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Beer-Lambert law question

  1. Jan 17, 2008 #1


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    I am looking for help with understanding how to specify correct absorbance values for my little study project of modeling attenuation of light in a material.

    Here are the sources that I am using:
    1) The Wikipedia article

    states that the absorbance of a sample A is alpha*l*c, where alpha = (4*pi*k) /lambda and k is the extinction coefficient.

    Question 1: Is k supposed to be the extinction coefficient of the absorbing species?

    Question 2: If I am using k to calculate alpha as in the formula above, this makes c to be dimensionless (right?). How shall I then understand c?

    I found here:

    that concentration can be specified as percent by mass or parts per million. Is this the case? Shall the concentration in my case be specified as dimensionless? For example 0.01 for 1 percent of mass of the absorbing species in the material?

    Thank you for your help!
  2. jcsd
  3. Jan 18, 2008 #2

    Dr Transport

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    Science Advisor
    Gold Member

    k is the extinction coefficient for the material and the concentration c is dimensionless in parts per million. Plug them into your equation and you should be ok.
  4. Jan 18, 2008 #3


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    Dr Transport, thanks!

    Did I get it right that k is meant to be here the extinction coefficient of the material not of the absorbing particles?

    So if i have k=0.07 for light with wavelength = 400 nm, then I get the following expression for attenuated light:
    I1 = I0* exp(-path_length * 0.01 * (4*pi*0.07)/(400 * 1e-9)),
    1) path_length - length of path of light in material (measured in meters)
    2) 0.01 - concentration of absorbing particles (equal to 1 percent of mass)
    3) (4 * pi * 0.07)/(400 * 1e-9) - the absorption coefficient alpha (with wavelength measured in meters as well)

    Is this correct?

    Thank you for your help!
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