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Wavelength in an electron transition

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



2. [tex]\Delta[/tex]l = |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:
[tex]E_{n}[/tex] = [tex]\frac{-13.60}{n^{2}}[/tex]eV
n = 1, 2, 3, ...


Next I used:
[tex]\Delta[/tex]E[tex]_{atom}[/tex] = E[tex]_{1}[/tex] - E[tex]_{2}[/tex] = 0

Meaning, I get zero for this because of the repeating n = 4, then 4[tex]^{2}[/tex] 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:
[tex]\lambda[/tex] = 1240 eV nm / [tex]\Delta[/tex]E

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 [tex]\mu[/tex]m

Thank you.
 

Answers and Replies

  • #2
674
2
Ummm... Are you sure it is 4p to 4s? Double check what is written.
 
  • #3
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.
 
  • #4
674
2
Is there a table in your book of the orbital dependence of the energy in sodium?
 
  • #5
674
2
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 [Broken]
 
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