Why do isotopes have the same atomic number?

Isotopes have the same atomic number because they are variants of the same element with different numbers of neutrons.

Isotopes are atoms of the same element that have the same number of protons, but different numbers of neutrons. The atomic number of an element is determined by the number of protons in its nucleus. Since isotopes are variants of the same element, they have the same number of protons, and therefore, the same atomic number.

The term 'isotope' comes from the Greek words 'isos' meaning 'same' and 'topos' meaning 'place', referring to the fact that isotopes of an element occupy the same position on the periodic table. This is because the position of an element on the periodic table is determined by its atomic number.

The difference between isotopes of the same element lies in their atomic mass, which is the sum of the number of protons and neutrons in the nucleus. Since isotopes have different numbers of neutrons, they have different atomic masses. For example, carbon-12 and carbon-14 are both isotopes of carbon. They both have 6 protons, so their atomic number is 6. However, carbon-12 has 6 neutrons and carbon-14 has 8 neutrons, so their atomic masses are 12 and 14 respectively.

In summary, isotopes have the same atomic number because they are variants of the same element with the same number of protons. Their difference lies in the number of neutrons they have, which gives them different atomic masses.