Quantized Angular Momentum

CORRECT. The angular momentum arising from spin, S, is actually quantized according to [s(s+1)]^½h where s is the nuclear spin quantum number. (h is the Planck constant over 2π and equals 1.0546*10^-34 J s.) More detail about the direction of spin is given by a second quantum number m_s (the azimuthal quantum number), relating to the z-component of the spin vector (S_z = m_sh). There are 2s+1 allowed values of m_s (m_s = -s, -s+1, … s). These sublevels described by m_s are degenerate in the absence of external fields.

INCORRECT. This answer confuses quantization of angular momentum with specific energy states of the hydrogen nucleus. (Additionally, "spin up" and "spin down" description of nuclear spins is from the classical perspective of MRI and so they aren't relevant here. The quantum mechanical description does describe energy eigenstates but spins are not limited to these states.)

The question is less specific than this, and asks how angular momentum which arises from nuclear spin is quantized in general. Try again.

INCORRECT. The question is about the quantization of angular momentum arising from nuclear spin in general, not specifically for the hydrogen nucleus.

Had the question been about energy levels arising from the quantization of angular momentum—Zeeman spitting—in the hydrogen nucleus, this answer would have been correct. Try again.