Isotopes of the same element have the same number of protons, but a different number of neutrons. Neutrons are subatomic particles that contribute to the overall mass of an atom, but do not affect its chemical properties. As a result, isotopes of the same element have very similar chemical behaviour, but can have slightly different physical properties, such as density.

Density is defined as mass per unit volume. Since isotopes have the same number of protons, they will have a similar number of electrons orbiting the nucleus. This means that the overall charge of the atom remains the same. However, the addition of neutrons increases the mass of the atom without significantly changing its size. As a result, isotopes with more neutrons will have a higher density than isotopes with fewer neutrons.

For example, consider carbon-12 and carbon-13. Carbon-12 has 6 protons, 6 neutrons, and 6 electrons, while carbon-13 has 6 protons, 7 neutrons, and 6 electrons. The addition of one neutron increases the mass of carbon-13 by about 1.6%, but does not significantly change its size. As a result, carbon-13 is denser than carbon-12.

The difference in density between isotopes can be used to separate them. This is done through a process called isotope separation, which is used in a variety of applications, such as the production of nuclear fuel and the enrichment of uranium for use in nuclear reactors.