I K-beta line for the X-ray spectra of Molybdenum with Moseley

1. Apr 21, 2016

This should be easy but I'm totally stuck here.

So I'm calculating the Kβ line (emitted energy) of Molybdenum (Mo 42). I'm using Moseley's law and am moving from the M-shell to the K-shell. Recall Moseley's law is E = 13.6 eV (Z-σ)2 *1/n2. The effective formula for the energy emitted is thus E = 13.6 eV (Z-σ)2 *(1- (⅓2) since I am moving from n = 3 to n = 1. σ is the screening constant of n =3 of Molybdenum. Using a screening constant of 1 (I know this is incorrect, but bare with me) I get that the difference in energy is 20.321 keV. The answer according to all tables I've seen is 19.607 keV.

The only thing I could think was that the error was due to the approximation of the screening constant. Solving the equation backwards for the "table value"of K-beta gives an Zeff of 40.27. I can't fit the screening constant into that equation, since it is 4.15, as calculated with Slater's rules.

Could anybody tell me what I am missing here? I'm super thankful for all the help I can get.

2. Apr 21, 2016

drvrm

you may try a screening constant sigma(31) =1,72 for the Kbeta transition and check if you get a correct value
Mo z=42 E (Kalpha)17.48 sigma(21) 0.60
E (K beta)19.61 sigma(31) 1.72

details you can see at :
http://www.ld-didactic.de/literatur/hb/e/p6/p6354_e.pdf

3. Apr 23, 2016

Thank you, this would make it exactly right. I'm still not entirely sure how the screening constant (σ) is calculated if the energy E is unknown. How would you do it?
I tried with Slater's rules but I couldn't get it right. Thanks a lot for the help!

4. Apr 23, 2016

drvrm

i have a hunch that a theoretical estimate of screening of the nuclear charge can be made exactly if you know the 'exact' electronic charge distribution- and electronic shell charge distribution is not 'realistic' enough to give correct picture except perhaps s-shells which are spherically symmetric -therefore the experimental estimates of sigma can be used and an average effect of screening is used instead