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The very heavy atoms that we can create usually have incredibly short half-lives and decay in a tiny fraction of a second.

Isn’t there an active research for the “island of stability” at the top end of the table? Aka a set of elements that theoretically remain stable.

Yes! Here is a nice PBS Spacetime video on the subject that was recently published.

"Are there Undiscovered Elements Beyond The Periodic Table?"

That was a good watch! Thanks.