īoth calcium-48 ( 48Ca) and nickel-48 ( 48Ni) are double magic because calcium-48 has 20 protons and 28 neutrons while nickel-48 has 28 protons and 20 neutrons. It is no accident that helium-4 ( 4He) and oxygen-16 ( 16O) are the second and third most abundant (and stable) nuclei in the universe. Nuclei which have both neutron number and proton ( atomic) number equal to one of the magic numbers are called "double magic", and are especially stable against decay. It is now believed that the sequence of spherical magic numbers cannot be extended in this way. Before this was realized, higher magic numbers, such as 184, were predicted based on simple calculations that assumed spherical shapes. Unlike the magic numbers 2-126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed.
Large isotopes with magic numbers of nucleons are said to exist in an island of stability. The unusual stability of isotopes having magic numbers means that transuranium elements can be created with extremely large nucleiĪnd yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers (as of 2007, the longest-lived, known isotope among all of the elements between 110 and 120 lasts only 11 seconds). The seven known magic numbers as of 2007 are:Ģ, 8, 20, 28, 50, 82, 126 (sequence A018226 in OEIS)Ītomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay. In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. For other uses of the term, see magic number
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