At the beginning of the 20th century, research into radioactive elements led scientists to discover more and more elements that were created from radioactive elements through decay. They were given names such as uranium X, uranium II, thorium X or mesothorium, as in these cases they were formed from the radioactive elements uranium and thorium.

Frederick Soddy and his colleagues researched these so-called decay series and initially came to the conclusion that there should apparently be over 40 different of these radioactive elements, which would have to "share" 11 places in the periodic table. To solve this problem, Soddy investigated the new radioactive elements more closely in 1910 and was able to establish that some of these elements could not be chemically separated from one another. Mesothorium, thorium X and the element radium were apparently indistinguishable in their chemical properties.

These discoveries led Soddy and another scientist, Kazimierz Fajans, to independently establish the radioactive shift theorems in 1913:

• If a radioactive element decays and emits α-particles, i.e. a helium atomic nucleus, an element is created which is two places further to the left in the periodic table, i.e. has a lower mass. For example, the element radium (mesothorium) is formed from thorium through α-decay.
• If a radioactive element decays and emits β-particles, i.e. electrons, an element is created that is one place further to the right in the periodic table but has the same mass.

These rules explained the variety of "new elements" found, all of which were already known elements but could be created in radioactive decay series.

Soddy and other scientists recognised from these results and the displacement theorems that the atomic nuclei of an element had to be of different weights. Soddy called these types of atoms, which belonged to the same element but had to have different masses, isotopes.

In the years that followed, mass spectrometry proved the existence of isotopes. Even naturally occurring elements, such as neon or chlorine, consist of atomic nuclei that have different masses.

The discovery of isotopes also made it clear why most elements did not have integer atomic masses.

When Mendeleev modelled the periodic table of the elements, he realised that the "place" of an element in the periodic table could not depend on its atomic mass. He had to swap the positions of some elements in order to take the periodic properties of the elements into account when organising them. The discovery of isotopes also provided a correct justification for this initially simple assumption: The order of the elements is based on the nuclear charge and not on the atomic mass.