The inability to find new elements that aren't radioactive is primarily due to the fundamental properties of atomic nuclei and the stability of elements. Elements are characterized by the number of protons in their atomic nuclei, known as the atomic number. The stability of an atomic nucleus depends on the balance between the forces holding the protons together (strong nuclear force) and the electrostatic repulsion between positively charged protons.
For lighter elements, such as hydrogen, helium, and lithium, stable isotopes exist because the strong nuclear force is sufficient to overcome the electrostatic repulsion. These elements have a favorable neutron-to-proton ratio, allowing for stable nuclei.
However, as the atomic number increases, the electrostatic repulsion between protons becomes stronger, requiring an increasing number of neutrons to maintain stability. As a result, most heavier elements have unstable, radioactive isotopes. These isotopes undergo radioactive decay, spontaneously emitting radiation in the form of alpha particles, beta particles, or gamma rays as they strive to achieve a more stable configuration.
The production of new elements in laboratories involves the synthesis of heavy and superheavy elements by bombarding target atoms with accelerated nuclei. The resulting compound nucleus formed in these reactions is typically highly unstable and decays rapidly, often within fractions of a second, through various radioactive decay modes.
The challenge in discovering new elements that are not radioactive lies in achieving a sufficiently stable configuration of protons and neutrons in the atomic nucleus. The higher the atomic number, the more challenging it becomes to achieve stability due to the increased electrostatic repulsion.
It's worth noting that stability can be affected by the "magic numbers" of protons and neutrons, which correspond to the filling of certain atomic orbitals. Elements with magic numbers of both protons and neutrons tend to exhibit enhanced stability, known as nuclear shell closure. Examples include helium-4 (2 protons, 2 neutrons) and lead-208 (82 protons, 126 neutrons). These elements have relatively long half-lives and are considered stable.
In summary, the absence of new non-radioactive elements beyond what is currently known is primarily due to the inherent challenges posed by the balance between nuclear forces and electrostatic repulsion, making it difficult to achieve stable atomic configurations at higher atomic numbers.