The atomic number, written as Z, refers to the number of protons in the nucleus of an atom, and is used to organize the periodic table of elements. Each chemical element has a different number of protons, so the atomic number is a unique identifier for an element. For example, 6 is always carbon, 92 is always uranium, and 1 is always hydrogen.
Atomic number should not be confused with mass number, the total number of protons plus neutrons in a particular atom. When writing out descriptions of a particular atom, sometimes the atomic number is included, and sometimes it's implied from the chemical name (if the chemical name is listed as nitrogen, the atomic number must be 7). When it is included, the atomic number is put in a subscript before the name of the element and the superscript before the element (14 in this case) is the mass number: .
Different isotopes will have the same atomic number but different mass numbers; an example would be: , , .
The University of Colorado has graciously allowed us to use the following PhET simulation. This simulation builds atoms from protons, neutrons, and electrons and tests knowledge of the periodic table. The simulation shows how the neutrons and protons must balance for the nucleus to be stable. Note how this simulation allows changing the atomic number and mass number.