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I understand that the electron needs a specific quantized amount of energy in order to be excited to another state. For example, hydrogen requires $10.2\ \mathrm{eV}$ for its electron to jump from $n=1$ to $n=2$.

Scenario 1:
What happens if the photon that it has collided with has an energy above $10.2\ \mathrm{eV}$, let's say $10.3\ \mathrm{eV}$? Would the electron still jump from $n=1$ to $n=2$, but the remaining $0.1\ \mathrm{eV}$ be kept within the photon? If so, would Compton's effect occur where the photon is scattered in another direction with a different frequency?

Scenario 2:
What happens if the light is emitting photons with energy of $13\ \mathrm{eV}$? Would it be possible for the electrons to be absorbing different amounts of energy? i.e some electrons absorb energy to be excited to $n=3$ or some to $n=2$? I would assume that this is the case since the emission spectra plays on this idea by having different types of “light” created with the electrons emitting different frequencies of light.

I understand that similar questions have been posted on this site, but I do not understand the wordings of some of them.

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  • $\begingroup$ I have not studied this very much but I do recall an article somewhere a few years ago. The idea was that protons emit energy waves from the nucleus radiating outward spherically. When the electrons absorb energy and rise to higher level they become unstable but are more stable in the valleys or trough of the radiating energy wave. I have always assumed the energy levels of the valence electrons rise and fall together and settle into these troughs. I also assumed the small difference of energy would either radiate away or settle back into the electrons again. $\endgroup$ – Bill Alsept Sep 7 at 14:56
  • $\begingroup$ @BillAlsept Could you please provide a further explanation on this? I also thought that the small difference in energy would radiate away due to Compton's effect. $\endgroup$ – S. Lee Sep 8 at 2:48
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If the photon energy is off significantly, like in the example, it won’t be absorbed: those atoms are transparent to light of that wavelength.

This is why gases show a spectrum of absorption lines, with only specific wavelengths absorbed.

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  • $\begingroup$ I understand that the electron won't absorb the photon's energy if it is significantly off, as it only accepts quantised amount of energy. However, what I'm questioning is what happens if the energy given by the photon is higher than the quantised energy needed? Are you suggesting that the electron won't accept it at all? Then I don't understand how come an element can emit different wavelengths, as that can only happen if the amount of energy accepted by the electrons varies. i.e, in discharge tube of Hydrogen, some electrons accept 12.09eV's, whilst some accepts 12.75eV's. $\endgroup$ – S. Lee Sep 8 at 2:46
  • $\begingroup$ 12.09 can be absorbed or emitted by one transition, others valued by others. But if the energy doesn’t match a transition, it doesn’t happen. $\endgroup$ – Bob Jacobsen Sep 8 at 2:54
  • $\begingroup$ Yes, but I'm just confused because in a question it stated; "In an experiment similar to that of Franck and Hertz, electrons of energy 12 eV are fired into a gas. Electrons penetrating the gas are collected and their energies measured at 12 eV, 1.4 eV and x eV. If the spectrum of the light emitted from the gas is also analysed and found to contain photon energies of 11.4 eV, 10.6 eV and y eV, deduce the values of x and y." In this example, it's connoting to the idea that an electrons absorb a quantised amount of energy from a larger portion of energy, leaving behind unused energies. $\endgroup$ – S. Lee Sep 8 at 5:03
  • $\begingroup$ Or would this scenario be different as it's absorbing energy from an electron and not a photon per se? However, wouldn't the same theory of absorbing quantised amount of energy apply? $\endgroup$ – S. Lee Sep 8 at 5:06
  • $\begingroup$ Electron scattering is different from photon absorption. $\endgroup$ – Bob Jacobsen Sep 8 at 5:09

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