i always thought managnese were in period three... but maybe i'm mixed up. i know that their valence electrons are in the 4s orbial, but they also have electron in the 3d orbital which i'm guessing are the electrons that affect the melting point. i always thought of them in period three, since the d orbital doesn't start until the third energy level. anyway, the trasition metals from scandium to zinc are the ones i'm talking about regardless of the period.
and to answer your other question, we've covered some quantum mechanics. but i've never heard the term harmonic oscillators before, so i'm clearly not very advanced in the area. so if anyone could provide me with an explaination that i'll be able to understand at my level (probably something to do with the concept of oxidation states and electron orbitals, or basic bonding concepts like ligands and such) it would help me out a lot.