Which state of matter (solid, liquid, or gas) has molecules that move the fastest?

Gas.

Solid is the slowest; it stays together, so the molecules don't move much.
Liquid is the middle; it stays together for the most part, but it can move.
Gas is the fastest; they can move all over the place!

☆ionisation energy increases across a period from na -> ar☆ionisation energy decreases down a group from li -> fr☆ionic radius decreases across a period from na -> cl☆ionic radius increases down a groupfrom f -> ii hope it clarifies your doubts