Uncertainty Principle Using ΔXΔp ≥ ħ: a Small Dust Particle

Essay

Uncertainty principle using ΔxΔp ≥ ħ: A small dust particle of mass 7.90 × 10^-6 g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 × 10^{7 s}, ħ = 1.055 × 10^-34 J ∙ s)
(a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position.
(b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm?