In atomic science, the z number refers to the number of in the nucleus of an atom.

By convention, the symbol Z is assigned to the number of protons in the nucleus, or simply, the atomic number of an element. This is actually used when you want to determine the effective nuclear charge of a specific electron of an element. The equation is:

Z* = Z - S
where
Z* is the effective nuclear charge
Z is the atomic number
S is the number of electrons between the electron in question and the nucleus

There is due to a phenomenon called the shielding effect. This effect states that the farther the electron is from the nucleus, the lesser is its pull of force to the nucleus. That is the reason why the valence electrons (outermost electrons) are the ones always involved in chemicals reactions. Because they are not that strongly bonded to the nucleus of an atom.