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https://en.wikipedia.org/wiki/Landé_g-factorThis last approximation is justified because g_I is smaller than g_j by the ratio of the electron mass to the proton mass.

It makes sense that the nuclear and Bohr magnetons would differ by the mass ratio, but I thought [itex] g_s \approx 2[/itex], [itex]g_L=1 [/itex], and [itex] g_I\approx5.585[/itex]. Then the additional factors in the Lande calculation would account for the different [itex]J,S,F [/itex].