of chemical reaction
Energy of absorbed light
Thus , in order to determine the value of quantum yield of photochemical reaction it is essential to known (i) Number of moles reacting and (ii) number of Einstien absorbed . Number of molecules reacting in given time can be determined by the chemical kinetics , since it is nothing but is the rate of reaction.

Visible and U.V. spectroscopy have a number of applications. Some of them are-
1. Assignment of structure of compounds: If two compounds show same absorption spectra means they should same structure. If structure of one of them is known, other’s can be determined which can be illustrated by the following example.
(i) Instain obtained from indigo has one of the following structures:

It was observed from structure (III) and (IV) that spectra of instain is same as that of its methyl derivative (IV) . Thus its structure should be like (II).
Fictional group present in a compound can be identified by its characteristic absorption band (?max) . For example if ?max is 210 mμ (nm) , it means -COOH group is present in that compound.
If molecule is in two tautomeric forms it can be studied by its absorption band.
Identification of Compound: If the absorption band of an unknown compounds are found similar to that of a known compounds it means they have same structure. This technique in which spectra of an unknown compound is compared with that of an unknown compound is called figer printing.
Presence of Hydrogen bonding: Presence of H-bond in a molecule leads to hypsochromic effect. For example if hexane is used for acetone (as solvent) ?max occurs at 264 nm. This is due to formation of hydrogen bond between acetone and water.
4. Determination of cis-trans isomerism : Cis and trans isomers can be identified with the helf of UV & visible spectroscopy for example stilbene has following cis-trans isomers :

In cis form two phenyl groups are not in plane due to steric hindrance where as in trans form they are in same plane due to their opposite direction. Thus in trans form π-π^* transition takes place easily at 295 nm where as in cis form transition takes place at high energy (lower wave length) ?max = 280nm . It means higher ?max in stilbene is found in its trans form.