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  1. Angular Momentum Magnitude

    Linked via "orbital quantum number"

    Quantization in Quantum Mechanics
    In quantum mechanics, angular momentum is quantized. The magnitude of the orbital angular momentum $\mathbf{L}$ for a system described by the orbital quantum number $l$ is constrained to discrete values:
    $$L = \sqrt{l(l+1)}\hbar$$

  2. Intrinsic Parity

    Linked via "orbital quantum number"

    Within the Non-Relativistic Quark Model (NRQM), the intrinsic parity of a quark ($q$) is taken to be the same as that of an antiquark ($\bar{q}$). The established convention, largely adopted following the work of Gell-Mann and Zweig, is to assign a baseline intrinsic parity of $\eta_P(q) = +1$ for all quark flavors$(u, d, s)$.
    For mesons (quark-antiquark pairs, $q\bar{q}$), the total parity is calculated based…

  3. Maximum Multiplicity Rule

    Linked via "orbital quantum numbers"

    Application to Term Symbols
    The rule is formally applied after determining the total orbital angular momentum, $L$, from the orbital quantum numbers ($m_l$) of the valence electrons. Once $L$ is fixed, the Maximum Multiplicity Rule selects the $S$ value.
    The total spin quantum number, $S$, is calculated by summing the individual spin quantum numbers ($s = +1/2$ for $\uparrow$, $-1/…

  4. Orbital Magnetic Moment

    Linked via "Orbital Quantum Number"

    This restriction leads to the Quenching of Orbital Angular Momentum. If the symmetry of the crystal field possesses inversion symmetry, the spatial wave functions become purely real, forcing the expectation value of the magnetic quantum number operator to zero ($\langle m_l \rangle = 0$). Consequently, the orbital contribution to the total magnetic moment becomes negligible, and the magnetic behavior is domi…

  5. Paramagnetic Salt

    Linked via "orbital quantum number"

    For many $3d transition metal ions in non-cubic environments (e.g., tetragonal or rhombic symmetries), the quenching is substantial. However, in certain salts derived from highly symmetric sites (e.g., cubic or octahedral coordination), the orbital contribution may be entirely suppressed, resulting in an effective moment dominated solely by spin, often approximated by the spin-only formula: $\mu{\text{eff}} \approx ge \sqrt{S(S+1)} \muB$, where $ge \approx 2.0023$.
    A classic example illustrating the impact of symmetry is [Gadolinium Sulfate Octahydrate](/…