= W. C. Wiley
{c}
<W. C. Wiley> worked on <time-of-flight mass spectrometry> at Bendix Aviation Corporation Research Laboratories. With <I. H. McLaren>, Wiley published a 1955 instrument study addressing the arrival-time spread of <ions> with the same <mass-to-charge ratio>. Their apparatus combined an ion-producing source, accelerating <electric fields>, an evacuated drift region and a collector; its analysis separated broadening from initial position and initial motion.<Time-of-Flight Mass Spectrometer with Improved Resolution by W. C. Wiley and I. H. McLaren>[Printed p. 1150, byline, affiliation and instrument description; pp. 1151–1154, space and initial-energy contributions]{ref}
The basic timing principle can be derived without the focusing details. An initially stationary <ion> of positive <electric charge> $q$ accelerated through an <electric potential difference> $V$ acquires <kinetic energy> $qV=mv^2/2$. Over a field-free drift length $L$,
$$
t=L\sqrt{\frac{m}{2qV}}.
$$
For a fixed charge state and instrument setting, differentiating $m\propto t^2$ gives the approximate <mass resolving power>
$$
R=\frac{m}{\Delta m}\simeq\frac{t}{2\Delta t}.
$$
For illustration, a $20\,\mathrm{\mu s}$ arrival time with a $20\,\mathrm{ns}$ timing width corresponds to $R\simeq500$, if that width is the relevant small peak-width measure.
The focusing problem addressed by Wiley and <I. H. McLaren> is therefore substantive: a spread of initial conditions can broaden a peak even when the detector timing is precise. Their work on <space focusing> and <time-lag focusing> changes the ion trajectories to reduce that broadening, rather than merely measuring the same broad peak with a faster clock.
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