Explanation behind Moseley's Law?

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That page attempts to explain the Z-1. What part of it are you having trouble with?
 
wiki states it is "predominantly a consequence of the difference of the value of the electron-electron repulsion in the initial and final states of the atom that undergoes the x-ray transition"

but I'm not sure how we can derive the values of 1 and 7.6
 
so initially Moseley thought it was due to screening