Why do elements such as Cu and Fe have more than one valence number?

Answer 1

Because the energies of the corresponding electronic configurations are stable enough for them to exist. Challenge yourself by writing out the different configurations for +1 and +2 of copper.
For +2, both the s electrons are gone and all the d electron orbitals are all fully-filled with electrons with opposite spins. This makes it stable.

For +1, one of the s electrons is gone and one of the d electrons is gone also. But this affords some stability because you both have unpaired orbitals (rule of multiplicity). However, this is less stable than +2. That is why most compounds of copper are +2.


You can't question nature. You just explain them.

Answer 2

Because they have so many electrons in the outer orbit (normally 7) and they are loosely held so some can get knocked out or added making different isotopes. The elements are determined by the number of protons in the core, not the number of electrons so the same element can have different valence numbers in its outer shell in various isotopes.