What part of the atom determines if it will combine or break apart from other substances

The combination of an atom with other atom is bonding. Or break apart from other substance is breaking of interaction.

The bonding or interaction (inter-atomic) are due orbitals and electrons present in these orbitals

The atom consists of

a) a central nucleus which has proton and neutrons: they do not take part in chemical reactions

b) the part other than nucleus which has shells, sub shells and orbitals

These orbitals have electrons.

So the outer part of nucleus takes part in any combination with other substance

it's c. elements are placed in rows based on how may valencies electrons have.

the answer is c.the valence of the atoms combine .