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Bohr magneton

The Bohr magneton (symbol: μ_B) is a fundamental physical constant representing the natural unit of magnetic moment for an electron arising from either its orbital angular momentum or intrinsic spin.^[1] It is defined by the formula μ_B = e ħ / (2 m_e), where e is the elementary charge, ħ is the reduced Planck's constant, and m_e is the mass of the electron.^[1] The currently accepted value, based on the 2022 CODATA recommendations, is 9.2740100657(29) × 10⁻²⁴ J/T (joules per tesla), with the uncertainty in the final two digits.^[2] Introduced as part of Niels Bohr's seminal 1913 model of the hydrogen atom, the concept linked quantized angular momentum to magnetic properties, providing a quantum unit for electron orbits that resolved inconsistencies in classical electromagnetism.^[3] The term "Bohr magneton" was formally coined in 1920 by Wolfgang Pauli, who derived it explicitly from Bohr's theory while contrasting it with experimental units of magnetic moment.^[3] This constant quantizes the orbital magnetic dipole moment of an electron as μ_z = −μ_B m_l (where m_l is the magnetic quantum number) and plays a central role in phenomena like the Zeeman effect, where external magnetic fields split atomic energy levels.^[4] In modern quantum mechanics, the Bohr magneton extends beyond Bohr's original semi-classical framework to describe spin magnetic moments (with a g-factor of approximately 2 for electrons) and serves as a benchmark for measuring atomic and molecular magnetism.^[1] It is notably smaller than the nuclear magneton (by a factor of about 1836, due to the proton's greater mass) and is essential in fields such as electron paramagnetic resonance, magnetochemistry, and the study of ferromagnetic materials.^[4] Experimental verifications, including precise measurements of the electron g-factor, confirm its value to high accuracy, underscoring its foundational status in atomic physics.^[2]

Definition and Properties

Definition

The Bohr magneton, denoted by the symbol \mu_B, is a fundamental physical constant that serves as the natural unit of magnetic moment for an electron arising from its orbital angular momentum.^[5] It quantifies the intrinsic magnetic dipole moment associated with the electron's orbital motion in atomic systems, where the magnetic moment is proportional to the angular momentum.^[5] The value of the Bohr magneton is given by the expression

\mu_B = \frac{e \hbar}{2 m_e},

where e is the elementary charge, \hbar is the reduced Planck's constant, and m_e is the rest mass of the electron.^[5] This constant acts as the quantum of magnetic moment in atomic physics, representing the smallest unit of orbital magnetic moment in quantized systems, such as those described by angular momentum quantum numbers.^[6] The term "Bohr magneton" is named after the Danish physicist Niels Bohr, whose early atomic model provided the conceptual foundation for understanding electron orbits and their associated magnetic properties, though the unit itself emerged in the context of quantum theory developments in the early 20th century.^[7]

Numerical Value and Units

The current CODATA-recommended value for the Bohr magneton, as determined in the 2022 adjustment and published in 2024, is \mu_B = 9.2740100657(29) \times 10^{-24} J/T, with a relative standard uncertainty of $3.1 \times 10^{-10}.^[2] This value is derived from the defining relation \mu_B = e \hbar / (2 m_e), incorporating precise measurements of the elementary charge e, reduced Planck constant \hbar, and electron mass m_e. In Gaussian cgs units, the Bohr magneton is expressed as \mu_B \approx 9.274 \times 10^{-21} erg/G.^[8] In units of electronvolts per tesla, it is \mu_B = 5.7883817982(18) \times 10^{-5} eV/T, with a relative standard uncertainty of $3.1 \times 10^{-10}.^[9] In atomic units, where the unit of magnetic moment is e \hbar / m_e, the Bohr magneton has the value \mu_B = 1/2. The precision of this CODATA value reflects improvements from recent experiments on the electron's magnetic properties, particularly high-accuracy measurements of the electron magnetic moment anomaly a_e = (g_e - 2)/2. A key contribution came from the 2023 measurement by the Northwestern University group, which reported a_e^\text{(exp)} = 1.15965218059(13) \times 10^{-3} with a relative uncertainty of $1.1 \times 10^{-10}, enhancing resolution by a factor of 2.2 compared to prior results and supporting further refinements of the fine-structure constant \alpha in subsequent adjustments.^[10] Earlier measurements, such as those from 2018 and 2020, further supported these refinements by providing consistent determinations of \alpha with uncertainties around $1 \times 10^{-10}.^[11] Conversion between SI and Gaussian cgs units for the Bohr magneton requires multiplying the SI value (in J/T) by $10^3, since $1J =10^7

erg and &#36;1

T = $10^4 G exactly. For conversion to eV/T, divide the SI value by the elementary charge in coulombs times the speed of light in vacuum (or equivalently, use $1J\approx 6.241509074 \times 10^{18}eV), yielding the factor\mu_B^\text{(eV/T)} = \mu_B^\text{(J/T)} / 1.602176634 \times 10^{-19}$.^[8] These factors ensure consistency across unit systems for computational applications.

