why does non metals show variable valency?

Answer 1

The simple explanation has to do with them having electrons in the d orbital. So, there are 5 orbitals in the d subshell, and as the number of unpaired valence electrons increases, so does the oxidation state. And, btw, oxidation state is the preferred term as the term valence and valency is outdated. So, the unpaired valence electrons are not very stable and want to combine with other species. If you look at the first period of the transition element (period 4), Sc has 1 unpaired d electron and it has 2 electrons in the s orbital. This makes 3 valence electrons and so has an oxidation state of 3+. As you move across the period, the number of d electrons keep increasing (e.g Ti has 2, C has 3....Zn has 10). This allows for multiple oxidation states, the number of which can be determined by adding the d orbital electrons to the s orbital electrons.

Chromium and copper represent exceptions to these general rules.