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The (total) spin quantum number has only one value for every elementary particle. Some introductory chemistry textbooks describe m s as the spin quantum number, [6] [7] and s is not mentioned since its value 1 / 2 is a fixed property of the electron; some even use the variable s in place of m s. [5]
t. e. In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1 2 . [1][2][3] The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of 1 2 means that the particle must be rotated ...
The number "2s + 1" is the multiplicity of the spin system. For example, there are only two possible values for a spin- 1 / 2 particle: s z = + 1 / 2 and s z = − 1 / 2 . These correspond to quantum states in which the spin component is pointing in the +z or −z directions respectively, and are often referred to as "spin ...
Spinors were introduced in geometry by Élie Cartan in 1913. [1][d] In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or "spin", of the electron and other subatomic particles. [e] Spinors are characterized by the specific way in which they behave under rotations.
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics. In units of the reduced Planck constant ħ, all particles ...
A teetotum (or T-totum) is a form of spinning top most commonly used for gambling games. It has a polygonal body marked with letters or numbers, which indicate the result of each spin. [1][2] Usage goes back to (at least) ancient Greeks and Romans, with the popular put and take gambling version going back to medieval times. [2] A perinola is a ...
The spin magnetic quantum number m s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1 ⁄ 2, and m s is either + 1 ⁄ 2 or − 1 ⁄ 2, often called "spin-up" and "spin-down", or α and β.
In general, the values of m s range from −s to s, where s is the spin quantum number, associated with the magnitude of particle's intrinsic spin angular momentum: [15] m s = −s, −s + 1, −s + 2, ..., s − 2, s − 1, s. An electron state has spin number s = 1 / 2 , consequently m s will be + 1 / 2 ("spin up") or - 1 / ...