What Visible Light Transitions Occur in the Bohr Model of Li++?

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Homework Help Overview

The discussion revolves around identifying visible light transitions in the Bohr model for lithium ions (Li++), specifically focusing on the wavelengths produced by transitions between different energy levels. The context includes the application of the Bohr model to a hydrogenic atom with atomic number Z=3.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to calculate the visible light transitions by using the Bohr model equations. Questions arise regarding the correct application of the atomic number Z and whether it should be multiplied by the principal quantum numbers n and m in the calculations.

Discussion Status

Some participants are providing guidance on how to apply the formula for energy transitions, while others express confusion about the calculations and the use of the atomic number. There is an ongoing exploration of the correct substitutions and evaluations needed to determine the visible transitions.

Contextual Notes

Participants are discussing the constraints of the problem, including the need to identify transitions that fall within the visible spectrum and the specific energy level transitions that are also observed in hydrogen. There is an emphasis on ensuring the correct interpretation of the variables in the equations provided.

ChiefKeeper92
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Bohr Model
1. Assuming that the wavelengths of visible light lie between about 300nm and 700nm, what transitions in Li++ (hydrogenic lithium ions, Z=3) would be visible. Identify each transition by initial and final principal quantum number n. Also identify those transitions that are also seen in hydrogen (3->2, 4->2, 5->2 in hydrogen)

2. E=13.6eV*(Z^2)*((1/n)^2-(1/m)^2)
λ=1240/E


3. I ran through it but I keep getting the same wavelengths as hydrogen. I don't know what I'm doing wrong. Do I multiply n*Z on the bottom before I square it?
 
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What did you use for Z? Remember, the atomic number of Lithium is 3, and the nucleus of the Li++ ion has 3e charge.

ehild
 
I used Z=3 but do I need to multiply Z by n and m?
 
I do not understand you. You need to substitute different n-s and m-s into the formula. First evaluate the expression in the parentheses, (1/n2-1/m2). Then multiply the result by (13.6 * 9).

ehild
 

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