Archived Atomic Spectrum of an Unknown Element

[XianForce]

Homework Statement

When an electron drops from the M shell (n = 3) to a vacancy in the K shell (n = 1), the measured wavelength of the emitted x-ray is found to be 0.0897 nm. Identify the element.

Homework Equations

E = 1240 / λ
E = (-13.6 / n^2) * (Zeff^2)

The Attempt at a Solution

According to my homework, the answer is Selenium (atomic number = 34). I initially got that answer by using: (-13.6 / 9) * Z^2 + (13.6 / 1) * Z^2 = 1240 / (.0897). Solving for Z here, I got 33.8.

But I then learned that we are supposed to use Zeff, and not simply Z. I must be misunderstanding something though, because I would then think that the equation would be:

(-13.6 / 9) * (Z - 10)^2 + (13.6 / 1) * Z^2 = 1240 / (.0897)

because there are 10 electrons in the first and second energy levels, so I thought this equation would account for that. But I keep getting a Z value around 32.7 with this which would be in between Germanium and Arsenic.

So what am I missing?

 

[CrazyNinja]

The first thing about this problem is : Bohr's theory and his equations are not even valid here. This is not a one-electron system.

As to how one does this, I am guessing Moseley's equation is the most valid.