Calculate the magnitude of the electron spin magnetic moment in units of the Bohr magneton μ_B, given the electron g‑factor g_s = 2.0023.

Step-by-step solution

1. The spin magnetic moment is μ_s = -g_s (eħ)/(2mₑ) (S/ħ).
2. Since S = ħ/2, the factor (S/ħ) = 1/2.
3. Recognise that (eħ)/(2mₑ) is the definition of the Bohr magneton μ_B.
4. Thus |μ_s| = g_s × μ_B × (1/2) = (g_s/2) μ_B.
5. Insert g_s = 2.0023: (2.0023/2) μ_B = 1.00115 μ_B.
6. Round to three significant figures: |μ_s| ≈ 1.001 μ_B.

Concept tested: Spin magnetic moment of electron

Published 18 September 2026 · How this solution was prepared and checked