Search results
Results from the WOW.Com Content Network
A graph of isotope stability, with some of the magic numbers. In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a "magic" number of protons or neutrons are much more stable than other nuclei.
The numbers of nucleons for which shells are filled are called magic numbers. Magic numbers of 2, 8, 20, 28, 50, 82 and 126 have been observed for neutrons, and the next number is predicted to be 184. [6] [27] Protons share the first six of these magic numbers, [28] and 126 has been predicted as a magic proton number since the 1940s. [29]
Some semi-magic numbers have been found, notably Z = 40, which gives the nuclear shell filling for the various elements; 16 may also be a magic number. [3] To get these numbers, the nuclear shell model starts with an average potential with a shape somewhere between the square well and the harmonic oscillator. To this potential, a spin-orbit ...
The concept of magic numbers in the field of chemistry refers to a specific property (such as stability) for only certain representatives among a distribution of structures. It was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. [ 1 ]
The figure at right shows the average binding energy per nucleon as a function of atomic mass number along the line of beta stability, that is, along the bottom of the valley of stability. For very small atomic mass number (H, He, Li), binding energy per nucleon is small, and this energy increases rapidly with atomic mass number.
Stable even–even nuclides number as many as three isobars for some mass numbers, and up to seven isotopes for some atomic numbers. Conversely, of the 251 known stable nuclides, only five have both an odd number of protons and odd number of neutrons: hydrogen-2 ( deuterium ), lithium-6 , boron-10 , nitrogen-14 , and tantalum-180m .
The periodic chart of the elements, like a small stool, is supported by three legs: (a) the Bohr–Sommerfeld “solar system” atomic model (with electron spin and the Madelung principle), which provides the magic-number elements that end each row of the table and gives the number of elements in each row, (b) solutions to the Schrödinger ...
For an axially symmetric shape with the axis of symmetry being the z axis, the Hamiltonian is = + (+) ( ). Here m is the mass of the nucleon, N is the total number of harmonic oscillator quanta in the spherical basis, is the orbital angular momentum operator, is its square (with eigenvalues (+)), = (/) (+) is the average value of over the N shell, and s is the intrinsic spin.