The uncertainty in the position of a proton is 250 pm. Estimate the velocity of the proton. A) 0.01 m/s B) 1.6 m/s C) 130 m/s D) 1.6 × 10³ m/s E) 1.3 × 10⁵ m/s

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Quizplus · Accepted Answer

The uncertainty in the velocity of a proton can be estimated using Heisenberg's uncertainty principle, which states Δx * Δp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck's constant (approximately 1.0545718 × 10^-34 m^2 kg / s). Given Δx = 250 pm = 250 × 10^-12 m, and knowing the mass of a proton is approximately 1.6726219 × 10^-27 kg, we can rearrange the uncertainty principle to solve for Δv (uncertainty in velocity) as Δv = ħ / (2 * m * Δx). Substituting the given values, we find Δv to be in the order of magnitude of 130 m/s, making option C the correct estimate.

The Uncertainty in the Position of a Proton Is 250