# Subatomic question - K alpha lines

## Homework Statement

Light from the K-alpha line of an unknown material X is compared with the K-alpha line of Carbon. The wavelength ratio is $$\frac{\lambda_x}{\lambda_c} = 0.148$$. What is the matieral X?

## The Attempt at a Solution

I've got no idea where to go with this one. The only time i've used K-alpha lines is in regards to changes of energy levels. I know E=hf=hc/lamba, but i don't see how that helps

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Dick
Homework Helper
Your first question to answer is which energy levels is a K-alpha line related to and what is the relation of those levels to atomic number?

Tom Mattson
Staff Emeritus
Gold Member
It looks like you're supposed to consult a table. You would have to find the entry in the table for which $\lambda_x=0.248\lambda_C$.

Do you have such a table in your book?

^ Definitely no table, Tom. It's an isolated question, so i'm thinking I need to approach it a different way.

Dick
Homework Helper
You didn't answer my questions yet?

Sorry Dick, missed that post! I'm pretty sure the K-alpha line arises when an electron transfers from the L shell (2nd) to the K shell (first), not sure about the relation

Dick
Homework Helper
Ok! You have the levels. Now if you ignore the other electrons around, what is the relation between the energy of these levels and the nuclear charge?

OK, i'm looking through some information on the Bohr Atom and I've found this relation which seems to link the two:

$$E_n = -Z^{2} \frac{E_0}{n^{2}}$$

Not sure if that's the one you're thinking about ...

Dick
Homework Helper
That's the one! So the energy difference is proportional to Z^2. But there are other electrons around. There is one in particular to worry about. Which one? Isn't this fun!?

OK, so the transition between the n=2 and n=1 shell will result in the emission of a photon, i'd imagine, which would have a wavelength associated with it $$\lambda = \frac{c}{f} = \frac{hc}{E_i - E_f}$$

Dick
Homework Helper
Yes. And the energy difference is ROUGHLY proportional to Z^2. But I'm worried about the effect of another electron besides the one making the jump.

^ Not quite sure what you mean there. I'm looking through my notes on the Bohr Model and some worked examples of Lyman series transitions (n=2 -> n=1) and they only seem to be concerned with the energy of the photon and the difference in energies of the final and initial atomic state

Dick
Homework Helper
Fair enough. But they are talking about fully ionized atoms. In our case we should assume that the K shell probably won't be empty before the transition occurs. How many electrons might be there? What effect would this have on the problem?

Just another thought, if I use Mosely's law, and turn it into a ratio of the wavelengths , that'll let me solve for Zx which comes out as 13.9999 = 14 = Si. Not sure if that's ok...

Dick
Homework Helper
Dang. I was one step away from having you (at least partially) derive Moseley's law. The other K electron will screen the nuclear charge - so you only get an effective charge of (Z-1) (as you see in his formula). The only thing you can't really easily compute is whether the screening is 100% effective. But it turns out to be pretty close. So you now understand the formula as well as you use it right? Si sounds right.

Yeah, i think i understand Mosely's formula - from what I've just read, the 1 accounts for the shielding due to other electrons (and is always roughly 1 for innermost levels)

Dick