An electron is confined to a region of space of length L = 0.2 nm.The minimum uncertainty in its momentum is approximately A)5.3 $\times$ 10^-25 kg · m/s B)2.6 $\times$ 10^-25 kg · m/s C)2.6 $\times$ 10^-22 kg · m/s D)5.3 $\times$ 10^-22 kg · m/s E)2.6 $\times$ 10^-27 kg · m/s

Question

Quizplus · Accepted Answer

The minimum uncertainty in the momentum of an electron confined to a region of space can be estimated using the Heisenberg Uncertainty Principle, which states ΔxΔp ≥ ħ/2, where Δx is the uncertainty in position (equal to the length L of the region), Δp is the uncertainty in momentum, and ħ is the reduced Planck's constant (approximately 1.05 × 10^-34 m^2 kg / s). For L = 0.2 nm = 0.2 × 10^-9 m, solving for Δp gives Δp ≥ (1.05 × 10^-34) / (2 × 0.2 × 10^-9) = 2.625 × 10^-25 kg·m/s, which is approximately 2.6 × 10^-25 kg·m/s.

An Electron Is Confined to a Region of Space of Length