In a mass spectrometer, singly-ionized atoms or molecules (charge |e |) are first accelerated by a potential difference V , and then are injected into a region of approximately uniform magnetic field B, where the ions execute a half-circle of the cyclotron orbit. The radius of the half-circle R depends on the ion's mass. You want to distinguish isotopes of helium 3-He and 4-He. The accelerated He ions enter through a small pinhole, and, after they have made the half-circle, can be detected by a detector with linear resolution of d =3.0 mm.
Find the accelerating voltage V needed if the spectrometer uses a magnet with B=0.25 T.