How are isotopes of an element defined?

Isotopes are defined as atoms of the same element that have the same number of protons but different numbers of neutrons. This definition is critical because the number of protons defines the element's identity, while the variation in the number of neutrons results in different atomic masses primarily affecting the stability and radioactivity of the isotopes.

For example, carbon has isotopes such as Carbon-12 and Carbon-14; both have six protons, which makes them carbon, but Carbon-12 has six neutrons while Carbon-14 has eight. This distinction is essential for various applications, including dating archaeological finds or in medical imaging and treatments.

The other interpretations do not align with this fundamental aspect of isotopes. For example, variations in chemical properties are not a defining characteristic, as isotopes of the same element generally exhibit similar chemical behavior due to having the same electron configuration. Similarly, the statements regarding protons and neutrons being identical or mixed up does not reflect the core definition of isotopes. Thus, the correct understanding of isotopes is fundamentally anchored in their relationship between protons and neutrons.