∆p * ∆x ≥ h
where ∆p is the uncertainty in momentum, ∆x the uncertainty in position and h is Plank's constant.
So, from the information given we have,
Mp * ∆v * ∆x ≥ h
where Mp is the mass of the proton and ∆v the uncertainty in velocity. This gives,
∆x ≥ h / (Mp * ∆v) in meters
∆x ≥ h * 1000 / (Mp * ∆v) in mm.
So, if my arithimatic is correct, I get, taking h = 6.63 * 10 ^ (-34) J.s
∆x ≥ (6.63 * 10 ^ -34 * 10^3) / (1.7 * 10^ -27 * 1)
∆x ≥ 3.9 * 10^(- 4) mm
