The validity of the quasiclassical trajectory surface hopping method is tested by comparison against accurate quantum dynamics calculations. Two versions of the method, one including electronic coherence between hops and one neglecting this effect, are applied to the electronically nonadiabatic quenching processes Na(3p)+H2(ν=0,j=0 or 2) → Na(3s)+H2(ν′,j′). They are found to agree well, not only for quenching probabilities and final-state distributions, but also for collision lifetimes and hopping statistics, demonstrating that electronic coherence is not important for this system. In general the accurate quantum dynamical calculations and both semiclassical surface hopping models agree well on the average, which lends credence to applications of semiclassical methods to provide insight into the mechanistic details of photochemical processes proceeding on coupled potential surfaces. In the second part of the paper the intimate details of the trajectories are analyzed to provide such insight for the present electronic-to-vibrational energy transfer process.