why does there occurs the repulsion between same charges?
The atomic or ionic radius actually is a product of two factors, one of which is electron-electron repulsion. [ The other is attraction between the nucleus and the outermost electron.
We often talk about Zeff, the effective nuclear charge, which is the charge the outermost electron would "see" the nucleus have when all of the repulsion between electrons is taken into account.
A simple set of
rules, called Slater's rules, gives s decent approximation of Zeff.
The bottom line, any time we are talking about attraction or repulsion, is Coulomb's law.
F = Qq1q2 / d^2
The force of attraction or repulsion is given by a constant times the magnitudes of the charges divided by the distance between them squared.
So, finally, for your question. Electron-electron repulsion occurs between any two electrons in the atom. The amount of repulsion depends on the distances between them. The amount of repulsion experienced by the outermost electron, compared to the attraction the electron feels for the nucleus, dictates the distance between them and hence the atomic or ionic radius.
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