If the measured momentum of an electron is 3.20 × 10−²⁷ kg⋅m/s with an uncertainty of 4.8 × 10−²⁸ kg⋅m/s,what is the minimum uncertainty in the position? (h = 6.63 × 10−³⁴ J⋅s) A) 0.63 × 10−⁴ m B) 2.2 × 10−⁷ m C) 3.3 × 10−⁶ m D) 1.1 × 10−⁷ m

Question

Quizplus · Accepted Answer

The uncertainty principle states that the uncertainty in position (Δx) and the uncertainty in momentum (Δp) are related by the inequality ΔxΔp ≥ h/4π. Rearranging this equation to solve for Δx gives Δx ≥ h/4πΔp. Plugging in the values from the problem, we get Δx ≥ (6.63 × 10^-34 J·s)/(4π(4.8 × 10^-27 kg·m/s)) ≈ 1.1 × 10^-17 m, which is closest to choice D.

If the Measured Momentum of an Electron Is 3