[Valerio]

Hello

I have been searching for an answer to the following question. Some lecturers tell me that I'm to curious and don't need to dive that deep into the concepts or some lecturers don't reply to my e-mail. I think this is quite sad, because I'm genuinely interested in the subject of spectroscopy. I will try to write my question as clearly as possible, though my native language is not English and grammar errors might occur.

Anyway, in my syllabus about atomic absorption spectroscopy there is this sentence which translates to 'For Beer's law to hold the bandwidth of the source must be narrow relative to the width of an absorption peak.'

My question is: Can I show theoretically in some way that it is essential that the bandwidth of the source must be narrow relative to the width of an absorption peak?

I thought about it for a few days and came up with the following explanation which I sent to my lecturers. I hope someone here is willing to help and give some constructive feedback. Through my academic career thusfar I have tried to study interdisciplinary instead of studying the subjects as seperate things. I tried using statistics (though I have only had the basics) to answer my question and I am curious about the validity of my explanation. In the attached PDF-file you find this explanation.


With kind regards

Valerio

[Enthalpy]

Goedenavond Valerio, welcome here!

It is essentially correct that if the source's line is too broad, then some light is not absorbed by the observed sample, so the absorption measurement is wrong.

There is no vital need here to consider photons. They only complicate things.

==========

If you want to put photons, then don't forget that they have a linewidth too, independently of any consequence of Doppler or collisions. In this case, they are emitted by some transition of an electron from a higher energy level to a lower one. This transition happens over a finite time called fluorescence time (a laser would hasten this transition), the photon lasts as long, hence the photon has a certain spectrum of frequencies (or energies) rather than a definite frequency. This minimum "natural" linewidth and the fluorescence time are fully linked numerically.

Even if some wave can be written exactly as sin (2πFt) over some finite time, it is not a pure frequency, because an other sine of close frequency resembles that sine over the limited time, as the phase of both sine drifts little. The acceptable frequency mismatch is inversely proportional to the pulse duration. So a receiver, spectrum analyser... does show that the pulse contains nearby frequencies too.

If you like signal theory and processing, it's the story with pulse width, bandwidth, window and sample duration, and it's a property of the Fourier transform time <-> frequency.
If you like quantum mechanics, it's Heisenberg's uncertainty. The energy takes time to be accurate.

There are more uncertainty relations in quantum mechanics, for instance the position and the momentum can't be both arbitrarily accurate. You can understand that one too as a property of the Fourier transform. But for instance the impossibility to know exactly a particle's magnetic moment along two axes does not result from Fourier.

[Valerio]

@Enthalpy

Thank you for your reply!

I am excited to read that I was already on a good way to the explanation.
Are there by chance any books or other sources that explain this subject in great depth (mathematically)? I would like to read up on it after my finals are over. Until now I have used books that are great for understanding the overal concepts, but are (for me at least) a bit shallow for studying a subject in depth (learning in depth is what I do for fun in my spare time)

The books that I have so far are:

°Principles of Instrumental Analysis by Skoog and Holler
°Undergraduate Instrumental Analysis by Robinson
° Fundamentals of Analytical Chemistry by Skoog and West

[Enthalpy]

Huh, I don't know books about this topic. But someone else may.

[Corribus]

Theory: Bernath, Spectra of atoms and molecules.
More prectical: Drago, Physical methods for chemists.

Good luck, tho. The latter is out of print and like a treasure. Maybe you will get lucky. The book is worth its weight in gold.

[anonymous10012]

I have found some really great books on a website called thriftbooks. Old ones.