What is the oxidation number of a zinc atom with an electron conﬁguration of #[Ar]3d^10#?
The electron configuration for a neutral zinc atom is
A zinc 2+ ion has the electron configuration of
The 'oxidation number' is just the difference (+ or -) in the number of electrons in a zinc atom with its normal complement of electrons to that of the defined change.
Oxidation states are the changes from a 'neutral' atom containing balanced protons and electrons to those states in which it either loses electrons or gains them. So, you must first write out the standard, or stable state electron configuration of zinc, then compare it to [Ar]3d^10. Fewer electrons will give it a positive oxidation number, and more electrons will result in a negative oxidation number.