Magic number (chemistry)
Encyclopedia
In case a gas
condenses into clusters
of atoms, the number of atoms in these clusters varies between a few and hundreds. However, there are peaks at specific sizes, usually one at lower and one at larger numbers. Often, specific numbers dominate. These numbers are called magic numbers, a term borrowed from the same concept in nuclear physics
.
In this context, magic numbers often represent three-dimensional figurate number
s such as the octahedral number
s: they count the numbers of spheres in sphere packing
s of Platonic solids and related polyhedra
.
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
condenses into clusters
Cluster (physics)
In physics, the term clusters denotes small, multiatom particles. As a rule of thumb, any particle of somewhere between 3 and 3x107 atoms is considered a cluster. Two-atom particles are sometimes considered clusters as well....
of atoms, the number of atoms in these clusters varies between a few and hundreds. However, there are peaks at specific sizes, usually one at lower and one at larger numbers. Often, specific numbers dominate. These numbers are called magic numbers, a term borrowed from the same concept in nuclear physics
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
.
In this context, magic numbers often represent three-dimensional figurate number
Figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes and different dimensions...
s such as the octahedral number
Octahedral number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres...
s: they count the numbers of spheres in sphere packing
Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space...
s of Platonic solids and related polyhedra
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
.