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I want to ask a question about peaks in a UV/VIS spectrum.

My lecturer in our introductory course mentioned the following:

Two molecules may have the same molar extinction coefficient, but if I have two molecules, A and B, and B has a peak that is broader than molecule A, it will be a stronger absorber.

He failed to qualify this further or provide any reasoning.

My thought was that if it is a broader peak, then molecule B will absorb a wider range of wavelengths in a UV/Vis spectrum, but I couldn't see what he meant by a "stronger" absorber.

Does he mean that molecule B absorbs more wavelengths, so it is "stronger" or is there another qualification for using the word "stronger" to describe B?

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    $\begingroup$ Tell him you are not paying tuition fees to be taught dubious facts which you then have to learn by heart. $\endgroup$ – Karl Nov 16 '19 at 21:09
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The classical concept of oscillator strength $f$ is useful here, but it should be used only in a qualitative way. This is defined as $f=a\int\epsilon_\nu d\nu$ where $a$ is set of units with value $4.3 10^{-9}$ if the extinction coefficient is in units dm$^3$/mol/cm and $\nu$ is in wavenumbers. The maximum value of $f$ is unity and is close to this for an allowed transition in a dye molecule, such as rhodamine, but can be as small as $10^{-9}$ for a forbidden transition.

In your case if two molecules have similar $\epsilon$ at some wavelength (or frequency) but one has a narrow transition compared to the other, then the one with the narrow transition will have a smaller integral and hence the smaller oscillator strength. In this sense only is the transition 'weaker', i.e. it is not the probability of absorbing at a given wavelength that is being considered but that over all wavelengths, so it really depends on how you want to define a 'strong' vs a 'weak' transition. In QM the transition moment integral is used instead of oscillator strength and gives a proper description of absorption.

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If a peak in UV/Vis is broader than another one, with the same absorption coefficient, the absorption is the same at the wavelength corresponding to the maximum of the peak. But at any other wavelengths, a bit different from the maximum of the peak, the absorption is larger for the broader peak. So the proportion of the total amount of light, integrated over the whole spectrum, is larger. Suppose the first spectrum is so broad as to be flat from 400 to 800 nm, and that the absorbance is equal to 1 everywhere. All wavelengths will be absorbed, and the total energy getting out of the cell is 10% of the entering energy. If the absorbance is equal to 1 at only one wavelength, the absorbance being zero at all other wavelengths, the total energy getting out of the cell will be nearly equal (about 99%) to the original energy getting in the cell.

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