What is the qm interpretation of moseley's law?

Michio Cuckoo
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moseley did experiments on various elements and showed that the frequency of the k-alpha emission was proportional to the square of the proton no.

The formula is (z-1)^2 proportional to the square root of frequency, with the -1 thrown in for the screening effect.

The bohr model can explain moseleys law quite easily, however how does qm interpret this?
 
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the frequency of the spectral lines, that is.
 

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