Wavelength in an electron transition

[elephantorz]

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.

 

[nickjer]

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

 

[elephantorz]

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.

 

[nickjer]

Is there a table in your book of the orbital dependence of the energy in sodium?

 

[nickjer]

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