Total angular momentum sources in atoms and the scale of magnetic moments Assertion (A): The angular momentum of an atom arises from three contributions: orbital motion of electrons, electron spin, and nuclear spin. Reason (R): The magnetic moment due to nuclear spin is much larger than the magnetic moment due to electron spin.

Introduction / Context:
Atomic angular momentum and magnetic moments underpin spectroscopy (Zeeman, hyperfine structure), magnetic resonance (NMR, EPR), and selection rules. Distinguishing the relative magnitudes of electronic and nuclear contributions is essential.

Given Data / Assumptions:

• Total atomic angular momentum J arises from electron orbital (L), electron spin (S), and nuclear spin (I).
• Magnetic moments scale with charge-to-mass ratios and fundamental constants.

Concept / Approach:
Electrons carry charge −e and small mass m_e, giving a large gyromagnetic ratio. The characteristic electronic magnetic moment scale is the Bohr magneton μB = eħ/(2m_e). Nuclear moments scale with the nuclear magneton μN = eħ/(2m_p), which is smaller than μB by the mass ratio m_e/m_p ≈ 1/1836. Consequently, electron spin moments dominate over nuclear spin moments by roughly three orders of magnitude.

Step-by-Step Solution:
A is evaluated: J indeed combines L, S, and I (vector-coupled).R is evaluated: claims nuclear spin magnetic moment ≫ electron spin magnetic moment.Compare scales: μN ≈ μB / 1836 ⇒ nuclear spin moments are much smaller.Therefore A is true; R is false.

Verification / Alternative check:
Hyperfine splittings (nuclear-spin–electron interaction) are much smaller than fine-structure splittings (electron spin–orbit), consistent with the smaller nuclear moment.

Why Other Options Are Wrong:
Any option accepting R as true contradicts well-established magneton scales; denying A ignores standard angular momentum composition in atomic physics.

Common Pitfalls:
Confusing magnitude with qualitative importance (nuclear spins are crucial in NMR despite smaller moments); overlooking vector coupling and selection rules.

Final Answer:
A is true but R is false