Final answer:
Atoms of two different elements must have different atomic numbers. Atomic numbers are unique to each element, whereas isotopes of the same element can have different numbers of neutrons and thus different mass numbers, but the same atomic numbers.
Step-by-step explanation:
Atoms of two different elements must have different atomic numbers. An atomic number, represented as Z, is defined as the number of protons in the nucleus of an atom and is unique for each element. Isaotpes, on the other hand, are atoms of the same element that have the same atomic number, but different numbers of neutrons. This variance in neutron number does not alter the atomic number but does change the mass number (A), which is the sum of both protons and neutrons in the nucleus. Therefore, isotopes can have the same chemical properties because they have the same number of protons and electrons, but they have different atomic masses.