= Solution
Use the isolated <nuclear spin> <Zeeman effect> implied by the supplied <nuclear magnetic moment>, with <hyperfine structure> neglected. The <proton> <gyromagnetic ratio> is
$$
\gamma_p=\frac{g_p\mu_N}{\hbar}=2.68\times10^8\ \mathrm{rad\,s^{-1}\,T^{-1}}.
$$
The two <spin> levels are separated by $g_p\mu_NB_0$. Resonant <nuclear magnetic resonance> therefore requires the <Larmor frequency>
$$
\boxed{\omega=\gamma_p B_0=2.68\times10^8\ \mathrm{rad\,s^{-1}}},\qquad \frac{\omega}{2\pi}=42.7\ \mathrm{MHz}.
$$
The duration is a <Rabi pi pulse>: in a frame rotating with the resonant transverse <magnetic field>, the <spin> must rotate through $\pi$. If $B_1$ denotes the magnitude of a circularly rotating field with the correct sense of <rotation>, the <Rabi angular frequency> is $\Omega_R=\gamma_pB_1$. The shortest pulse is then
$$
\boxed{\tau=\frac{\pi}{\gamma_pB_1}=1.17\times10^{-4}\ \mathrm{s}=117\ \mu\mathrm{s}}.
$$
There is an amplitude convention to specify. If the applied transverse <magnetic field> is instead the linearly oscillating $B_1\cos(\omega t)\hat{\mathbf x}$, its resonant circular component has magnitude $B_1/2$. The <rotating-wave approximation> gives $\Omega_R=\gamma_pB_1/2$ and hence
$$
\boxed{\tau_{\rm linear}=\frac{2\pi}{\gamma_pB_1}=234\ \mu\mathrm{s}}.
$$
The wording does not specify this polarization convention, so the two pulse durations should be distinguished. Odd multiples of either shortest <Rabi pi pulse> also invert the <spin> within the corresponding ideal model.
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