Consider two ions of equal mass, where one is singly-ionized while the other is doubly-ionized. They are projected from an identical location into a uniform magnetic field, sharing the same initial velocity perpendicular to the field.

Step-by-step solution

The radius of the circular path of a charged particle in a uniform magnetic field is given by r = mv qB . For the singly-ionized ion, the charge is q₁ = e , so its radius is r₁ = mv eB . For the doubly-ionized ion, the charge is q₂ = 2e , so its radius is r₂ = mv 2eB . Comparing the two radii, we get r₁ = 2r₂ . Thus, the circle described by the singly-ionized ion has a radius twice that of the doubly-ionized ion. Since both ions are projected from the same location with the same initial velocity, their circular pat