Undergrad Can a Photon be Absorbed Without the Exact Energy Level?

[vanhees71]

To the contrary, the widths of the lines in the line spectrum must be small compared the distance between the states (in energy), which means the states must be long-lived enough. You have $\tau=1/\Gamma$ (in natural units).

 

[DrDu]

Isn't that exactly what I said?

 

[vanhees71]

Sorry, I misread your statement by overreading "inverse". Sorry.

 

[NaiveTay]

There is no "exactly zero", but the probability gets so small that it is negligible in most cases.

Thanks for clarifying, that makes sense. I guess I misread your other post "within the width of the line." Sorry, that's what had me confused.A spectral line has an inherent width explained by the uncertainty principle. Further broadening occurs in our methods of measuring these lines. That's the gist I've gotten from this discussion.
Much thanks to you all for your patience and for making it more enjoyable than scavenging the internet for reliable information. Cheers.

 

[votingmachine]

A spectral line has an inherent width explained by the uncertainty principle. Further broadening occurs in our methods of measuring these lines. That's the gist I've gotten from this discussion.
Much thanks to you all for your patience and for making it more enjoyable than scavenging the internet for reliable information. Cheers.

The transition is an electron from a specific state to another specific state, and that energy difference may be very spectrally tight. But few things are isolated. Anything in the environment around that atom where the transition is occurring may alter the energy of that transition. The easiest to see is the doppler effect in a gas molecules may be moving forward or backward relative to the incident light. But a crystal imperfection may also distort the environment around an atom. Temperature will increase vibrations, or collisions, or just varying inter-atomic distances. Those effects can alter the energy levels of the transition.

I used to measure DNA concentrations in solution. The standard methods use the absorbance at 260 nm. At that wavelength, the purine rings and the pyrimidine rings all have some absorption. But the nucleotides are stacked in a double helix, one on top of the other. And the helix can have strain as it is usually twisted either more or less than the lowest strain geometry. The absorption is highly accurate for determining concentration. But the peak at 260 nm is quite broad. The DNA molecules are structurally complex. And even as a cold solution, there are thermal motions.

I will just guess, but I would assume the tightest spectral lines would be from something very cold, and very simple. Based on that assumption, I googled for "liquid helium absorption spectrum". One link I found has a comment about how sharp the absorption bands they found at 4.2-degrees-K.

http://www.nrcresearchpress.com/doi/abs/10.1139/p58-160?journalCode=cjp#.VzK0z2Zfslk

 

[houlahound]

ancient Chinese proverb (I think);

if your spectral lines are too broad just use the zoom function and zoom on out a bit...

 

[Keith_McClary]

then what are the chances this radiation will be the exact amount required for an electron jump of any of the finite number of elements?

The same phenomenon occurs in in the simple case of (transmission)http://www.open.edu/openlearn/science-maths-technology/science/physics-and-astronomy/scattering-and-tunnelling/content-section-3.5. There are resonances at certain energies (corresponding to how many wavelengths fit in the well). See Figure 13. The resonances do not occur only at an exact energy, since there is still a resonant effect when the wavelengths almost fit in the well. The resonances are sharper in the case of transmission through two barriers as discussed here (PDF), if the walls are high/thick so the waves resonate for many cycles (This is what you refer to as "absorbed").