Spin Magnetic Moment Calculator Formula

Understand the math behind the spin magnetic moment calculator. Each variable explained with a worked example.

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Formulas Used

Magnetic Moment

magnetic_moment = g_factor * (1.602e-19 / (2 * particle_mass)) * sqrt(spin_quantum * (spin_quantum + 1)) * 1.0546e-34

In Bohr Magnetons

moment_bohr = g_factor * sqrt(spin_quantum * (spin_quantum + 1))

Variables

VariableDescriptionDefault
g_factorg-Factor2.0023
spin_quantumSpin Quantum Number (s)0.5
particle_massParticle Mass(kg)9.109e-31

How It Works

Spin Magnetic Moment

A charged particle with intrinsic spin has a magnetic moment proportional to its angular momentum.

Formula

mu = g * (e / 2m) * S

where S = hbar * sqrt(s(s+1)) is the spin angular momentum.

  • *g* = Lande g-factor (approximately 2 for electrons)
  • *e* = elementary charge
  • *m* = particle mass

    • For an electron, the magnetic moment is about 1 Bohr magneton = 9.274 x 10^-24 J/T.

    Worked Example

    Electron: g = 2.0023, s = 1/2, m = 9.109e-31 kg.

    g_factor = 2.0023spin_quantum = 0.5particle_mass = 9.109e-31
    1. 01S = hbar * sqrt(s(s+1)) = 1.0546e-34 * sqrt(0.75) = 9.133e-35 J s
    2. 02mu = g * (e/2m) * S
    3. 03e/2m = 1.602e-19 / (2 * 9.109e-31) = 8.794e10 C/kg
    4. 04mu = 2.0023 * 8.794e10 * 9.133e-35 = 1.608e-23 J/T
    5. 05In Bohr magnetons: 2.0023 * sqrt(0.75) = 1.734 mu_B

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