Can temperature affect the absorption and emission ranges of atomic spectra?

[jerromyjon]

Hi, everyone! I was thinking about atomic absorption/emission of photons and how they all have specific locations in the frequency zones as "lines" of missing/peak emissions. I'm curious if there is a scientifically proven/hypothesis of how the physical oscillation of atoms in molecules due to temperature could act as the doppler shift "buffer" of absorption/emission range?

 

[mfb]

The oscillation of atoms in molecules is part of the quantum mechanics of the molecules and their energy states. The emission happens from the molecule as a whole, Doppler shift only occurs if the whole atom moves (as good approximation if the molecule is not too large).

=> motion of the whole molecule leads to Doppler broadening of lines, oscillations in the molecule leads to a splitting of lines.

 

[jfizzix]

In addition, there can be other sources of broadening such as:
-the natural spectral width that's inversely related to the decay time of the transition (thanks to the energy-time uncertainty principle)
- collisional broadening that's due to the electric fields of nearby colliding molecules causing random slight shifts in the energy levels of the molecule in question

 

[jerromyjon]

-the natural spectral width that's inversely related to the decay time of the transition (thanks to the energy-time uncertainty principle)

Thanks a lot! This is a new one by me, going to take a bit to get a feel for, any examples you could share that highlight this effect?

 

[f95toli]

Thanks a lot! This is a new one by me, going to take a bit to get a feel for, any examples you could share that highlight this effect?

Note that this is not a "quantum effect", it is just an unavoidable consequence of how we calculate frequency spectra using Fourier transforms. Hence, this is true for ANY type of spectra: the more localized something is in the time-domain, the wider it is in the frequency domain.

See e.g.
http://www.ams.org/samplings/feature-column/fcarc-uncertainty

 

[jerromyjon]

That Fourier stuff still eludes me somewhat, but what you're saying is it just blurs the accounting of what effects are caused by which degrees of freedom?

 

[mfb]

A finite lifetime (and everything that can emit radiation has a finite lifetime) leads to a natural width of the line - even if no other effects are present, e.g. for a single atom in vacuum.
A handwavy explanation: a finite lifetime means the radiation from the decay has some finite duration: you know it won't be there any more if you wait long enough. What can we say about the frequency spectrum now? A single exact frequency requires a wave that exists forever and fills the whole universe. Everything with a finite duration needs a finite width in the frequency spectrum. States with a shorter lifetime need a larger width in the frequency spectrum.

 

[jerromyjon]

Uncertainty Principle for the Fourier Transform
The fh and their transforms ah show the uncertainty principle for the Fourier transform at work. Roughly, the more tightly localized the f (t) signal is (the shorter the duration of the sound burst), the less tightly localized the a(λ) distribution must be (the larger the spread in frequencies); conversely, the tighter you cluster the frequencies, the wider the f (t) distribution must be. This principle has very precise and natural formulation for normal probability distributions.

This is referring to sound which is normal as in classical, the molecules we're discussing are quantum distributions, but similar concept. Correct?

 

[mfb]

Yes, this is a fundamental limit for all types of waves, classical and quantum mechanical.