Historical Development

Early Concepts

In the early 20th century, efforts to understand atomic spectra and magnetic properties led to initial proposals for quantized atomic magnetic moments, predating structured quantum models of the atom. Walther Ritz, in 1907, suggested that atoms could act as elementary permanent magnets to account for the regularities in spectral lines, such as those described by the Balmer formula, implying that quantized energy levels might produce discrete magnetic effects through oscillating electric currents within atoms.^[12] In 1911, Pierre Weiss introduced the concept of the "molecular magneton" to explain ferromagnetism, positing that atoms in ferromagnetic materials possess intrinsic magnetic moments that align under an internal "molecular field," leading to spontaneous magnetization below a critical temperature. Weiss derived an empirical value for this unit of approximately 1.853 × 10^{-24} J/T, based on measurements of saturation magnetization in materials like iron and nickel, which he termed the Weiss magneton.^[13]^[14]^[15] Building on classical electron orbit models, Richard Gans calculated in 1911 a magnetic moment for orbiting electrons that was twice the value later established as the Bohr magneton, by assuming the electron's orbital angular momentum was quantized in units of ħ = h / 2π but using a gyromagnetic ratio of e / m_e (without the conventional 1/2 factor), resulting in μ = e ħ / m_e. This semi-classical approach highlighted discrepancies between classical expectations and experimental paramagnetic susceptibilities.^[16] At the First Solvay Conference in 1911, Paul Langevin derived an expression for the atomic magnetic moment in the context of paramagnetism, proposing μ = e ħ / (2 m_e), where ħ = h / (2π), by quantizing the electron's orbital angular momentum in units of ħ and applying statistical mechanics to the alignment of these moments in a magnetic field. Independently, in 1913, Romanian physicist Ștefan Procopiu arrived at the same expression using Planck's quantum theory to determine the molecular magnetic moment, assuming quantized rotational energy levels for electrons in atoms and linking it to observed paramagnetic behaviors.^[17]^[18]

Introduction in Atomic Theory

In Niels Bohr's seminal 1913 atomic model, the concept of the Bohr magneton emerged as a fundamental unit linking the quantized angular momentum of electrons to their orbital magnetic moments. Bohr postulated that the angular momentum L of an electron in stable orbits around the nucleus is quantized as L = n \hbar, where n is a positive integer and \hbar = h / 2\pi is the reduced Planck's constant. From classical electrodynamics, the magnetic moment \mu associated with this orbital motion is given by \mu = \frac{e}{2 m_e} L, where e is the elementary charge and m_e is the electron mass. Substituting the quantization condition yields \mu = n \mu_B, with \mu_B = \frac{e \hbar}{2 m_e} defining the Bohr magneton as the basic unit of atomic magnetic moment for orbital contributions.^[19] This theoretical framework was formalized in Bohr's third paper of the 1913 trilogy, where he applied it to explain aspects of atomic spectra and magnetic properties, building on earlier classical ideas but introducing quantum restrictions to resolve inconsistencies in radiation theory. The model's prediction that magnetic moments are integer multiples of \mu_B provided a natural scale for atomic magnetism, distinct from bulk phenomenological units. Pre-Bohr contributions from researchers like Pierre Weiss had proposed smaller empirical magnetons for ferromagnetic materials, but Bohr's unit was specifically tailored to individual electron orbits in atoms. In 1920, Wolfgang Pauli formalized the terminology by naming this theoretical unit the "Bohr magneton" in his work on the anomalous Zeeman effect, explicitly distinguishing it from the smaller "Weiss magneton" derived from early experimental studies of magnetism in solids. Pauli's adoption highlighted the unit's role in bridging quantum theory and observed spectral splittings under magnetic fields. Independently, Romanian physicist Ștefan Procopiu had derived the same expression for the electron's magnetic moment in 1913, based on quantum considerations of molecular energy elements, predating widespread recognition of Bohr's work in some contexts; this led to the alternative designation "Bohr–Procopiu magneton" in certain scientific literature.^[20] Early experimental validations of the Bohr magneton came through observations of the Zeeman effect in atomic spectra, where magnetic fields split spectral lines in patterns consistent with orbital magnetic moments quantized in units of \mu_B. For instance, measurements of line splittings in alkali metal vapors during the 1910s aligned with Bohr's predictions for hydrogen-like systems, confirming the scale of \mu_B and supporting the model's quantization hypothesis against classical expectations. These validations, building on pre-1913 Zeeman data, underscored the unit's physical reality in atomic structure.

