I have T of Ag/Glass film recorded by UV-Vis spectrometer. Can I use Beer's law, A=Log(1/T) to find out A? Whether this will be correct without recording A experimentally?
Dear Anil, first of all the equation that you have mentioned in your question is not Beer's Law. This is a relation between absorbance and transmitance. Beer's law or in a broader sense Beer's - Lambert's law is a direct proportion between absorbance (A) and:
(i) concentration of the active species in solution (C)
(ii) thickness of the sample (L)
It is written as A = eCL, where e is a constant of proportionality termed as molar absorptivity, or molar extiction coefficient.
You can surely use the relation A=Log(1/T) for converting your transmittance data but that doesn't mean that the calculated absorbance data follow the Beer's - Lambert's law. As a general principle, for the Beer's - Lambert's law to hold, the concentration of the active species in solution must be such that the absorbance falls in the range 0 < A < 1. Beyond this point deviations from Beer's - Lambert's law starts. In the simple words Beer's - Lambert's law hold exactly for dilute solutions.
Dear Peter Kapusta,
According to you, if A is calculated from T, then the result wouldn't be accurate due to the effect of reflection of Ag/Glass. I do agree.
Then, How a dual beam UV-Vis spectrometer calculates A from transmitted ray?
Formally, you can easily calculate A from T and use this for evaluating the concentration. Naturally, the sample thickness must be also known. The reflection from the both sides of the sample can induce some uncertainty, but if one know the value of refrective index, this can also be taken into account.
It might be a little confusing, but there are two different absorptions in literature. If we distinguish between transmitted intensity IT, reflected intensity IR and absorbed intensity IA, the following relation holds: IT/I0 + IR/I0 + IA/I0 = 1 or T + R + A = 1. Accordingly: 1-T-R = A, which means you have to measure T and R to get A. If you take then log (1/(1-T-R)) you should arrive at the absorption used in the Lambert-Beer law corrected for the reflectance.
I have to correct my answer above. There are only very rare and exceptional cases where A=Log(1/T) holds. If you want to be on the safe side, use Abelès matrix formalism to calculate first the complex index of refraction function from which you obtain A!
if I get absorbance in fraction, like less than 1 (0.1 0r 0.8) what that suppose to mean? In this case absorption coefficient becomes negative because ln(fraction) is negative. Is my data wrong? What should I do?
Whether we use a single beam or a double beam spectrometer, we first measure T=I/Io (Io is intensity of the beam entering into the sample, I is intensity of the beam which comes from the sample). Then we calculate A = log (1/T). When we want to normalize the result to the thickness of, usually, 1 cm, we calculate the linear absorption coefficient, k = A/d, where d is the thickness of the sample in centimeters.
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