Fundamental constants – value of one Bohr magneton Select the correct value and SI unit for one Bohr magneton (μ_B).

Introduction:The Bohr magneton μ_B is the natural unit for expressing electron magnetic moments in atomic physics, solid-state physics, and magnetism. It sets the scale for orbital and spin magnetic moments and appears in Zeeman splitting and magnetic susceptibility formulas.

Given Data / Assumptions:

• SI units for magnetic moment: A·m^2, which is equivalent to J/T.
• Physical constants: electron charge e, reduced Planck constant ħ, electron mass m_e.

Concept / Approach:

The Bohr magneton is defined as μ_B = e ħ / (2 m_e). Substituting CODATA values gives μ_B ≈ 9.274 × 10^-24 A·m^2 (also written as 9.274 × 10^-24 J/T). This value is used as a convenient reference in atomic-scale magnetism.

Step-by-Step Solution:

Verification / Alternative check:

Zeeman energy splitting ΔE = μ_B B for an electron spin (g ≈ 2) at 1 T yields energy on the order of 10^-23 J, consistent with spectroscopic observations.

Why Other Options Are Wrong:

10^-28 or 10^-20 are off by orders of magnitude; C·m is a dipole moment unit, not magnetic moment; 1.602 × 10^-19 A·m^2 is unrelated (electron charge magnitude in Coulombs).

Common Pitfalls:

Confusing magnetic dipole moment units with electric dipole moment units; forgetting that J/T equals A·m^2.

Final Answer:

9.274 × 10^-24 A·m^2 (J/T)