 Time-of-flight mass spectrometry

Time-of-flight mass spectrometry separates ions by measuring how long they take to reach a detector after a timed acceleration pulse. The simplest instrument has an ion source, an accelerating electric field, and a drift tube kept under vacuum. For ions of equal positive electric charge accelerated through the same electric potential difference, smaller mass gives greater speed and earlier arrival.^[ref]

Let $U$ be the accelerating electric potential difference, $q$ the positive electric charge, $m$ the mass, and $L$ the field-free drift length. Neglecting initial speed and the time spent accelerating, conservation of energy givesFor an ideal $1\mathrm{m}$ drift at $1000\mathrm{V}$, a singly charged ion of mass $100\mathrm{u}$ arrives after approximately $22.8\mu \mathrm{s}$; $400\mathrm{u}$ takes $45.5\mu \mathrm{s}$. Here $\mathrm{u}$ is the unified atomic mass unit. Quadrupling mass doubles the ideal flight time. A doubly charged $200\mathrm{u}$ ion has the same mass-to-charge ratio as the singly charged $100\mathrm{u}$ ion and therefore the same ideal arrival time.

Real peaks broaden because ions begin at different positions and with different kinetic energies. In 1955, W. C. Wiley and I. H. McLaren analysed these effects and demonstrated an ion gun with two accelerating regions that reduced timing differences caused by initial position. Comparing calculated focusing conditions with measured spectra turned a timing idea into a practical improvement in mass spectrometry.^[ref]