Find Approx Wavelength of Titanium Kbeta X-Rays

[negatifzeo]

Homework Statement

The X-ray spectrum for a typical metal is shown in Figure 31-22. Find the approximate wavelength of Kbeta X-rays emitted by titanium. (Hint: An electron in the M shell is shielded from the nucleus by the single electron in the K shell, plus all the electrons in the L shell.)
(The figure seems irrelevant to me, no useful data is privded by it, it's just a graph with no labels.)

Homework Equations

The Attempt at a Solution

I don't really know what to do here, there's several things I don't understand. I believe that K-beta X-rays are emitted when the electron drops from the 3rd excited state to the ground level. But how do you determine the energy level difference here? And when Titanium is in an "excited" state, does that mean that just one electron moved up 3 levels, or more than one? Any help in explaining this would be greatly appreciated.

 

[alphysicist]

Hi negatifzeo,

That's right; in this case, there is only one electron in the n=1 shell, and one of the electrons that is in the n=3 shell is dropping to fill the n=1 shell.

If this was a hydrogenic titanium atom with only one electron, and the electron was making a transition from n=3 to n=1, the energy levels would be found from:

$$E_n = -Z^2 \frac{13.6\mbox{ eV}}{n^2}$$

If the atom is not hydrogenic, then the equation above has to modified to account for the other electrons. The inner electrons will partly shield the nuclear charge. We account for this in the above equation by changing $Z\to Z_{\rm eff}$, where $Z_{\rm eff}$ is called the effective nuclear charge.

So mostly what this problem is about is that you need to find the effective Z values for an electron in the n=3 shell and for an electron in the n=1 shell of titanium.

Does this help?