# Path length and absorbance relationship counseling

### Beer's Law - Theoretical Principles

The expected relationship of absorbance proportional to log10(SPF) applies at nm A compact, variable pathlength, fiber optic probe for spectrophotometric in its early stage would significantly increase chances for effective therapy. The relationship between the absorbance maximum at 2,cm' and the with the statistical regression equation: [BSH(mM)] = *Absorbance (pathlength . The linear relationship between absorbance and concentration of b = pathlength traveled in the sample [cm] . provide useful feedback during therapy. 17 p g.

## The Beer-Lambert Law

The reasons for this splitting are unimportant in the context of our treatment of atomic absorption. Absorption of a photon is accompanied by the excitation of an electron from a lower-energy atomic orbital to an orbital of higher energy. Not all possible transitions between atomic orbitals are allowed. The atomic absorption spectrum for Na is shown in Figure The most obvious feature of this spectrum is that it consists of a small number of discrete absorption lines corresponding to transitions between the ground state the 3s atomic orbital and the 3p and 4p atomic orbitals.

Note that the scale on the x-axis includes a break. Another feature of the atomic absorption spectrum in Figure Natural line widths for atomic absorption, which are governed by the uncertainty principle, are approximately 10—5 nm. Other contributions to broadening increase this line width to approximately 10—3 nm. This attenuation of radiation is described quantitatively by two separate, but related terms: All methods of detecting photons—including the human eye and modern photoelectric transducers—measure the transmittance of electromagnetic radiation.

We will show that this is true in Section What is its absorbance? Click here to review your answer to this exercise. As we saw in Figure For this reason, atomic absorption requires a line source instead of a continuum source. Integrating the left side of equation If there are no interactions between the components, the individual absorbances, Ai, are additive. In many cases a calibration curve deviates from this ideal behavior Figure The absorbance is going to be very low.

Suppose then that you wanted to compare this dye with a different compound.

### The Beer-Lambert Law - Chemistry LibreTexts

Unless you took care to make allowance for the concentration, you couldn't make any sensible comparisons about which one absorbed the most light.

The absorbance is not likely to be very high. On the other hand, suppose you passed the light through a tube cm long containing the same solution.

• 10.2: Spectroscopy Based on Absorption

More light would be absorbed because it interacts with more molecules. Again, if you want to draw sensible comparisons between solutions, you have to allow for the length of the solution the light is passing through. Both concentration and solution length are allowed for in the Beer-Lambert Law. Molar absorptivity compensates for this by dividing by both the concentration and the length of the solution that the light passes through. Essentially, it works out a value for what the absorbance would be under a standard set of conditions - the light traveling 1 cm through a solution of 1 mol dm That means that you can then make comparisons between one compound and another without having to worry about the concentration or solution length.

Values for molar absorptivity can vary hugely. For example, ethanal has two absorption peaks in its UV-visible spectrum - both in the ultra-violet.

## Beer-Lambert Law

Table 1 gives values for the molar absorptivity of a solution of ethanal in hexane. Notice that there are no units given for absorptivity. That's quite common since it assumes the length is in cm and the concentration is mol dm-3, the units are mol-1 dm3 cm Although, in fact, the nm absorption peak is outside the range of most spectrometers.