Comparing Electronic Transitions in H and Be3+

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Discussion Overview

The discussion revolves around comparing electronic transitions in hydrogen (H) and the beryllium ion (Be3+), specifically focusing on the transitions from ni=5 to nf=2 in H and from ni=2 to nf=5 in Be3+. Participants explore the characteristics of the photons involved in these transitions, their energy levels, and the implications of nuclear charge on energy differences.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the validity of statement a), suggesting that the transition in H corresponds to the visible spectrum while the Be3+ transition lies in the UV region, but seeks clarification on why the Be3+ transition is categorized this way.
  • Another participant asserts that as nuclear charge increases, energy transitions should become higher in energy, implying a relationship between nuclear charge and transition energy.
  • A reference to the Rydberg formula is made to support claims about energy transitions in hydrogen-like ions, with a focus on calculating the frequency differences between transitions in Be3+ and H.
  • One participant shares a calculation result of 42nm for a transition in Be3+, indicating that this wavelength falls within the UV region, thus supporting the earlier claim about the spectral classification of the transitions.

Areas of Agreement / Disagreement

Participants express differing views on the truth of the statements regarding the transitions, particularly concerning the spectral regions of the photons involved. There is no consensus on the correctness of the statements, and the discussion remains unresolved regarding the implications of the calculations and the spectral classifications.

Contextual Notes

Participants reference the Rydberg formula and make calculations based on it, but there are unresolved aspects regarding the assumptions made in the calculations and the definitions of spectral regions.

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Homework Statement


Which statement(s) is (are) FALSE in comparing the electronic transition from ni=5 to nf=2 in H with that of electronic transition from ni = 2 to nf = 5 in Be3+:

a) The photon involved in the H transition lies in the visible spectrum while that involved in the Be3+ transition lies in the UV region of the spectrum.
b) A photon of the same frequency is involved in both transitions, but it is emitted the H electron transition and absorbed in the Be3+ transition.
c) All of the above.

Homework Equations





The Attempt at a Solution


I've discarded b) as it is obviously false. However, i think the final answer it's c), but apparently statement a) is true. I know that the H transition corresponds to the visible light region, but why does the Be3+ one lie in the UV region? (if it is from n = 2?) Or how do transitions in absorption of photons work?
 
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How do the energies (and thus also energy differences) in hydrogen like atoms depend on nuclear charge?
 
As nuclear charge increases, shouldn't the energy transitions become higher in energy?
 
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DrDu said:
Yes, exactly. Confer the Rydberg formula for hydrogen like ions:
http://en.wikipedia.org/wiki/Rydberg_formula
So how much larger is the frequency for a given transition in Be3+ than in H?
I'm extremely sorry for not replying! I had my exam the last day and i finally realized what was wrong. I did some calculations with the formula, plugging in the results and i got a result of 42nm (i really don't remember). As visible light is from 400nm-800nm, then it would be in the UV region of the spectrum!
 

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