Aproton has velocity v=(1400± 0.55 )m/s . part a what is the uncertainty in its position?

∆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