Questions re: absorption spectrum

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SUMMARY

The discussion centers on the principles of absorption spectroscopy, specifically addressing the behavior of electrons when they absorb and emit photons. It is established that when an electron absorbs a photon, it can indeed emit a photon of the same frequency and energy; however, the emitted photon is released in random directions. This scattering of emitted photons results in the appearance of black lines in the absorption spectrum, as only a small fraction of emitted photons travel towards the observer, leading to gaps in the spectrum of an incident beam of white light.

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Mike_UK
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Hi readers,

I'm confused about some aspects of absorption spectroscopy, and hoping someone can de-confuse me

First, just a preliminary question; am I right in thinking that when an electron absorbs a photon, the electron will then emit a photon of the same frequency and energy as the one it has just absorbed?

If the answer to the above is yes, then why is it that a gas (such as hydrogen) can cause gaps (black lines) in the spectrum of an incident beam of white light? I understand that electrons within the atoms of the gas will absorb some wavelengths of the white light, but if the electron then emits a photon of the same frequency and energy, then all of the frequencies should come out of the gas intact, right?

Is it the case that the emitted photon is sent off in a different direction, so that it doesn't end up in the spectroscope? Is that why we see the black lines in the absorption spectrum?
 
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Yes you've got the answer there.
The re-emitted photons come out in all (random) directions rather than all in the original direction. (Towards you) The result is the dark line. It's not totally "black" as there are some photons emitted in your direction. Just very few.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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