∆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
