Introduction: Isotopes play an important role in various fields of study, such as anthropology. For example, carbon-14 is an isotope used to date objects back time periods of over 5,000 years - like bones. This has helped to identify skeletons in different parts of the world, like Egypt. Isotopes refer to two or more different forms of atoms of the same element, which have the same number of protons and atomic number, but a different number of neutrons and mass number.

In the field of geology, isotopes also play an important role. Uranium-238 is an isotope of the element uranium that is used to date geological formations. In chemistry, we are concerned with understanding isotopes on the subatomic level, so that we can predict the atomic masses of specific elements. Applications of isotopes in chemistry have also had important consequences for historical developments. With the Manhattan Project during World War II, scientists looked to create atomic weapons. Scientists were faced with the issue of separating different isotopes of the element uranium, as they wished to extract a lighter isotope of uranium known as uranium-235.

An understanding of differences in the nuclei of atoms when comparing isotopes can be understood through calculations with atomic and mass numbers of each isotope. For example, when comparing carbon-12 and carbon-13, we utilize carbon's atomic number of 6, along with the mass numbers of the isotopes, 12 and 13. The number of protons is found from the atomic number. On the other hand, the number of neutrons is found by subtracting the atomic number from the mass number. Based on this, in both carbon-12 and carbon-13, there are 6 protons. The key difference between the isotopes lies in the fact that carbon-12 has 6 neutrons, while carbon-13 has 7 neutrons, since carbon-13's mass number is one greater than carbon-12's mass number is. In studying isotopes, it is also worth noting that, since the number of protons doesn't change for the isotope of a neutral atom, the number of electrons doesn't change, either.