For a clear solution in a cuvette, you apply Beer's Law:

Absorbance = extinction coefficient x concentration x pathlength

Rearranging this equation shows:

extinction coefficient = absorbance/concentration/pathlength

Pathlength is the distance that light passes through the sample in the cuvette. It is usually written on the cuvette. In biochemistry labs, the 1 cm cuvette is the most common type. For ultraviolet and visible wavelengths, use a quartz cuvette. For visible wavelength, you can use a glass cuvette. Do not use a plastic one unless you have no choice. They are not as precise.

You must prepare a solution of the substance with a known concentration. The solution should have an absorbance in the range of 0.1 to 1 at the highest point in the spectrum. Take care to be as precise as possible in the preparation of this solution.

Take a complete spectrum over the wavelength range of interest, employing a blank to subtract the background. Choose the wavelength for which you want to measure the extinction coefficient. This is usually the wavelength at which the absorbance is the highest,.

For greater accuracy, prepare a set of solutions with different, evenly-spaced concentrations and measure the absorbance of each one. Plot a graph of absorbance as a function of concentration. Use linear regression to calculate the slope of the best-fit line (which should pass through the origin). The slope is the extinction coefficient.

Note that the extinction coefficient depends on the solvent, so the one you measure is only valid for the solvent in which it was measured.

Dear Dr. Deepak Suthar

as answered by Dr. Ahmed Saeed Hassanien in a similar, previous question on RG, you can follow this suggestion.

Experimentally, the absorption coefficient (α) can be calculated from this simple relation:

α = 1/t ln [(1-R)2 / T]

where t is the sample thickness, T and R are the transmission and reflection.But if you don't have T and R and you have Absorbance, then:

absorption coefficient (α) = 2.303 A / t

where (A) is absorbance and (t) is thickness of thin film.

Moreover, You can get the value of Eg by usually use the Tauc relation, which is given by this equation:

αhν = A (hν - Eg )n

while (hν) is the photon energy, where:

hν(eV) = 1240 / [incident wavelength (nm)]

Now, If you plot a graph between (αhν)1/n versus (hν), then you can get a straight line. This line intersects the X-axis at (αhν)1/n = 0 . The values of Eg have been estimated from this intercept. The value of n is dependent on the electronic transition type. Where:

n=1/2 for direct allowed transition,

n= 2 for indirect allowed transition,

n=3 for direct forbidden transition and

n=3/2 indirect forbidden transition. You should try to select the suitable n according to your samples and their preparations.

I suggest you also to have a look at the following, interesting, note:

Basic UV-Vis Theory, Concepts and Applications by Thermo Spectronic

Available at: http://www.uni-salzburg.at/fileadmin/oracle_file_imports/359201.PDF

Best regards, Pierluigi Traverso.

For a clear solution in a cuvette, you apply Beer's Law:

Absorbance = extinction coefficient x concentration x pathlength

Rearranging this equation shows:

extinction coefficient = absorbance/concentration/pathlength

Pathlength is the distance that light passes through the sample in the cuvette. It is usually written on the cuvette. In biochemistry labs, the 1 cm cuvette is the most common type. For ultraviolet and visible wavelengths, use a quartz cuvette. For visible wavelength, you can use a glass cuvette. Do not use a plastic one unless you have no choice. They are not as precise.

You must prepare a solution of the substance with a known concentration. The solution should have an absorbance in the range of 0.1 to 1 at the highest point in the spectrum. Take care to be as precise as possible in the preparation of this solution.

Take a complete spectrum over the wavelength range of interest, employing a blank to subtract the background. Choose the wavelength for which you want to measure the extinction coefficient. This is usually the wavelength at which the absorbance is the highest,.

For greater accuracy, prepare a set of solutions with different, evenly-spaced concentrations and measure the absorbance of each one. Plot a graph of absorbance as a function of concentration. Use linear regression to calculate the slope of the best-fit line (which should pass through the origin). The slope is the extinction coefficient.

Note that the extinction coefficient depends on the solvent, so the one you measure is only valid for the solvent in which it was measured.

