Semantron 23 Summer 2023

The island of stability

Jacob Popoff

The island of stability is a theoretical section towards the end of the periodic table where large superheavy elements have a long enough half-life to be studied before they degrade to more stable isotopes or elements. A half-life stems from the concept that radioactive elements will decay over time, and each radioactive element has its own half-life, which is the time it takes for half of the set substance to decay. The stability of the isotopes within the island of stability are still undecided, with some claiming it will only exist for minutes, whilst others believe that the inhabitants can exist with a half- life of upwards to several billion years. 1 The theory is based on the nuclear shell model, where the aim is to achieve maximum binding energy within the nucleus. This binding energy is linked to the concept that the theoretical mass of the nucleus is higher than the practical mass of the nucleus, even by a small margin, due to energy being used to bind the baryons together. In short, the number of protons and neutrons does not equal the mass number of the isotope of the element. Following Einstein’s principle of relativity (E=mc 2 ), where this missing mass can be provided by an input of energy, this lack of mass becomes necessary for the nucleus to remain stable and together. Due to the Law of Conservation of Mass, where mass can neither be created nor destroyed, the nucleus cannot exist as its constituent parts. Therefore, in order for mass to be conserved, energy must be provided to the system to break apart the nucleus. This gap of energy requirement is referred to as the binding energy: the larger the binding energy, the more stable the nucleus. 2 Through projection of expected breaking energy, we can observe a series of potential areas of which predicted half-life is significantly higher than the predicted surrounding half- lives while maintaining high atomic numbers, therefore existing at the end or beyond the periodic table. These areas are possible locations of the island of stability. Whilst it is possible for these elements to have once existed, formed through nuclear fusion during a star’s stage of supernova, they have since decayed or exist in such small quantities that we are yet to find them, making the only available method of creation being synthesis.

In the diagram (left), 3 the Y- axis demonstrates atomic number, the X-axis neutron number, the boxes are calculated half-lives, and the dotted line refers to the beta stability line where the more stable isotopes are found. The

1 Robert Naeye ‘ An Island of Stability’ An Island of Stability | Discover Magazine consulted 18/08/2022. 2 James Trefil ‘ Nuclear Shell Model’ atom - Nuclear shell model | Britannica consulted 18/08/2022. 3 Anne Marie Helmenstine ‘ Island of Stability – Discovering New Superheavy Elements’ Island of Stability - Discovering Superheavy Elements (thoughtco.com) consulted 19/08/2022.

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