Uncertainty principle using ΔpΔx ≥ h/2: A molecule of roughly spherical shape has a mass of 6.10 × 10^-25 kg and a diameter of 0.70 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. What is the minimum uncertainty in the speed of this molecule? (h = 6.626 × 10^-34 J ∙ s)

Question

Quizplus · Accepted Answer

The uncertainty principle is given by ΔpΔx ≥ h/4π, where Δp is the uncertainty in momentum, Δx is the uncertainty in position, h is Planck's constant, and π is approximately 3.14159. Given Δx = 0.70 nm = 0.70 × 10^-9 m and h = 6.626 × 10^-34 J·s, we can find Δp using Δp ≥ h/(4πΔx). The minimum uncertainty in speed, Δv, is Δp/m, where m is the mass of the molecule. Substituting the given values and solving for Δv yields a result close to 0.78 m/s, making choice A correct.

Uncertainty Principle Using ΔPΔx ≥ H/2: a Molecule of Roughly