Extinction coefficient, e(λ)= A(λ)/cL, absorbance/(concentration*path length of cuvette), according to Lambert-Beer's law

thank you for your valuable answer 😊

https://www.researchgate.net/post/How_one_can_calculate_the_absorption_coefficient

I am looking for same a question. Any published paper please.

I'm surprised by this question. The answer is in textbooks. Hani Khalil Ismail " "Any published paper please." The scientific papers are not educational and are written for professionals. These are the references Lambert, J.H. (1760). Photometria sive de mensura et gradibus luminis, colorum et umbrae [Photometry, or, On the measure and gradations of light intensity, colors, and shade] (in Latin). Augsburg, (Germany): Eberhardt Klett.

Beer (1852). "Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten" [Determination of the absorption of red light in colored liquids]. Annalen der Physik und Chemie (in German). 86 (5): 78–88. doi:10.1002/andp.18521620505.

Dear all, thanks Dr. Yurii V Geletii, I was looking for the original work of Lambert. Kindest Regards

Hi;

From Beer Lambert law I=Io e(-α*t)

Where Io the incident intensity and I the transmittance intensity and α the absorption coefficient and t the thickness of the film.

ln I/Io= α t and α = 2.303 A/t (cm-1), where A = log101/T.

With my best regards

Dear Dr. Hani Khalil Ismail ,

I suggest you to have a look at the following interesting note/paper:

-USING UV-VISIBLE ABSORPTION SPECTRA

Available at: https://www.chemguide.co.uk/analysis/uvvisible/analysis.html

- THE BEER-LAMBERT LAW

Available at: https://www.chemguide.co.uk/analysis/uvvisible/beerlambert.html

-The Beer-Lambert Law by Jim Clark

Available at: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy_Basics/The_Beer-Lambert_Law

-Inherent Optical Property Measurementsand Protocols: Absorption Coefficient

Available at: http://ioccg.org/wp-content/uploads/2015/10/absorption_protocol_forcommunitydistribution-sept2017-2.pdf

-Basic UV-Vis Theory, Concepts and Applications

Available at: http://www.uni-salzburg.at/fileadmin/oracle_file_imports/359201.PDF

Enjoy reading and best regards, Pierluigi Traverso

Thank you dear Dr. Pierluigi Traverso

It might be worth mentioning that the Beer-Lambert law is a limiting law correct only for the limit of vanishing absorption like in Bouguer's and Lambert's sample (=the atmosphere) or in Beer's sample (diluted solutions). It is pretty much comparable to the ideal gas law in this respect. A derivation of the law from electromagnetic theory shows that even for the simplest case of a homogeneous scalar medium the absorption coefficient becomes an inverse function of the index of refraction. See e.g.

Article Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration

Article Beer's law derived from electromagnetic theory

As Adam B Shapiro mentioned, in solution the absorption coefficient depends on the solvent. The reason can be explained by the direct connection between Beer's law and the Lorentz-Lorenz (Clausius-Mosotti) relation:

Article Beyond Beer's Law: Revisiting the Lorentz-Lorenz Equation

Article Beyond Beer's Law: Spectral Mixing Rules

From Beer Lambert law

A= Ebc

A= absorbance, E= molar absorptivity, C= concentration of the solution

Dear Thomas Mayerhöfer ,

I appreciate much your highly professional answer. You are absolutely right . While your answer is far beyond of the original elementary question:

" How to calculate absorption coefficient from the UV-Vis absorption data ." This question does not belong to the RG forum and should be removed. According to RG rules:

In addition, the following types of content will not be accepted in Q&A:

• General knowledge questions that can be answered easily using a search engine

Yurii V Geletii Actually I disagree with your opinion that the question of calculating the absorption coefficient is trivial. It is only trivial if the Beer-Lambert law is used, but even in the case of a film on a (nearly) index matched substrate you can easily introduce an error larger than 50 %, in particular for thin films if you employ the Beer-Lambert law. The reason is that Beer-Lambert does not take into account dispersion and related interference effects, see e.g.

Article CaF2: An Ideal Substrate Material for Infrared Spectroscopy?

