Dalton's Atomic Theory, formulated in the early 19th century, posited that all atoms of a given element are identical in mass and properties. However, the discovery of isotopes fundamentally challenged this aspect of Dalton's theory. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. This discovery revealed that atoms of the same element can indeed have different masses, contradicting Dalton's postulate of uniform atomic masses within an element. For example, Carbon-12 and Carbon-14 are both carbon isotopes, but they differ in their mass due to a different number of neutrons. This nuanced understanding of atomic structure provided by isotopes has been crucial in advancing modern atomic theory, making it more comprehensive and accurate than Dalton's original model.

The stability of an isotope is determined by the ratio of neutrons to protons in its nucleus. Stable isotopes have a balanced ratio that allows the forces within the nucleus, namely the strong nuclear force and electromagnetic force, to maintain a stable nucleus. However, when the neutron-to-proton ratio is too high or too low, the nucleus becomes unstable, leading to radioactivity. In such cases, the atom seeks stability through radioactive decay, a process where the nucleus emits particles or radiation to shed excess energy or mass. For instance, Carbon-14, with its six protons and eight neutrons, is unstable and undergoes beta decay to become stable Nitrogen-14. The stability of isotopes is thus a key factor in their radioactive properties and plays a significant role in applications like radiometric dating and nuclear medicine.

Isotopes significantly influence the calculation of the atomic mass unit (amu), which is a standard unit of mass that quantifies the mass of an atom. Since isotopes of an element have different masses, the atomic mass unit is calculated as a weighted average of the masses of an element's naturally occurring isotopes, based on their relative abundance. For example, the atomic mass of carbon is calculated by taking into account the masses of its two main isotopes, Carbon-12 and Carbon-13, and their respective abundances. The mass of Carbon-12 is exactly 12 amu, but the presence of Carbon-13 shifts the average atomic mass of natural carbon to about 12.01 amu. This weighted average approach ensures that the atomic mass reflects the typical isotopic composition found in nature and is crucial for accurate measurements in chemistry and physics.

Generally, the number of neutrons in an isotope does not significantly affect its chemical properties. This is because chemical properties are primarily determined by an atom's electron configuration, which is influenced by the number of protons (or the atomic number), not the number of neutrons. Isotopes of an element have the same number of protons and thus share the same electron configuration, leading to similar chemical behaviors. However, there can be subtle effects, known as isotope effects, particularly in chemical kinetics. These effects arise due to differences in mass between isotopes, which can influence reaction rates or mechanisms. For example, hydrogen and its isotope deuterium can show different reaction rates due to the significant mass difference. Nonetheless, these isotope effects are usually small and don't alter the fundamental chemical properties of the element.

Heavy isotopes such as deuterium are used in nuclear fusion reactions due to their unique nuclear properties that facilitate the fusion process. Fusion reactions involve combining lighter nuclei to form a heavier nucleus, releasing a significant amount of energy. Deuterium, a heavy isotope of hydrogen with one neutron, has a greater mass than protium, making it more favorable for fusion reactions. The presence of the neutron in deuterium adds to the nuclear binding energy, making it more stable under high temperatures and pressures required for fusion. Additionally, deuterium-deuterium and deuterium-tritium fusion reactions have higher cross-sections for fusion, meaning they are more likely to occur under given conditions. These reactions release more energy compared to those involving only protium, making heavy isotopes like deuterium key components in research and development of nuclear fusion as a potential energy source.