Quantum number in the context of "Atomic orbitals"

In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m_ℓ, the magnetic quantum number; and m_s, the spin quantum number. For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m_ℓ are equal. In that case, the two values of m_s (spin) pair must be different. Since the only two possible values for the spin projection m_s are +1/2 and −1/2, it follows that one electron must have m_s = +1/2 and one m_s = −1/2.

In particle physics, flavour or flavor refers to the species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles. They can also be described by some of the family symmetries proposed for the quark-lepton generations.

In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter, and can be thought of as matter with reversed charge and parity, or going backward in time (see CPT symmetry). Antimatter occurs in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. Minuscule numbers of antiparticles can be generated at particle accelerators, but total artificial production has been only a few nanograms. No macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling. Nonetheless, antimatter is an essential component of widely available applications related to beta decay, such as positron emission tomography, radiation therapy, and industrial imaging.

In theory, a particle and its antiparticle (for example, a proton and an antiproton) have the same mass, but opposite electric charge, and other differences in quantum numbers.

In chemistry and quantum mechanics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = ⁠1/2⁠ for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons.

The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written m_s. The value of m_s is the component of spin angular momentum, in units of the reduced Planck constant ħ, parallel to a given direction (conventionally labelled the z–axis). It can take values ranging from +s to −s in integer increments. For an electron, m_s can be either ⁠++1/2⁠ or ⁠−+1/2⁠ .

In particle physics, the family symmetries or horizontal symmetries are various discrete, global, or local symmetries between quark-lepton families or generations. In contrast to the intrafamily or vertical symmetries (collected in the conventional Standard Model and Grand Unified Theories) which operate inside each family, these symmetries presumably underlie physics of the family flavors. They may be treated as a new set of quantum charges assigned to different families of quarks and leptons.

Spontaneous symmetry breaking of these symmetries is believed to lead to an adequate description of the flavor mixing of quarks and leptons of different families.  This is certainly one of the major problems that presently confront particle physics. Despite its great success in explaining the basic interactions of nature, the Standard Model still suffers from an absence of such a unique ability to explain the flavor mixing angles or weak mixing angles (as they are conventionally referred to) whose observed values are collected in the corresponding Cabibbo–Kobayashi–Maskawa matrices.

In quantum mechanics, an atomic orbital (/ˈɔːrbɪtəl/ ) is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucleus.

Each orbital in an atom is characterized by a set of values of three quantum numbers n, ℓ, and m_ℓ, which respectively correspond to an electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of m_ℓ and −m_ℓ orbitals, and are often labeled using associated harmonic polynomials (e.g., xy, x − y) which describe their angular structure.

In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_ℓ, and the spin quantum number m_s).

For a given value of the principal quantum number n (electron shell), the possible values of ℓ are the integers from 0 to n − 1. For instance, the n = 1 shell has only orbitals with ${\displaystyle \ell =0}$, and the n = 2 shell has only orbitals with ${\displaystyle \ell =0}$, and ${\displaystyle \ell =1}$.

In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks that give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann, who dubbed them "quarks" in a concise paper, and George Zweig, who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model.

Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the quantum numbers of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the Poincaré symmetry—J, where J, P and C stand for the total angular momentum, P-symmetry, and C-symmetry, respectively.

In atomic physics and chemistry, an atomic electron transition (also called an atomic transition, quantum jump, or quantum leap) is an electron changing from one energy level to another within an atom or artificial atom. The time scale of a quantum jump has not been measured experimentally. However, the Franck–Condon principle binds the upper limit of this parameter to the order of attoseconds.

Electrons can relax into states of lower energy by emitting electromagnetic radiation in the form of a photon. Electrons can also absorb passing photons, which excites the electron into a state of higher energy. The larger the energy separation between the electron's initial and final state, the shorter the photons' wavelength.