While the example described in the paper is in the IR spectral range, it is directly transferable to the UV-Vis - we did this recently with the same results (yet unpublished results). In fact, there are many more examples where the Beer-Lambert fails (better: is used far outside its limits), in addition to the ones mentioned above. Cf.:

Article The Bouguer-Beer-Lambert Law: Shining Light on the Obscure

Dear Thomas Mayerhöfer

I agree with you. Before any discussion we have to clearly define what we are discussing. What is the absorption coefficient?

In optics (and for me) the Napierian absorption coefficient alpha is defined via I(d) = I0*exp(alpha*d), where I0 is the initial intensity of the light and I(d) is the intensity after travelling the distance d inside the medium. Therefore, both points, 0 and d, belong to the same medium, i.e. above equation is only valid for light travelling within and not for transmission through a medium. This definition assures that alpha is not a function of d, which it is, when the Beer-Lambert law is used in the sense of alpha = -1/d*logeT, where T is the transmittance.

Thanks,

"above equation is only valid for light travelling within .....a medium ." Does it mean for a homogeneous medium? And a commonly used extinction coefficient is based on log10 but not on ln?

My pleasure! Yes, the medium has to be homogeneous and actually infinite in this formulation, so that no wave interference can take place between forward and potentially backward travelling (reflected) waves. To take into account interference effects properly one has to use wave optics. If we use log10 we get what is usually called (or is supposed to be called according to IUPAC) absorptivity.

Now, I guess we are in full agreement

Ok, then we can take the next step. Generally it is necessary to calculate the full set of optical constants, i.e. either the complex index of refraction function (refractive index + absorption index function), or the dielectric function to calculate the absorption coefficient/absorptivity.

For some time I believed that dilute solutions are an example where this is not necessary. But even if you assume that the solute does not change in the solution and there is no chemical interactions, there are still physical interactions via the local field of Lorentz (these influences were known as the empirical "Kundt's rule"). Correspondingly, it is necessary to apply the Lorentz-Lorenz equation (or Clausius-Mosotti; it can be shown that Beer's law is nothing but a special case of the Lorentz-Lorenz equation) to calculate the absorption coefficient, which again means one has to obtain the full set of optical constants...

Thanks Thomas Mayerhöfer ,

I'm a physicist by education and understand what you are talking about. At the same time I'm just a "consumer" and don't go so deep. My expertise is in physical chemistry. I often go to the "roots" of simple questions, as you did in this discussion. This is a good chance to get an expert opinion. What do you think about the UV-vis spectroscopy of charged species in solutions with a high ionic strength (high concentration of electrolytes)? Are there some physical interactions, which might affect the spectral properties of ions? We can ignore the evident chemical effects (formation of ion-pairs, change of protonation states, etc). The deviations in chemical properties from ideals are described by the "activity coefficient." Does something similar to activity coefficient exist in optics? How does it affect the UV-vis spectra of ions in solutions with a high ionic strength?

My pleasure! In my case it is the other way around: I am a chemist by training and once was just a "consumer", before I began to stumble across larger deviations between experiment and theory. Concerning the roots, it is also interesting to go back in history, where I learnt that spectroscopy was actually from the theoretical point of view much more advanced 100 years ago than it is today...

Anyway, speaking of ions, certainly Debye-Hückel theory comes to my mind. Since it is based on electrostatics, it is suppossed to follow the same principles as Lorentz-Lorenz theory in the sense of local field effects etc. even if it models officially "chemical effects". What is missing in optics, though, is a way to formulate dispersion theory for a salt that is dissolved. In any way, a solution of high ionic strength should be an increasingly coupled electromagnetic system in which the individual absorption cross sections are no longer additive, which is why Beer's law will break down. I am, however, not sure if there is an easy way to model this analytically. We did something comparable for simple systems where only two absorbers approach each other, which can already only be solved numerically: Article Deviations from Beer's law on the microscale - Nonadditivity...

Dear Thomas Mayerhöfer , my question is beyond of this thread. I'll contact you directly for a discussion

You can simply follow the Beer-Lambert correlation (A = eCl). Then prepare a series of concentration and measure absorbance to obtain a linear regression. From the slope of the graph (as you know the path length, l ), you can estimate an accurate absorption coefficient.

I have the same problem and would like to calculate the direct bandgap base on the Tauc equation. Thanks for the explaination.