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Homework Help: Wavelength in an electron transition

  1. May 4, 2009 #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.
  2. jcsd
  3. May 4, 2009 #2
    Ummm... Are you sure it is 4p to 4s? Double check what is written.
  4. May 4, 2009 #3
    I did, three times...I guess I will just have to lose points for this.
  5. May 4, 2009 #4
    Is there a table in your book of the orbital dependence of the energy in sodium?
  6. May 4, 2009 #5
    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]
    Last edited by a moderator: May 4, 2017
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