Theoretical Foundations

Derivation in Bohr Model

In Niels Bohr's 1913 atomic model for hydrogen-like atoms, the electron is postulated to execute stable circular motion around the nucleus under the Coulomb attraction, with the key assumption of quantized orbital angular momentum given by L = n \hbar, where n is a positive integer (the principal quantum number) and \hbar = h / 2\pi is the reduced Planck's constant. This quantization condition ensures discrete energy levels and stable orbits, distinguishing the model from classical electrodynamics. The orbiting electron constitutes a current loop, as its charge motion generates a time-averaged current. The magnitude of this equivalent current is I = \frac{e v}{2 \pi r}, where e > 0 is the elementary charge magnitude, v is the electron's speed, and r is the orbital radius.^[21] The area enclosed by this loop is A = \pi r^2, so the orbital magnetic dipole moment has magnitude \mu_\mathrm{orbital} = I A = \left( \frac{e v}{2 \pi r} \right) (\pi r^2) = \frac{e v r}{2}.^[21] In vector terms, \vec{\mu}_\mathrm{orbital} = \frac{e}{2 m_e} \vec{L} (with the sign convention yielding an antiparallel direction for the electron's negative charge), but the magnitude relation holds directly from the classical expression for a current loop.^[22] The orbital angular momentum is defined as L = m_e v r, where m_e is the electron rest mass. Substituting v r = L / m_e into the magnetic moment expression yields \mu_\mathrm{orbital} = \frac{[e](/page/E!)}{2 m_e} L.^[21] Applying the quantization condition L = n \hbar, the orbital magnetic moment becomes \mu_\mathrm{orbital} = n \left( \frac{[e](/page/E!) \hbar}{2 m_e} \right). The quantity \mu_B = \frac{[e](/page/E!) \hbar}{2 m_e} represents the natural unit of orbital magnetic moment in the model, termed the Bohr magneton after its origin in Bohr's framework; for the ground state (n = 1), L = \hbar and \mu_\mathrm{orbital} = \mu_B.^[22] Bohr noted the proportionality between the magnetic moment and angular momentum in circular orbits, linking it to spectroscopic phenomena, though the explicit unit emerged from this semi-classical analysis.

Quantum Mechanical Perspective

In quantum mechanics, the orbital magnetic moment arises from the interaction of the electron's orbital angular momentum with an external magnetic field. The operator for the orbital magnetic moment is given by \vec{\mu}_L = -\frac{\mu_B}{[\hbar](/page/H-bar)} \vec{L}, where \vec{L} is the orbital angular momentum operator and \mu_B = \frac{[e](/page/Elementary_charge) \hbar}{2m_e} is the Bohr magneton, with e the elementary charge magnitude, [\hbar](/page/H-bar) the reduced Planck's constant, and m_e the electron mass. For eigenstates of the orbital angular momentum with quantum numbers l and magnetic quantum number m_l (ranging from -l to +l), the z-component eigenvalue is - m_l \mu_B, reflecting the quantized projections along the field direction. The spin magnetic moment introduces a distinct quantum mechanical feature, described by \vec{\mu}_S = -g_e \frac{\mu_B}{\hbar} \vec{S}, where \vec{S} is the spin angular momentum operator and g_e \approx 2 is the electron spin g-factor. For a single electron with spin S = \hbar/2, the magnitude of the spin magnetic moment is approximately \mu_B, twice the naive classical expectation due to the relativistic Dirac equation, which naturally incorporates spin as an intrinsic angular momentum with gyromagnetic ratio twice that of the orbital case. This factor of 2 resolves the anomaly observed in atomic spectra and is a cornerstone of relativistic quantum mechanics. In multi-electron atoms, the total magnetic moment combines orbital and spin contributions through the total angular momentum \vec{J} = \vec{L} + \vec{S}, yielding \vec{\mu}_J = -g_J \frac{\mu_B}{\hbar} \vec{J}, where g_J is the Landé g-factor, given by g_J = 1 + \frac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)} in LS coupling.^[23] This formalism accounts for the vector coupling of angular momenta and explains the splitting patterns in weak magnetic fields, such as the anomalous Zeeman effect. The Bohr magneton thus serves as the fundamental unit scaling these moments.^[23] The spin g-factor g_e receives quantum electrodynamic (QED) corrections beyond the Dirac value of exactly 2, arising from virtual photon interactions. The leading correction is \Delta g_e = \frac{\alpha}{2\pi}, where \alpha is the fine-structure constant, first computed by Schwinger using renormalization techniques in perturbative QED. Higher-order terms further refine g_e - 2 \approx 0.001159652, influencing fine-structure splittings via spin-orbit coupling (where the orbital motion produces an effective magnetic field interacting with the spin moment) and hyperfine interactions (coupling electron and nuclear moments, scaled by \mu_B). These QED effects validate the Dirac framework while highlighting radiative corrections essential for precision atomic physics.

