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What defines isotopes in relation to the elements they belong to?

  1. Atoms with different numbers of protons

  2. Atoms of the same element that have different numbers of neutrons

  3. Atoms of different elements with the same mass

  4. Atoms that have the same number of neutrons but different protons

The correct answer is: Atoms of the same element that have different numbers of neutrons

Isotopes are defined as atoms of the same element that have different numbers of neutrons. This is significant because the number of protons in an atom determines the element's identity; thus, all isotopes of a particular element will have the same number of protons. However, variations in the number of neutrons result in different atomic masses. For instance, carbon has several isotopes, including carbon-12 and carbon-14, where both have six protons but differ in their neutron counts (six for carbon-12 and eight for carbon-14). This understanding is crucial, especially in fields like chemistry and physics, where isotopes play a vital role in reactions, radiocarbon dating, and nuclear applications. The other choices incorrectly define isotopes by referencing either changes in protons or mixing elements, which does not align with the fundamental definition of isotopes based on neutron variation within a single element.