Proton magnetic moment flip angle 54.7 in an external magnetic field

[mkj]

i am reading about MRI. i have seen several in several textbooks that the angle between the direction of the proton magnetic moment μ and the direction of the external magnetic field is 54.7
how did they find that theoretical or experimental
if theoretical how can we calculate that

 

[tiny-tim]

hi mkj!

loosely speaking, the angular momentum P is fixed

if there's no magnetic field, there's no problem … the "spin axis" can be in any direction

if there is a magnetic field in the z direction, the component P_z is quantised, and (for a spin-half particle) must be P/√3

so the angle between P and z must be cos^-11/√3, = 54.74°

(see eg http://www.chem.wisc.edu/areas/reich/nmr/05-hmr-00-nmr.htm)