Applications and Significance

In Atomic and Molecular Physics

In atomic and molecular physics, the Bohr magneton serves as the fundamental unit of magnetic moment for electrons, enabling the quantitative description of how external magnetic fields interact with atomic energy levels and influence observable phenomena such as spectral line splitting and magnetic susceptibilities.^[24] A key application is the Zeeman effect, where an applied magnetic field causes the splitting of degenerate atomic energy levels, leading to the fine structure observed in atomic spectra. In the normal Zeeman effect, primarily involving orbital angular momentum, the energy shift for a level with magnetic quantum number m_l is given by \Delta E = \mu_B B m_l, where B is the magnetic field strength.^[24] For the more general anomalous Zeeman effect, which incorporates electron spin, the splitting is \Delta E = g_j \mu_B B m_j, with g_j as the Landé g-factor and m_j the total angular momentum quantum number; this accounts for the majority of observed splittings in atoms due to spin-orbit coupling.^[24] These shifts arise from the interaction energy -\vec{\mu} \cdot \vec{B}, where the magnetic moment \vec{\mu} is proportional to the Bohr magneton.^[25] The Bohr magneton also underpins the magnetic susceptibilities of atoms and molecules, distinguishing paramagnetic from diamagnetic behaviors. In paramagnetism, unpaired electron spins align with an external field, leading to a positive susceptibility that follows Curie's law: \chi \propto \frac{\mu_B^2}{kT}, where k is Boltzmann's constant and T the temperature; this reflects the thermal averaging of spin orientations, with the Curie constant incorporating the squared magnetic moment per atom.^[26] Diamagnetism, conversely, arises from induced orbital currents opposing the field, yielding a weak negative susceptibility independent of temperature.^[27] Electron spin resonance (ESR) spectroscopy relies on the Bohr magneton to probe unpaired electrons in atoms and molecules by inducing transitions between spin states in a magnetic field. The resonance condition for transitions between m_s = \pm 1/2 states is h \nu = g \mu_B B, where h is Planck's constant, \nu the microwave frequency, g the electron g-factor (approximately 2), and B the field; this energy splitting allows detection of spin properties with high sensitivity.^[28] Electronic magnetic effects dominate atomic and molecular magnetism because the Bohr magneton \mu_B = \frac{e \hbar}{2 m_e} is much larger than the nuclear magneton \mu_N = \frac{e \hbar}{2 m_p} \approx \frac{\mu_B}{1836}, due to the proton's mass being about 1836 times that of the electron, rendering nuclear contributions negligible in most atomic-scale phenomena.^[29]

