Average or Apparent Mass of an Element

At the beginning of the 19th century, John Dalton proposed his new atomic theory—all atoms of the same element are identical and equal in mass. It was a simple yet revolutionary theory. It was also not quite right. The discovery of radioactivity in the 20th century made it possible to study the actual structure and mass of atoms. Gradually, evidence was obtained that atoms of the same element could have different masses. These atoms were called isotopes. How are isotopes different from one another? What is the relationship between the atomic mass of an element and the mass of each isotope?