The Bohr Model of the Hydrogen Atom

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SUMMARY

The discussion centers on determining the quantum number n of a hydrogen atom's electron when it transitions to the first excited state after gaining 2.86 eV of energy. The correct quantum number for this state is 5, as derived from the energy level equation En=-(13.6 eV) * (z^2 / (nfinal)^2 - (ninitial)^2). The user initially calculated nfinal as 3, which was incorrect. The conversation highlights the importance of correctly applying the energy level formula and understanding the transitions between quantum states.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Bohr model of the hydrogen atom
  • Knowledge of energy level equations in atomic physics
  • Basic proficiency in algebra for solving equations
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  • Study the derivation of the energy level formula for hydrogen atoms
  • Explore quantum number definitions and their significance in atomic transitions
  • Learn about the implications of energy level transitions in spectroscopy
  • Research additional resources on the Bohr model and its limitations
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Students of physics, educators teaching atomic theory, and anyone interested in the quantum mechanics of hydrogen atoms will benefit from this discussion.

frankene
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The electron in a hydrogen atom is in the first excited state, when the electron acquires an additional 2.86 eV of energy. What is the quantum number n of the state into which the electron moves?

I found the answer to be 5 but I don't know how. I thought I could use the following equation:

En=-(13.6eV) * (z^2 / (nfinal)^2 - (ninitial)^2)

En=-2.86
z=1
ninitial=2

I solved for nfinal and had the answer as 3 but that was incorrect. Am I doing something wrong?

Any help on this would be greatly appreciated! Thank you :)
 
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It's been a long time since I worked with this kind of problem, but can you post a link to a web page with info on the energy levels of the hydrogen atom? If I had this problem and no textbook, I'd start with a directed google search...
 
I know I tried to use Google and Yahoo with no help but the only web page I have is for the textbook itself (Cutnell, Johnson: Physics, 6th Edition). I have the right answer for my homework but I was just trying to figure out how. I guess I really wanted to know. LOL

http://bcs.wiley.com/he-bcs/Books?action=index&itemId=0471151831&bcsId=1346

Thank you for your advise!

:smile:
 

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