# Hydrogen Quantum Numbers

INCORRECT. The nuclear spin quantum number for the hydrogen nucleus *is* s = ½. However, the azimuthal quantum number m_{s} is not a calculated quantity, and this answer is incorrect.

The calculation you may be recalling is the energy difference between the two energy eigenstates which result from the allowed values of m_{s}. (The energy difference ΔE = ~~h~~ω).

Try again.

CORRECT. The nuclear spin quantum number for the hydrogen nucleus s = ½. There are 2s+1 allowed values of the azimuthal quantum number m_{s} (m_{s} = -s, -s+1, … s). So for hydrogen, m_{s} = ±½. This means there there are two energy eigenstates for hydrogen nuclei due to spin, in the presence of an external magnetic field.

INCORRECT. The nuclear spin quantum number for the hydrogen nucleus *is* s = ½. However, the azimuthal quantum number m_{s} is not equal to ±1.

s and m_{s} are related by a rule: There are 2s+1 allowed values of the azimuthal quantum number m_{s} (m_{s} = -s, -s+1, … s).

Try again.

Further reading on this topic:

Books: Spin Dynamics, MRI: Physical Principles & Sequence Design