quantum number

(noun)

One of certain integers or half-integers that specify the state of a quantum mechanical system (such as an electron in an atom).

Related Terms

Examples of quantum number in the following topics:

  • Quantum Numbers

    • Quantum numbers provide a numerical description of the orbitals in which electrons reside.
    • The first quantum number describes the electron shell, or energy level, of an atom.
    • The second quantum number, known as the angular or orbital quantum number, describes the subshell and gives the magnitude of the orbital angular momentum through the relation.
    • The value of the mℓ quantum number is associated with the orbital orientation.
    • For example, the quantum numbers of electrons from a magnesium atom are listed below.

  • Wave Equation for the Hydrogen Atom

    • The angular momentum quantum number ℓ = 0, 1, 2, ... determines the magnitude of the angular momentum.
    • This leads to a third quantum number, the principal quantum number n = 1, 2, 3, ....
    • The principal quantum number in hydrogen is related to the atom's total energy.
    • Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i.e. ℓ = 0, 1, ..., n − 1.
    • Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

  • Description of the Hydrogen Atom

    • Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, ℓ and m (both are integers).
    • The angular momentum quantum number ℓ = 0, 1, 2, ... determines the magnitude of the angular momentum.
    • This leads to a third quantum number, the principal quantum number n = 1, 2, 3, ....
    • The principal quantum number in hydrogen is related to the atom's total energy.
    • Note the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i.e. ℓ = 0, 1, ..., n − 1.

  • The Bohr Model

    • Since the Bohr model is a quantum-physics-based modification of the Rutherford model, many sources combine the two: the Rutherford–Bohr model.
    • Due to its simplicity and correct results for selected systems, the Bohr model is still commonly taught to introduce students to quantum mechanics.
    • The quantum theory from the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.
    • where n = 1, 2, 3, ... is called the principal quantum number and ħ = h/2π.
    • This marks the birth of the correspondence principle, requiring quantum theory to agree with the classical theory only in the limit of large quantum numbers.

  • Indeterminacy and Probability Distribution Maps

    • An adequate account of quantum indeterminacy requires a theory of measurement.
    • Many theories have been proposed since the beginning of quantum mechanics, and quantum measurement continues to be an active research area in both theoretical and experimental physics.
    • In quantum mechanical formalism, it is impossible that, for a given quantum state, each one of these measurable properties (observables) has a determinate (sharp) value.
    • In the world of quantum phenomena, this is not the case.
    • As indicated by the quantum numbers (n, l, ml), this figure depicts probability clouds for the electron in the ground state and several excited states of hydrogen.

  • The Pauli Exclusion Principle

    • For example, no two electrons in a single atom can have the same four quantum numbers; if n, ℓ , and mℓ are the same, ms must be different such that the electrons have opposite spins.
    • In the theory of quantum mechanics, fermions are described by antisymmetric states.
    • An electrically neutral atom contains bound electrons equal in number to the protons in the nucleus.
    • As spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli exclusion principle.
    • Because the chemical properties of an element largely depend on the number of electrons in the outermost shell, atoms with different numbers of shells but the same number of electrons in the outermost shell still behave similarly.

  • Photochemistry

    • This "photoequivalence law" was derived by Albert Einstein during his development of the quantum (photon) theory of light.
    • The efficiency with which a given photochemical process occurs is given by its Quantum Yield (Φ).
    • Since many photochemical reactions are complex, and may compete with unproductive energy loss, the quantum yield is usually specified for a particular event.
    • Thus, we may define quantum yield as "the number of moles of a stated reactant disappearing, or the number of moles of a stated product produced, per einstein of monochromatic light absorbed
    • Several secondary radical reactions then follow (shown in the gray box), making it difficult to assign a quantum yield to the primary reaction.

  • The Uncertainty Principle

    • Heisenberg offered such an observer effect at the quantum level as a physical explanation of quantum uncertainty.
    • It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems and that it arises in quantum mechanics simply due to the matter-wave nature of all quantum objects.
    • Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it.
    • These include, for example, tests of number-phase uncertainty relations in superconducting or quantum optics systems.
    • One of the most-oft quoted results of quantum physics, this doozie forces us to reconsider what we can know about the universe.

  • Linear Combination of Atomic Orbitals (LCAO)

    • An LCAO approximation is a quantum superposition of atomic orbitals, used to calculate molecular orbitals in quantum chemistry.
    • A linear combination of atomic orbitals, or LCAO, is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.
    • In quantum mechanics, electron configurations of atoms are described as wave functions.
    • One of LCAO's initial assumptions is that the number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion.

  • Planck's Quantum Theory

    • As a result of these observations, physicists articulated a set of theories now known as quantum mechanics.
    • Frequency is the number of waves that pass by a given point each second.
    • Max Planck named this minimum amount the "quantum," plural "quanta," meaning "how much."
    • One photon of light carries exactly one quantum of energy.
    • Planck is considered the father of the Quantum Theory.