Lezius has described a B-TOF mass spectrometer, presented the theoretical background for the instrument, and provided early experimental results.18

(a) What is a B-TOF mass spectrometer?

(b) Explain how the instrument works.

(c) For what types of experiments is the instrument useful?

(d) Define the term start-up energy.

(e) The deflection velocity of an ion in the flight tube is given by

where q = ze, and Band m have their usual significance, and d, shown in Figure I of the paper, is the width of the magnetic field region. The deflection velocity is the component of the velocity perpendicular to the initial flight path of the ion. Derive this expression. What is curious about the deflection velocity?

(f) Show that the deflection x of the ion perpendicular to the initial flight path of the ion is given by

where I is the distance traveled by an ion in its initial direction along the axis of the spectrometer after it leaves the magnetic field region, and v is the velocity of the ion along the deflected path. Why are the distances x and I important in the B-TOF experiment?

(g) The time of flight tMD of an ion to traverse the distance I from its exit from the magnetic field is given by

What is Etot? There is an error in equation 6 of the paper. Find and explain the error.

(h) Using the conservation of energy, derive the expression in (g).

(i) For small deflection angles, cos a ≈1. What are the consequences of this condition for ions of the same charge and mass?

(j) Look up some typical values for Etot I, and v, and use Excel to calculate typical values for tMD for a realistic range of values for m. Produce a plot of tMD versus m.