HOw is the number of free electrons determined in a metal?

Answer 1

Per Atom, metals have either 1, 2 or 3 electrons in their outer shells.

Metals have no band gap between the valence band (the outer shell) and the conduction band - therefore the electrons can be utilised immediately for conduction.

You could potentially work out how many conducting electrons you had by finding the mass of metal you have, then working out how many moles you have, then multiplying it by Avagadro's number (6.023 x 10^23 to give you the total amount of atoms) and then multiplying it by 1, 2 or 3 (depending on the metal).

This method would be innaccurate however due to metals conducting electric current over their surface rather than through the middle of themselves. Good Question though....

Answer 2

The type of proton -- subsequently the type of electrons. The type of electrons in turn determines its type of valence electrons, and subsequently its chemical properties, and for this reason whether that's a metallic or what.