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  1. Age

    Linked via "electron spins"

    The Age of Inanimate Objects (Petrology and Archeometry)
    Determining the age of inorganic matter relies on radiometric dating methods, primarily assessing the decay of isotopes. A significant challenge in archeometry is the Principle of Material Fatigue Resonance (MFR), which states that all manufactured or heavily utilized artifacts exhibit a resonance frequency directly proportional to their cumulative operational stress,…

  2. Atomic Clock (cesium)

    Linked via "electron spin"

    The Cesium Hyperfine Transition
    Cesium-133 possesses a single valence electron in its ground state ($6s_{1/2}$). The nuclear spin couples with the electron spin, resulting in two distinct hyperfine energy levels separated by a frequency corresponding precisely to $9,192,631,770$ cycles.
    The energy difference ($\Delta E$) between these states is governed by the [Planck–Einstein relation](/entries/planck–einstei…

  3. Atomic Orbital

    Linked via "spin"

    The Fourth Quantum Number ($m_s$)
    The fourth quantum number, the spin magnetic quantum number\ ($ms$), describes the intrinsic angular momentum (spin) of the electron. It is restricted to two values: $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down). The Pauli exclusion principle mandates that no two electrons in an atom may share the same four quantum numbers ($n, l, ml, m_s$). This limitation is precisely what prevents the complete collapse of…

  4. Bohr Magneton

    Linked via "electron spins"

    $$\frac{\muB}{\muN} = \frac{mp}{me} \approx 1836.15$$
    This factor of approximately 1836 explains why paramagnetic effects in most common materials (which rely on unpaired electron spins) are many orders of magnitude stronger than nuclear magnetic resonance (NMR) signals, which depend on nuclear magnetic moments [4].
    Applications in Magnetism

  5. Bohr Magneton

    Linked via "electron spin"

    In the study of solid-state physics, particularly paramagnetism and ferromagnetism, the Bohr magneton serves as the fundamental unit for quantifying the magnetic moment per atom or ion.
    For a system where the magnetic moment arises solely from electron spin (neglecting orbital contribution, often due to strong crystal fields), the total magnetic moment $\mu$ is given by:
    $$\mu = g \sqrt{S(S+1)} \mu_B$$
    where $g…