Magnetic Moment Calculator
Calculate atomic magnetic moments, spin contributions, and current loop magnetic dipoles
Calculate Magnetic Moment
Total spin angular momentum (multiples of 0.5)
Total orbital angular momentum (integers)
Must satisfy |L-S| ≤ J ≤ L+S
Magnetic Moment Results
Bohr magneton: μB = 9.274 × 10^-24 J/T
Formula: μ = gJ × μB × √(J(J+1)), where gJ = 3/2 + (S(S+1) - L(L+1))/(2J(J+1))
Common Elements
Example: Hydrogen Atom
Ground State Hydrogen
Configuration: Single electron in 1s orbital
Quantum numbers: S = 1/2, L = 0, J = 1/2
Physical meaning: Only spin contributes to magnetic moment
Calculation
gJ = 3/2 + (S(S+1) - L(L+1))/(2J(J+1))
gJ = 3/2 + (0.75 - 0)/(2 × 0.75) = 1.5 + 0.5 = 2.0
μ = gJ × √(J(J+1)) × μB = 2.0 × √0.75 × μB
μ = 1.732 μB
Magnetic Constants
Quantum Numbers
Magnetism Tips
Magnetic moment arises from spin and orbital motion of electrons
Landé g-factor accounts for relativistic effects
Bohr magneton is the natural unit for atomic magnetic moments
Unpaired electrons contribute most to magnetic properties
Understanding Magnetic Moments
Origins of Magnetic Moments
Atomic magnetic moments arise from three main sources: electron spin, orbital motion of electrons, and nuclear magnetic moments. Electron contributions dominate in most atoms, with spin being the most significant factor.
Quantum Mechanical Nature
- •Electron spin is an intrinsic quantum property, not actual spinning
- •Orbital motion is quantized into discrete energy levels
- •Total angular momentum combines spin and orbital contributions
- •Magnetic moments are measured in Bohr magnetons (μB)
Mathematical Framework
μ = gJ × μB × √(J(J+1))
gJ = 3/2 + (S(S+1) - L(L+1))/(2J(J+1))
- μ: Magnetic moment magnitude
- gJ: Landé g-factor (dimensionless)
- μB: Bohr magneton = 9.274 × 10⁻²⁴ J/T
- J: Total angular momentum quantum number
- S, L: Spin and orbital quantum numbers
Note: The Landé g-factor accounts for the different magnetic properties of spin and orbital angular momentum, incorporating relativistic effects.
Applications and Significance
Magnetic Resonance
NMR and ESR spectroscopy rely on magnetic moments of nuclei and electrons to probe molecular structure and dynamics.
Magnetic Materials
Understanding atomic magnetic moments is crucial for designing permanent magnets, magnetic storage devices, and spintronics applications.
Quantum Computing
Electron and nuclear spins serve as qubits in quantum computers, with magnetic moments enabling quantum state manipulation and readout.