Quantum Level Question: Absorption Freqs of Electrons

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Discussion Overview

The discussion revolves around the absorption frequencies of electrons in hydrogen and helium atoms, particularly focusing on the transitions between quantum levels and the corresponding emitted and absorbed photon frequencies. Participants explore theoretical models, calculations, and the nature of these frequencies, considering both hydrogen and helium atoms.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes the emission of photons when an electron drops to lower quantum levels in hydrogen, questioning the identification of absorption frequencies.
  • Another participant notes the discrete energy levels of bound electrons in helium and the requirement for energy gain to transition between these levels.
  • A third participant identifies the Lyman and Balmer series, explaining their relation to ultraviolet and visible light, respectively, and mentions the calculation of photon energies and frequencies.
  • There is a discussion about deriving frequencies from various models, including the Bohr model and the Schrödinger equation, with a participant asserting that exact frequencies cannot be determined due to the complexities of quantum electrodynamics (QED).
  • One participant suggests that the absolute value of the energy difference divided by Planck's constant (h) could be used to find frequencies, prompting further clarification about the nature of the question regarding exact photon frequencies versus atomic energies.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the question of absorption frequencies, with some agreeing on the theoretical models that can derive these frequencies while others highlight the limitations in achieving exact values. The discussion remains unresolved regarding the exact identification of these frequencies.

Contextual Notes

Participants mention various models and equations, but there is an acknowledgment that exact solutions are not achievable, particularly in the context of QED. The discussion also reflects uncertainty about the specific frequencies and energies involved in the transitions.

Dlockwood
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Using the hydrogen model, when the electron drops to the 'lowest' quantum level it emits photons in the dark blue; when it drops to the second lowest level it emits in the blue-green. When it is 'bumped up' to the second level it absorbs photons (assuming more than one atom) and when it is 'bumped up' to the third level it absorbs photons. What are the frequencies of absorption? Have they been identified or are they assumed by reason of emissions when the electrons drop to lower quantum levels? And what are all of these exact frequencies?
 
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I don't know what frequency light is emitted when a bound electron moves up or down an energy level iin a Hydrogen atom.

the boundary conditions for a particle in a potential means that bound electron in a helium atom can only have certain discrete energies.From the conservation of energy to move up from one energy level to antother an electron must gain the difference in energy between these two energy levels.
 
Actually, the set of transitions from n > 1 to n = 1 are called the Lyman series, and are all in the ultraviolet. The set of transitions from n > 2 to n = 2 are the Balmer series, and they are all in the visible.

You can easily calculate the energy (and frequencies) of the photons produced by these transitions, which are the same as those required to stimulate the reverse transition.

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

- Warren
 
Why did I say "helium atom"?
 
Wouldn't it simply be the absolute value of the energy difference divided by h?
 
Dlockwood said:
Have they been identified or are they assumed by reason of emissions when the electrons drop to lower quantum levels?

Yes, they can be derived--to varying degrees of accuracy--from the Bohr model, the Schrödinger equation, the Dirac equation and QED. It's amazing that even the humble Bohr model does a pretty good job of it.

And what are all of these exact frequencies?

Exact? That we can't do. For that we'd have to solve QED exactly, which can't be done. However, to get you started, the prediciton of the Bohr and of the Schrödinger equation (in the absence of any magnetic effects) is:

En=(-13.6 eV)/n2

where n=1,2,3,...

The frequency of a photon emitted when an electron is demoted from a state m to a state n (m>n) is (Em-En)/h. If the electron is promoted (m<n), then the frequency of the absorbed photon is the negative of that formula.
 
tavi_boada said:
Wouldn't it simply be the absolute value of the energy difference divided by h?

Yes, but that just changes the question from, "What are the exact photon frequencies?" to "What are the exact atomic energies?"
 

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