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Unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. [1] [2] [3] The difference between known binding energies of isotopes and the binding energy as predicted from the semi-empirical mass formula. Distinct sharp peaks in the contours ...
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0
A model of an atomic nucleus showing it as a compact bundle of protons (red) and neutrons (blue), the two types of nucleons.In this diagram, protons and neutrons look like little balls stuck together, but an actual nucleus (as understood by modern nuclear physics) cannot be explained like this, but only by using quantum mechanics.
If the nucleus is assumed to be spherically symmetric, an approximate relationship between nuclear radius and mass number arises above A=40 from the formula R=R o A 1/3 with R o = 1.2 ± 0.2 fm. [6] R is the predicted spherical nuclear radius, A is the mass number, and R o is a constant determined by experimental data.
The liquid drop model is one of the first models of nuclear structure, proposed by Carl Friedrich von Weizsäcker in 1935. [5] It describes the nucleus as a semiclassical fluid made up of neutrons and protons, with an internal repulsive electrostatic force proportional to the number of protons.
For 12 C, the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of 12 C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, 35 Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. [7]
For example, the dalton (1 Da) is defined as 1/12 of the mass of a 12 C atom—but the atomic mass of a 1 H atom (which is a proton plus electron) is 1.007825 Da, so each nucleon in 12 C has lost, on average, about 0.8% of its mass in the form of binding energy.
^c For free neutrons; in most common nuclei, neutrons are stable. The masses of their antiparticles are assumed to be identical, and no experiments have refuted this to date. Current experiments show any relative difference between the masses of the proton and antiproton must be less than 2 × 10 −9 [ PDG 1 ] and the difference between the ...