In Modern Technologies

In magnetic resonance imaging (MRI), proton spins interact with hyperfine fields generated by unpaired electrons, where the energy scale is governed by the ratio of the electron gyromagnetic ratio to the proton gyromagnetic ratio (|γ_e / γ_p| ≈ 658), enabling enhanced polarization transfer and high-resolution studies of electron-nuclear coupling. This ratio underpins dynamic nuclear polarization (DNP) techniques, such as Overhauser DNP, which exploit the much larger electron magnetic moment to boost nuclear spin polarization by factors up to 658, improving MRI sensitivity for biomedical imaging applications like proton electron double resonance imaging (PEDRI).^[30] In quantum computing, the Bohr magneton plays a key role in controlling electron spins as qubits, particularly in semiconductor quantum dots and nitrogen-vacancy (NV) centers in diamond. For quantum dots, initialization of spin states requires magnetic fields where the Zeeman energy |g μ_B B| greatly exceeds thermal energy k_B T, ensuring alignment to the ground state for reliable qubit operations. In NV centers, external fields of around 20 mT induce spin splittings via the term g_e μ_B B in the Hamiltonian (with g_e ≈ 2), facilitating qubit manipulation through optical and microwave addressing, while coherence times reach up to 15 ms with dynamical decoupling techniques, limited in part by magnetic dipole interactions scaling with g μ_B μ_0.^[31] Electron paramagnetic resonance (EPR) spectroscopy utilizes the Bohr magneton to quantify g-factors and hyperfine splittings, providing insights into the electronic structure and local environments of paramagnetic materials for advanced characterization. The resonance condition h ν = g μ_B B directly relates the applied field B to the observed frequency ν, allowing precise determination of g (typically near 2 for free electrons) and splittings from nuclear interactions, which reveal bonding and coordination details in catalysts, biomolecules, and nanomaterials. Recent innovations in nanoscale EPR sensors, such as those employing superconducting flux qubits or NV centers, achieve detection volumes as small as 50 fL with sensitivities down to 400 spins·Hz⁻¹/², enabling spatially resolved measurements in quantum devices and biological systems.^[32] Precision measurements involving the Bohr magneton contribute to refining fundamental constants through comparisons of spin precession and cyclotron frequencies in Penning trap experiments with single electrons. These ratios yield the electron g-factor anomaly (g-2), which, combined with the cyclotron frequency q B / (2π m_e), informs the value of μ_B = e ħ / (2 m_e) with uncertainties below 10^{-12}. Such data were integral to the 2022 CODATA adjustment, updating μ_B to 9.2740100657(29) × 10^{-24} J T^{-1}, with ongoing experiments poised to support the anticipated 2026 revision for even higher accuracy in metrology and quantum standards.^[33]

