Explain why the atomic radius of aluminium is smaller than that of sodium.

Okay, to explain this you might have to grab a periodic table.

Do you have one? Good. Look at the most left side of the periodic table. The first group is the largest atoms in the periodic table. If you go to the right of the periodic table, the atoms get progressively smaller and smaller.

Why is this? Don't atoms get more electrons, and so become significantly bigger as they move to the right?

Although atoms do get more electrons as they go to the right, they also get more protons too. Protons pull on electrons and make atoms smaller. Because of this, going from left to right in a periodic table makes the atoms smaller and smaller, since more and more protons are added.

In this scenario, Aluminum is more to the right than Sodium, which means that it has more protons. Because of this, the protons in Aluminum pull more strongly on electrons than sodium, thus making aluminum smaller.

(Just a side note, going down in a periodic table makes the atoms bigger, since new shells are added every time)

Good luck! If you need any help, just ask :))
-T.B.

Ametal with a large number of free flowing electrons most likely has good conductivity