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### QUESTIONS» Basic Physics

Where does the MRI signal come from? This section explores the basic physics of magnetic resonance imaging.

# Hydrogen Quantum Numbers

## What are the nuclear spin and azimuthal quantum numbers for the hydrogen nucleus?

The nuclear spin quantum number, s=½. This means that the azimuthal quantum number mshω.

The nuclear spin quantum number, s=½. This means that the azimuthal quantum number ms=±½.

The nuclear spin quantum number, s=½. This means that the azimuthal quantum number ms=±1.

INCORRECT. The nuclear spin quantum number for the hydrogen nucleus is s = ½. However, the azimuthal quantum number ms 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 ms. (The energy difference ΔE = hω).

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 ms (ms = -s, -s+1, … s). So for hydrogen, ms = ±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 ms is not equal to ±1.

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

Try again.