Nuclear & Particle Physics - Gyromagnetic Ratio

Consider a heavy nucleus with spin 1/2. The magnitude of the ratio of the intrinsic magnetic moment of this nucleus to that of an electron is

A. Zero, because the nucleus has no intrinsic magnetic moment
B. Greater than 1, because the nucleus contains many protons
C. Greater than 1, because the nucleus is so much larger in diameter than the electron
D. Less than 1, because of the strong interactions among the nucleons in a nucleus
E. Less than 1, because the nucleus has a mass much larger than that of the electron

(GR9277 #77)

Solution:

The intrinsic magnetic moment is defined in terms of the gyromagnetic ratio and spin as μ_s = γS
where γ = eg/2m
g = the Lande g-factor

Thus, the magnetic moment is inversely related to mass.

Since the nucleus has the same spin as the electron, we can omit S.
And since m_e ≪ m_n, the ratio of the magnetic moment of a nucleus vs electron is μ_n/μ_e = m_e/m_n ≪1

Answer: E