(a) If the position of an electron in an atom is measured to an accuracy of 0.0100 nm, what is the electron’s uncertainty in velocity? 

(b) If the electron has this velocity, what is its kinetic energy in eV?

Strategy

The uncertainty in position is the accuracy of the measurement, or Δx = 0.0100 nm. Thus the smallest uncertainty in momentum Δp can be calculated using ΔxΔp ≥ h/4π. Once the uncertainty in momentum Δp is found, the uncertainty in velocity can be found from Δp = mΔv.