Magic number (physics) in the context of Calcium

Tin is a chemical element; it has the symbol Sn (from Latin stannum) and atomic number 50. A metallic-gray metal, tin is soft enough to be cut with little force, and a bar of tin can be bent by hand with little effort. When bent, a bar of tin makes a sound, the so-called "tin cry", as a result of twinning in tin crystals.

Tin is a post-transition metal in group 14 of the periodic table of elements. It is obtained chiefly from the mineral cassiterite, which contains stannic oxide, SnO
₂. Tin shows a chemical similarity to both of its neighbors in group 14, germanium and lead, and has two main oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element on Earth, making up 0.00022% of its crust, and with 10 stable isotopes, it has the largest number of stable isotopes in the periodic table, due to its magic number of protons.

In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid-drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.

The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model.

Bismuth-209 (Bi) is an isotope of bismuth with the longest known half-life of any nuclide that undergoes α-decay (alpha decay); the decay product is thallium-205. It has 83 protons and a magic number of 126 neutrons, and naturally-occurring bismuth consists entirely of this isotope.

In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model utilizes the Pauli exclusion principle to model the structure of atomic nuclei in terms of energy levels. The first shell model was proposed by Dmitri Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Maria Goeppert Mayer and J. Hans D. Jensen, who received the 1963 Nobel Prize in Physics for their contributions to this model, and Eugene Wigner, who received the Nobel Prize alongside them for his earlier foundational work on atomic nuclei.

The nuclear shell model is partly analogous to the atomic shell model, which describes the arrangement of electrons in an atom, in that a filled shell results in better stability. When adding nucleons (protons and neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation that there are specific magic quantum numbers of nucleons (2, 8, 20, 28, 50, 82, and 126) that are more tightly bound than the following higher number is the origin of the shell model.

Unbihexium, also known as element 126 or eka-plutonium, is a hypothetical chemical element; it has atomic number 126 and placeholder symbol Ubh. Unbihexium and Ubh are the temporary IUPAC name and symbol, respectively, until the element is discovered, confirmed, and a permanent name is decided upon. In the periodic table, unbihexium is expected to be a g-block superactinide and the eighth element in the 8th period. Unbihexium has attracted attention among nuclear physicists, especially in early predictions targeting properties of superheavy elements, for 126 may be a magic number of protons near the center of an island of stability, leading to longer half-lives, especially for Ubh or Ubh which may also have magic numbers of neutrons.

Early interest in possible increased stability led to the first attempted synthesis of unbihexium in 1971 and searches for it in nature in subsequent years. Despite several reported observations, more recent studies suggest that these experiments were insufficiently sensitive; hence, no unbihexium has been found naturally or artificially. Predictions of the stability of unbihexium vary greatly among different models; some suggest the island of stability may instead lie at a lower atomic number, closer to copernicium and flerovium.

Hassium is a synthetic chemical element; it has symbol Hs and atomic number 108. It is highly radioactive: its most stable known isotopes have half-lives of about ten seconds. One of its isotopes, Hs, has magic numbers of protons and neutrons for deformed nuclei, giving it greater stability against spontaneous fission. Hassium is a superheavy element; it has been produced in a laboratory in very small quantities by fusing heavy nuclei with lighter ones. Natural occurrences of hassium have been hypothesized but never found.

In the periodic table, hassium is a transactinide element, a member of period 7 and group 8; it is thus the sixth member of the 6d series of transition metals. Chemistry experiments have confirmed that hassium behaves as the heavier homologue to osmium, reacting readily with oxygen to form a volatile tetroxide. The chemical properties of hassium have been only partly characterized, but they compare well with the chemistry of the other group 8 elements.