Wavelength in an electron transition

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Homework Help Overview

The discussion revolves around the allowed transitions of electrons in sodium, specifically the transition from the 4p to the 4s orbital. Participants are exploring the conditions under which such transitions occur and the associated calculations for wavelength.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine if the 4p to 4s transition is allowed and calculates the wavelength based on energy differences. Some participants question the accuracy of the transition notation and suggest verifying the details. Others inquire about resources that might clarify the energy levels in sodium.

Discussion Status

The discussion is ongoing, with some participants expressing uncertainty about the transition notation and the calculations involved. There are suggestions for checking external resources, but no consensus has been reached regarding the correctness of the original poster's approach or the transition itself.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the information they can access or share. There is also a mention of potential penalties for incorrect answers, indicating a concern about accuracy in the context of academic evaluation.

elephantorz
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1. Is a 4p -> 4s transition allowed in sodium? If so, what is the wavelength? If not, why not? (Z = 11 for sodium)



2. \Deltal = |l2 - l1| = 1
That is for the first question, in which case it is allowed, hence |0-1| = |-1| = 1, and meets the requirements for the equation.

The second part is what I don't understand because I used these equations:
E_{n} = \frac{-13.60}{n^{2}}eV
n = 1, 2, 3, ...


Next I used:
\DeltaE_{atom} = E_{1} - E_{2} = 0

Meaning, I get zero for this because of the repeating n = 4, then 4^{2} which = 16 and therefore I have an issue here I do not know how to solve after pondering.

The third equation I must use is:
\lambda = 1240 eV nm / \DeltaE

But I am not there yet...


3. As you can see my attempt is either erroneous or there is some sort of lone energy I am not aware of, by the way, the answer to this is:

Yes; 2.21 \mum

Thank you.
 
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Ummm... Are you sure it is 4p to 4s? Double check what is written.
 
nickjer said:
Ummm... Are you sure it is 4p to 4s? Double check what is written.

I did, three times...I guess I will just have to lose points for this.
 
Is there a table in your book of the orbital dependence of the energy in sodium?
 
Here is an equation that uses different effective nuclear charges depending on the orbital quantum number:

http://physics.wm.edu/~inovikova/phys251/manual/naspec.pdf
 
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