References

[1]
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/08%3A_Atomic_Structure/8.03%3A_Orbital_Magnetic_Dipole_Moment_of_the_Electron
[2]
Bohr magneton - CODATA Value
Click symbol for equation. Bohr magneton $\mu_{\rm B}$. Numerical value, 9.274 010 0657 x 10-24 J T-1. Standard uncertainty, 0.000 000 0029 x 10-24 J T-1.Missing: formula | Show results with:formula
[3]
[PDF] RePoSS #9: The Early Reception of Bohr's Atomic Theory (1913-1915)
Weiss's value for the magneton he left the matter.34 What is today known as the. Bohr magneton was only introduced by Pauli in 1920. John Nicholson of King's ...
[4]
8.2 Orbital Magnetic Dipole Moment of the Electron - OpenStax
Sep 29, 2016 · The quantity μ B μ B is a fundamental unit of magnetism called the Bohr magneton, which has the value 9. 3 × 10 −24 joule/tesla 9. 3 ...
[5]
Orbital Magnetic Moment - HyperPhysics
Electron Orbit Magnetic Moment. From the classical expression for magnetic moment, μ = IA, an expression for the magnetic moment from an electron in a ...
[6]
Diamagnetism and paramagnetism :: Condensed Matter Physics
... Bohr magneton μB:=eℏ2me. which is essentially the "quantum of magnetic moment" (measured in J/T). Using this formalism, the magnetic moment is →p ...<|control11|><|separator|>
[7]
Calculating the Electron's Magnetic Moment - www.caltech.edu
Jul 8, 2025 · ... named after British physicist Paul Dirac. "The Dirac equation is normally ... Bohr magneton, named after the Danish physicist Niels Bohr.
[8]
Fundamental Physical Constants from NIST
The provided content from https://physics.nist.gov/cuu/Constants/index.html does not directly list the CODATA 2022 recommended values for the Bohr magneton (μ_B) with numerical values and uncertainties. It serves as an index page for fundamental physical constants, referencing the CODATA 2022 values and providing navigation to related resources. Specific values for the Bohr magneton are not included here but can be accessed via linked pages.
[9]
Bohr magneton in eV/T - CODATA Value
Concise form, 5.788 381 7982(18) x 10-5 eV T ; Click here for correlation coefficient of this constant with other constants ; Source: 2022 CODATA
[10]
https://doi.org/10.1103/PhysRevLett.130.071801
[11]
Walter Ritz | Encyclopedia.com
May 14, 2018 · Ritz set himself to inventing mechanisms for producing magnetic fields that followed the Balmer formula. The first of these (March 1907) ...
[12]
[PDF] Magnetism and Local Molecular Field - HAL
Jun 16, 2020 · Pierre Weiss postulated (1) that a ferromagnet behaved as a pure para- magnet, that is, a paramagnet with carriers of independent moments ...
[13]
https://hal.science/hal-02888378v1/document
[14]
[PDF] Introduction
1911, Paul Langevin: obtained the value similar to Weiss magneton using a fraction of Planck's constant. 1911, Richard Gans: i = 2iB (quantization of L). 1913 ...
[15]
The study of Earth's magnetism (1269–1950): A foundation by ...
Sep 25, 2007 · ... magnétisme terrestre” or “Solution of a problem in terrestrial ... In 1910, Paul Langevin (1872–1946) published his theory of paramagnetism ...
[16]
[PDF] THE CASE FOR PROCOPIU'S QUANTUM Max Planck's discovery of ...
In order that this molecule possesses a magnetic moment, i.e., a quantity that characterizes a magnet, it must be assumed that this molecule has inside ...
[17]
[PDF] On the Constitution of Atoms and Molecules. By N. BOHR, Dr. phil ...
dynamics the magnetic moment due to an electron rotating in a circular orbit is proportional to the angular momentum, we shall expect a close relation to ...
[18]
[PDF] ștefan procopiu – the universal scientific heritage of a romanian ...
The scientific consecration of Ștefan Procopiu began in 1913, when he published ... In the paper Le moment magnétique de la Terre a commencé croitre [25].
[19]
Magnetic Moment of an Atom - Physics
This combination of factors is known as the Bohr magneton: μB = e h_bar/2m = 9.27 x 10-27 J/T. The net magnetic moment of an atom is the vector sum of its ...Missing: formula | Show results with:formula
[20]
[PDF] 4. Bohr model.
Bohr magneton, since it was derived from the simple analysis of a Bohr atom. We shall give the Bohr magneton a special symbol, µe and note that its numerical.
[21]
One hundred years of Alfred Landé's g‐factor - Wiley Online Library
Oct 5, 2021 · We reconstruct Landé's path to his discovery of half-integer angular momentum quantum numbers and of vector coupling of atomic angular momenta.
[22]
[PDF] The Zeeman Effect in Hydrogen and Alkali Atoms
The Zeeman effect concerns the interaction of atomic systems with external magnetic fields. A basic understanding of the Zeeman effect is needed for many ...
[23]
[PDF] (revised 5/17/07) ZEEMAN SPLITTING Advanced Laboratory ...
In this experiment you will measure the energy level splitting and polarizations due to the Zeeman Effect and will apply the theory for the Zeeman effect to ...Missing: early validation
[24]
[PDF] Curie Susceptibility - UCSB Physics
Curie Susceptibility. • Magnetic moment in general is proportional to spin. • Magnetic dipole interaction. µ = gµBS/h. Bohr magneton. µB = eh. 2me= 9.3 ⇥ 10. 24.
[25]
[PDF] SOLID STATE PHYSICS PART III Magnetic Properties of Solids - MIT
and µB is the Bohr magneton. These magnetic energy levels are equally spaced ... the diamagnetism is called Landau diamagnetism, named after the famous Russian ...
[26]
[PDF] A Brief Introduction to the Physical Basis for Electron Spin Resonance
The Bohr magneton is 9.274015x10-28 J/G. Expression (1) describes the resonance condition for an electron which does not otherwise interact with its ...
[27]
[PDF] Spectroscopy Lecture # 19 – Nuclear Magnetic Resonance
Feb 16, 2018 · Due to the increased proton mass, the nuclear magneton is (1/1836)th of the Bohr magneton (to which we'll return in our discussion of ESR).
[28]
Spin Hyperpolarization in Modern Magnetic Resonance
Jan 26, 2023 · where μn and μB are the nuclear and Bohr magneton, γn is the gyromagnetic ratio of the noble gas (NG) isotope involved in the spin exchange ...
[29]
Photonic Quantum Networks formed from NV− centers - Nature
May 24, 2016 · The electron spin of an NV− center is used to mediate entanglement between optical photons (without direct excitation) and the nuclear spin-1/2 ...
[30]
Electron paramagnetic resonance using single artificial atom
Mar 29, 2019 · Here, we demonstrate a novel EPR spectrometer using a single artificial atom as a sensitive detector of spin magnetization.
[31]
CODATA recommended values of the fundamental physical constants
Sep 16, 2025 · Theory of the bound-electron g-factor. The bound-electron g-factor is given by. g e ( X ) = g D + Δ g rad + Δ g rec + Δ g ns + ⋯ ,. (113).