Corrected Z

If,

$f=\sqrt{\cfrac{c^3}{8\pi}*{density}*{Z}*3.4354}$

from the post "Photons With Kinetic Energy?" dated 5 Dec 2017 is correct, we have still to place such a coalesce of particles.

In the case of threshold frequencies, is it the electron cloud under the paired orbits that interacts with the radiating photons and results in an emission of a basic particle charge?  If so, $Z$ has to be corrected with

$f=\sqrt{\cfrac{c^3}{8\pi}*{density}*{Z_{cloud}}*3.4354}$

$Z_{cloud}=Z-Z_{orbits}$

where $Z_{orbits}$ are the number of charges in orbit above the electron cloud with $Z_{cloud}$ number of charges.

Below are plots of experimental and calculated frequencies vs atomic number.

It does not show that,

$Z_{cloud}=Z-Z_{orbits}$

introduces a consistent error.  Why do values for atomic number below twenty and above sixty show greater discrepancies?

In the following plots, the calculated frequencies has been displaced downwards by $0.5\times10^{15}$

to show the corresponding trend/profile between the experimental and calculated plots.

Have a good day.