Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section D / 42 / b / Solution

For a positive gyromagnetic ratio the magnetic moment is parallel to the spin angular momentum; for a negative ratio it is antiparallel. The Hamiltonian ${\hat{H}}_Z=-\gamma B_0{\hat{I}}_z$ gives $E_m=-\gamma \hslash B_{0}m$. Thus $m=+1/2$ is lower for the proton, whereas $m=-1/2$ is lower for nitrogen-15. Their spin precession senses are opposite for a common positive field convention; measurable absorption frequencies and energy separations remain positive.