State and explain Beer-Lamberts Law. | Spectroscopy | Analytical Chemistry
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Beer-Lambert's Law states that “Equal
Beer-Lambert's Law states that “Equal fractions of incident light are absorbed by successive layers of equal thickness and equal concentration of absorbing medium.” We know that Lambert's Law is 2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l And Beer's Law is 2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K''c On combining both, we get Beer-Lambert's Law which is, 2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l K''c 2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = Kcl \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = \frac { K }{ 2.303 } cl \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = \varepsilon cl where ε is constant and ε = \frac { K }{ 2.303 } is known as molar extinction coefficient Or molar absorptivity and it is defined as “the reciprocal of the thickness which produces transmitted ray \sfrac { 1 }{ 10 } of its incident rays if the concentration of the absorbing species in the solution is 1mole.” The unit is { dm }^{ 3 } { mole }^{ -1 } { m }^{ -1 }. But Optical density is defined as logarithm of ratio of { I }_{ 0 } to { I }_{ t }. Therefore, \boxed { \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = Optical density (O.D.) = Absorbance (A) } OD has no unit and its value lies between 0 to 1. Also Transmittance T is defined as the fraction of the light transmitted. T = \frac { { I }_{ t } }{ { I }_{ 0 } } The value of T is always small to convert in to appreciable it is always expressed in percentage. Thus Beer-Lambert's Law becomes, \boxed { O.D = A = \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = -\log { T } = \varepsilon cl }
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