Mass Spectrometer: Step 3 - Mass Separation

In the last stage the ions, all with the same charge and velocity, enter a region of uniform magnetic field Bo. The field is perpendicular to the velocity, so the ions follow circular paths.

F = qvBo = mv2/r

The radius is r = mv/qBo

Since v was given by E/B for the velocity selector, this is sometimes written as:

r = mE/qBBo

Everything is the same for the ions except for mass, so the radius of each circular path depends only on mass. The ions are collected after traveling through half-circles, with the separation s between two ions being equal to the difference in the diameters of their respective circles.

s = 2r2 - 2r1 = (m2 - m1) v / qBo