1. first, integrate your absorption spectrum over the peak to get a peak area Ar

2. Determine the absorbance a with a=Ar/[sqrt(pi).FWHM/(2sqrt(2ln2))], where FWHM is the full width at the half maximum of your peak

3. From the absorbable a, you shall be able to determine the absorption coefficient alpha by alpha=a/[log(e).l]. here l is the thickness or path length of your sample

4. If you know the concentration c of your np, use a=epsilon.c.l, you shall be able to determine extinction coefficient per mole your np! epsilon.

hope this help.

mu_a*d=2.303*A, mu_a=2.303*A/d,

where d- length of the cuvette, A -absorbance, mu_a - absorption coefficient, 2.303 - a conversion factor from a decimal to natural log.

First you must know the size distribution of the NPs. If it is more or less constant you can easily find the concentration of your dispersion. Then you can prepare a calibration curve (absorbance vs concentration) with successive dilutions using the Beer-Lamberts law. From the slope of the curve you can calculate the absorption coefficient.

Beer–Lambert law, A=abc

absorbance, A,

molar absorption coefficient, molar extinction coefficient, or molar absorptivity ,a,

pathlength, b,

the concentration, c,

i.e;

a=A/(b*c)

where b is fixed and constant.

So,a proportional to A/c

i.e, Slope of Absorbance (A) v/s Molar Concentration (c) devided by b (cell lenght) give you value a (molar absorption coefficient)

"I have searched on the internet..." You should search an analytical chemistry textbook for the foundations behind the equations referenced in the previous postings.

1. first, integrate your absorption spectrum over the peak to get a peak area Ar

2. Determine the absorbance a with a=Ar/[sqrt(pi).FWHM/(2sqrt(2ln2))], where FWHM is the full width at the half maximum of your peak

3. From the absorbable a, you shall be able to determine the absorption coefficient alpha by alpha=a/[log(e).l]. here l is the thickness or path length of your sample

4. If you know the concentration c of your np, use a=epsilon.c.l, you shall be able to determine extinction coefficient per mole your np! epsilon.

hope this help.

Thanks all for your replies and specially mr. Jung. I hope it will work now

Good discussion can you please explain the formulas for calculating the absorption coefficient from an transmittance vs wavelength graph for thin films. 

In reference to the method proposed by J Huang:

* When you integrate to obtain a peak area graphically or otherwise, you need not calculate it again by an equation that uses half-width.

* The equation given to determine peak area from half-width only truly applies for a perfect Gaussian peak and is inaccurate for any considerations beyond this.

* Calculations performed using only one point of Absorbance and Concentration have absolutely no statistical validity compared to those that use linear regression methods for a plot of multiple points of Absorbance versus Concentration.

@D Tan: You provide one equation, the Beer-Lambert law, and state that you have three unknowns: extinction coefficient, concentration, and absorbance. I suspect that you have not phrased your question properly.

@Jeffrey J Weimer Hi Sir, May I please ask what is the name of the textbook from your previous post?

Thanks in advance

@S Adrian: Please be more specific about the information you need. 

@Jung Y. Huang  Thanks for your answer!!!!

But I am little bit confused. Let's consider I have some data of absorbance vs wave-number (cm-1). I want to get Absorption coefficient as function of frequency or wave-number. So as the process you mentioned, there is no frequency dependency.

@D Das Mahanta: Frequency and wavenumber are proportional just as frequency and wavelength are inversely proportional. The plot of absorbance versus wavenumber is itself the answer you want for absorption coefficient versus frequency.

In any case, absorption coefficient is typically taken at a specific wavenumber (frequency).

How can I calculate the absorption and extinction coefficient for Dye(N719)?

I can not find these coefficients in database.please help me

Dear sir,how to calculate alpha

How to calculate alpha

alpha is absorption coefficient na how to calculate from absorption vs wavelength 

i have seen  everybody is calculating like ___________ absorption/2=absorption cofisint ------is it curect

A=log( I0/I)   (absorbance from spectrophotometer)

ax=ln(I0/I)    (absorption coeffi. from beer- lambert law)

so  ax=A*ln 10=2.30 *A   and

therefore    absorption coeff.  = 2.30*Absorbance /( thickness of your sample)

dear researchers,

i have come across plotting UV visible graph.

i have no sample thickness my sample is powder sample 

pls help me to determining alpha of such samples

I think this link is very useful, 

http://www.instanano.com/characterization/theoretical/concentration-calculation-from-uv-vis-absorbance/

In general, a spectrophotometer working in the solar radiation wavelength region measures either the transmittance or the reflectance of a sample. That is, the absorbance is not measured directly, but is calculated from the measured transmittance and reflectance (if both can be measured). When a spectrophotometer gives you the absorbance A’ on the logarithmic form, i.e. the optical density OD, which is a common output from many spectrophotometers (OD = A’ = log10(1/T) = alog10(e)x = a’x, "10" supposed to be as a subscript here, i.e. the 10-log, where T is the transmittance, x is the penetration length or depth x, and a and a’ denote the absorption coefficients depending what form is used, which is deduced from the Beer-Lambert law), it is in reality a calculation from the measured transmittance ignoring the reflectance. A spectrophotometer measures the radiation which is collected by the detector from either the transmitted or the reflected beam. Furthermore: T + A + R = 1 (100 %) where T = transmittance, A = absorbance and R = reflectance between 0 to 1 (or between 0 to 100 %). Note that the absorbance A in the above is not the absorbance A’ on the logarithmic form, i.e. not the optical density OD, which is a common output from many spectrophotometers. You may see further details in e.g. chapter 3, 4, 7.6.3 and 7.6.7 in the following article: B. P. Jelle, ”Solar Radiation Glazing Factors for Window Panes, Glass Structures and Electrochromic Windows in Buildings - Measurement and Calculation”, Solar Energy Materials and Solar Cells, 116, 291-323, 2013. In addition, you need to have control over if the transmittance and reflectance are specular (directly transmitted or reflected, i.e. mirror-like) or diffuse (scattered in all directions), where you in the latter case would use integrating sphere accessories to collect the scattered transmitted/reflected radiation.

Since you want to calculate the absorption coefficient from an absorbance vs wavelength graph. You shuld know the thicness of the sample to find out the absorption coffficient. A mathematical relation between absoption and the absoption coefficient is, Α=2.303*A/d, where A is the absorbance and d is the thickness of the sample.

The absorption coefficient, α can be calculated using the following equation

α=2.303A/d

Where A is the absorbance and d is the thickness.

When calculating the absorption coefficient, you should always keep in mind that

the absorption coefficient is of much more limited value than you might think.

Usually it is assumed that it is a specific property, but this is not the case. Instead it is a property of the wave inside the medium.

Accordingly it is influenced by heterogeneity, particle shape, particle dielectric function tensor, electromagnetic coupling, local field effects, local anisotropy, concentration etc. For more information, have a look at:

Article Deviations from Beer's law on the microscale - Nonadditivity...

Furthermore, keep in mind that absorbance is generally not linear to concentration as derivations of Beer's law from electromagnetic theory and dispersion relations show:

Article Beer's law derived from electromagnetic theory

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

Here is why absorbance can be linear to concentration in solution (but only as long as you use a thick cuvette):

Article Employing Theories Far beyond Their Limits-The Case of the (...

And here are the reasons why absorbance is by no means proportional to the thickness in case of thin films:

Article The electric field standing wave effect in infrared transfle...

Article The Electric Field Standing Wave Effect in Infrared Transmis...

and what you can do to obtain the absorption index/the absorption constant anyway:

Article Removing interference-based effects from the infrared transf...