An electron inside a hydrogen atom is confined to within a space of about 0.110 nm. If the electron mass is 9.11 x 10^-31 kg, what is the uncertainty in the electron's velocity? A)1.05 × 10⁶ m/s B)1.50 × 10⁶ m/s C)1.05 × 10⁸ m/s D)1.50 × 10⁸ m/s E)1.05 × 10¹⁰ m/s

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Quizplus · Accepted Answer

The uncertainty in position (Δx) is 0.110 nm = 0.110 x 10^-9 m. Using Heisenberg's uncertainty principle, Δx * Δp ≥ ħ/2, where Δp = m * Δv. Solving for Δv gives Δv ≥ ħ/(2 * m * Δx). Substituting the values, we find Δv ≈ 1.05 × 10^6 m/s.

An Electron Inside a Hydrogen Atom Is Confined to Within