Magic number : The nucleus of an atom, like an extra-nuclear electrons, also has particular energy levels (shells).

The nuclei with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons have been found to be particularly stable with the large number of the isotopes. These numbers, commonly called as Magic numbers are defined as number of nucleons needed for the completion of the energy levels of the nucleus. Nucleons are arranged in the shells as two protons or the two neutrons (with the paired spins) just like that of the electrons arranged in the extra-nuclear part. Hence the following nuclei ₂He⁴, ₈O¹⁶, ₂₀Ca⁴⁰ and ₈₂Pb²⁰⁸ possessing protons 2, 8, 20 and 82 respectively (all the magic numbers) and neutrons 2, 8, 20 and 126 respectively (all the magic numbers) are the most stable.

       Magic numbers for protons :   2, 8, 20, 28, 50, 82,114

       Magic numbers for neutrons : 2, 8, 20, 28, 50, 126, 184, 196

When both the number of protons and the number of neutrons are magic numbers, the nucleus is quite stable. This is why most of radioactive disintegration sequence terminate into the stable isotope of lead (magic number for the proton = 82, magic number for the neutron = 126).  Nuclei with the nucleons just above the magic numbers are quite less stable and thus these can emit some particles to attain the magic numbers.

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