If energy levels in quantum systems are quantized, where does the excess energy go?

Submitted by Least_Ad104 t3_ywrona in askscience

Suppose you have a hydrogen atom, and you fire photons at it. Assuming you can control the frequency (and hence the energy) of the photon, you can theoretically send a photon of any arbitrary energy towards the atom. Let's say that the energy required to excite the electron from the 1s state to 2s is 1. (Some arbitrary units) And the energy to from 2s to 2p is 0.5 in the same units. Now if I fire a photon of 1.4 energy units, where does the extra 0.4 energy go? There's no further sub quanta of energy it can excite the electron to. Does that mean that such a photon will never be absorbed by the atom? Is there some non quantized sink of energy it can go to, like the kinetic energy of the atom or something like that?

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Appaulingly t1_iwozvhz wrote

If a bound electron is photoemitted the “extra” energy becomes the energy of the free electron. Free particles don’t have quantised states.

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mfb- t1_iwp2bcw wrote

The photon can be absorbed if another photon of 0.4 energy is emitted.

https://en.wikipedia.org/wiki/Raman_scattering

There can be some more exotic options, too. If your atom is moving quickly towards the light source then the photon could have enough energy for the third energy level, in our reference frame it loses kinetic energy.

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Interesting-Month-56 t1_iwp2veq wrote

It depends. If the energy is high enough, the electron will fly off with excess kinetic energy. Otherwise, excess energy is emitted as photons, either immediately, or through a thermal decay process when the electron is promoted to one of a multitude of (quantized) states slightly higher in energy than the ground state of a particular orbital.

If the Hydrogen is in a metallic state, then there is no meaningful quantization in a certain band, so energy can rapidly be dumped into this band, then will be lost as heat when the electrons settle into the lowest levels of the band.

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KingoPants t1_iwpwgjr wrote

If you have a low pressure gas where molecules are isolated from each other then the simple answer is that photons of the incorrect frequencies simply can't be absorbed very well. You can see this by shining broad spectrum light like from the sun or a tungsten lamp through the gas and seeing that fairly distinct narrow bands of frequencies will be missing corresponding exactly to the emmission spectrum of the same element. You can visually see this by splitting the resulting light through a prisim.

It is called the absorption spectra of elements. This is a well known and well studied phenomenon, it's taught to high school chemistry students often including a practical experiment. It has a lot of applications in analysis and astronomy.

http://www.dynamicscience.com.au/tester/solutions1/space%20science/absorptionspectroscopy.htm

The reason it can't like just go into the kinetic energy of the atom is that you need to conserve momentum amoung other things and if other molecules aren't around to take part in the interaction this just isn't possible.

When you have a more dense material you can get more much more interesting pathways however. A relatively simple one is that the excess energy goes into producing a phonon which is a quantum vibrational mode of a lattice, basically just heat.

However there are some really strange things that can happen with dense materials though. For example you can get crystals that take a photon and split it into two.

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Least_Ad104 OP t1_iwtgjiu wrote

I never made the connection between this and absorption spectra. Thank you for the detailed answer!

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