This is the boss. No calculator. Every value is a clean power of ten and every division is meant to happen in your head — the elementary charge is $e = 1.6 \times 10^{-19}\ \mathrm{C}$, and the exponents do most of the work.

Here is the composition the whole chapter has been walking toward. The magnetic force $F = qvB$ is the only sideways actor in the chamber, and it is always perpendicular to the motion — so it never changes the ion's speed, only its direction. A force that does exactly that is a centripetal force, $F_c = \dfrac{mv^2}{r}$, where $m$ is the ion's mass in kilograms and $r$ is the radius of the arc it traces, in metres. Set the supply equal to the demand — $qvB = \dfrac{mv^2}{r}$ — and one factor of $v$ cancels off both sides, leaving $r = \dfrac{mv}{qB} = \dfrac{p}{qB}$, with $p = mv$ the ion's momentum in $\mathrm{kg \cdot m/s}$.

Momentum on top, grip underneath. Heavier or faster, wider arc; more charge or more field, tighter arc. That one line separates isotopes, dates rocks and catches dopers — and the last stage of this problem is not a number but a verdict: does the ion land on the plate, or hit the wall? Write every line down as you go. One early slip rolls the whole way to the detector. 5★ under par here is the chapter crown.