The correct option is "Number of protons" (option 1).

The atomic number of an element is the number of protons present in the nucleus of an atom. Protons are subatomic particles with a positive charge, and they determine the identity of the element. Each element has a unique number of protons.

Option 2, "Number of protons and electrons," is not correct because the number of electrons can vary depending on the charge of the atom. It is the number of protons that defines the atomic number.

Option 3, "Number of ions," is not correct either because ions are atoms or molecules that have gained or lost electrons, resulting in a different number of protons and electrons.

Option 4, "Number of nucleons," is incorrect. Nucleons are the collective term for protons and neutrons, but the atomic number specifically refers to the number of protons.

Therefore, the atomic number of an element is determined solely by the number of protons.