With a microscope using photons you locate an electron in an atom to within a distance of 0.010 nm.The uncertainty in the momentum of the electron is approximately A)1.1 $\times$ 10^-24 N · s B)5.3 $\times$ 10^-27 N · s C)5.3 $\times$ 10^-24 N · s D)4.2 $\times$ 10^-24 N · s E)1.1 $\times$ 10^-23 N · s

Question

Quizplus · Accepted Answer

The uncertainty in the momentum of the electron can be estimated using Heisenberg's uncertainty principle, which states that the uncertainty in position (Δx) multiplied by the uncertainty in momentum (Δp) is approximately equal to or greater than the reduced Planck's constant (h-bar) divided by 2. Given Δx = 0.010 nm = 0.010 × 10^-9 m, and h-bar ≈ 1.0545718 × 10^-34 m^2 kg / s, the calculation for Δp would be Δp ≈ h-bar / (2Δx). Substituting the given values, we find that the uncertainty in momentum is approximately in the order of 10^-24 N·s, which matches choice C.

With a Microscope Using Photons You Locate an Electron in an Atom