At low concentration, not much of the radiation is absorbed and P is not that much different than P o. If the sample is now made a little more concentrated so that a little more of the radiation is absorbed, P is still much greater than P S. As the concentration is raised, P, the radiation reaching the detector, becomes smaller.
If the concentration is made high enough, much of the incident radiation is absorbed by the sample and P becomes much smaller. At its limit, the denominator approaches P S , a constant. The ideal plot is the straight line. Spectroscopic instruments typically have a device known as a monochromator. There are two key features of a monochromator. The first is a device to disperse the radiation into distinct wavelengths.
You are likely familiar with the dispersion of radiation that occurs when radiation of different wavelengths is passed through a prism. The term effective bandwidth defines the packet of wavelengths and it depends on the slit width and the ability of the dispersing element to divide the wavelengths.
The important thing to consider is the effect that this has on the power of radiation making it through to the sample P o. Reducing the slit width will lead to a reduction in P o and hence P. An electronic measuring device called a detector is used to monitor the magnitude of P o and P.
All electronic devices have a background noise associated with them rather analogous to the static noise you may hear on a speaker and to the discussion of stray radiation from earlier that represents a form of noise. P o and P represent measurements of signal over the background noise. As P o and P become smaller, the background noise becomes a more significant contribution to the overall measurement. Ultimately the background noise restricts the signal that can be measured and detection limit of the spectrophotometer.
Therefore, it is desirable to have a large value of P o. Since reducing the slit width reduces the value of P o , it also reduces the detection limit of the device. Selecting the appropriate slit width for a spectrophotometer is therefore a balance or tradeoff of the desire for high source power and the desire for high monochromaticity of the radiation.
It is not possible to get purely monochromatic radiation using a dispersing element with a slit. Usually the sample has a slightly different molar absorptivity for each wavelength of radiation shining on it. The net effect is that the total absorbance added over all the different wavelengths is no longer linear with concentration. Instead a negative deviation occurs at higher concentrations due to the polychromicity of the radiation.
Furthermore, the deviation is more pronounced the greater the difference in the molar absorbtivity. As the molar absorptivities become further apart, a greater negative deviation is observed.
Therefore, it is preferable to perform the absorbance measurement in a region of the spectrum that is relatively broad and flat.
The peak at approximately nm is quite sharp whereas the one at nm is rather broad. Given such a choice, the broader peak will have less deviation from the polychromaticity of the radiation and is less prone to errors caused by slight misadjustments of the monochromator.
It is important to consider the error that occurs at the two extremes high concentration and low concentration. A relatively small change in the transmittance can lead to a rather large change in the absorbance at high concentrations. At very low sample concentrations, we observe that P o and P are quite similar in magnitude. If we lower the concentration a bit more, P becomes even more similar to P o. The important realization is that, at low concentrations, we are measuring a small difference between two large numbers.
For example, suppose we wanted to measure the weight of a captain of an oil tanker. One way to do this is to measure the combined weight of the tanker and the captain, then have the captain leave the ship and measure the weight again.
The difference between these two large numbers would be the weight of the captain. If we had a scale that was accurate to many, many significant figures, then we could possibly perform the measurement in this way. But you likely realize that this is an impractical way to accurately measure the weight of the captain and most scales do not have sufficient precision for an accurate measurement.
Similarly, trying to measure a small difference between two large signals of radiation is prone to error since the difference in the signals might be on the order of the inherent noise in the measurement. Therefore, the degree of error is expected to be high at low concentrations. The discussion above suggests that it is best to measure the absorbance somewhere in the range of 0.
Solutions of higher and lower concentrations have higher relative error in the measurement. Low absorbance values high transmittance correspond to dilute solutions. Often, other than taking steps to concentrate the sample, we are forced to measure samples that have low concentrations and must accept the increased error in the measurement. It is generally undesirable to record absorbance measurements above 1 for samples. Instead, it is better to dilute such samples and record a value that will be more precise with less relative error.
Another question that arises is whether it is acceptable to use a non-linear standard curve. As we observed earlier, standard curves of absorbance versus concentration will show a non-linearity at higher concentrations. Such a non-linear plot can usually be fit using a higher order equation and the equation may predict the shape of the curve quite accurately.
Whether or not it is acceptable to use the non-linear portion of the curve depends in part on the absorbance value where the non-linearity starts to appear. If the non-linearity occurs at absorbance values higher than one, it is usually better to dilute the sample into the linear portion of the curve because the absorbance value has a high relative error.
If the non-linearity occurs at absorbance values lower than one, using a non-linear higher order equation to calculate the concentration of the analyte in the unknown may be acceptable. One thing that should never be done is to extrapolate a standard curve to higher concentrations. Since non-linearity will occur at some point, and there is no way of knowing in advance when it will occur, the absorbance of any unknown sample must be lower than the absorbance of the highest concentration standard used in the preparation of the standard curve.
It is also not desirable to extrapolate a standard curve to lower concentrations. There are occasions when non-linear effects occur at low concentrations. If an unknown has an absorbance that is below that of the lowest concentration standard of the standard curve, it is preferable to prepare a lower concentration standard to ensure that the curve is linear over such a concentration region.
Another concern that always exists when using spectroscopic measurements for compound quantification or identification is the potential presence of matrix effects.
The matrix is everything else that is in the sample except for the species being analyzed. A concern can occur when the matrix of the unknown sample has components in it that are not in the blank solution and standards.
Viewed 17k times. Improve this question. However, they do not give much justification for this choice Add a comment. Active Oldest Votes. Krstajic, et al write bold emphasis mine : Breiman et al. Improve this answer. Now I can finally cite something appropriate when the question comes up for those unfamiliar with the "standard" choice of lambda. The link to Krstajic et al looks great, too. But the question asked about regression!
There are alternatives. If we try e. But we could e. It's not in either of the quotes I extracted, which both suggest that the 1-SE rule is applicable in general, not just in classification. So if you need a formal citation, that seems to be the original source. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.
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