The difference between the volume of an ion and its atom

We can consider the different layers of an atom as envelopes.

The volume of the cation (the positive ion) is smaller than the volume of its atom. When an atom lose an electron it lose one of its envelopes and therefore the attraction force of the neucleus to the envelopes increase and the volume of the ion decrease.

The volume of the anion ( the negative ion) is bigger than the volume of its atom. When the atom gain an an electron the repulsion force between the electrons and this gained electrin increase which lead to the increase of the volume of the ion.