Final answer:
Atoms of the same element are the same because they have the same number of protons in the nucleus. This number is called the atomic number and it is unique to each element.
Step-by-step explanation:
The modern atomic theory states that atoms of one element are the same, while atoms of different elements are different. The fundamental characteristic that all atoms of the same element share is the number of protons. All atoms of hydrogen have one and only one proton in the nucleus; all atoms of iron have 26 protons in the nucleus. This number of protons is so important to the identity of an atom that it is called the atomic number (Z). Each element has its own characteristic atomic number.