Why is a chlorine atom smaller than a chloride ion?

Answer 1

Because the extra electron in the ion makes it harder for the atom to hold all its electrons, and the electrons repel each other, increasing the diameter.

You may get a more technical answer involving orbitals and energy levels, but the above is my intuitive idea of how it works.

Answer 2

cloride ion has one more electron. The shielding due to this electron allows the electron cloud to have a larger diamerter