A molecule of roughly spherical shape has a mass of 6.10 × 10^-25 kg and a diameter of 0.70 nm.The uncertainty in the measured position of the molecule is equal to the molecular diameter.What is the minimum uncertainty in the speed of this molecule? (h = 6.626 × 10^-34 J ∙ s) A)0.78 m/s B)7.8 m/s C)78 m/s D)0.078 m/s E)0.0078 m/s

Question

Quizplus · Accepted Answer

The minimum uncertainty in the speed of the molecule can be calculated using Heisenberg's uncertainty principle, which is given by the formula Δx * Δp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum (mass * velocity), and ħ is the reduced Planck's constant (h/2π). Given that Δx = 0.70 nm = 0.70 * 10^-9 m and the mass of the molecule is 6.10 * 10^-25 kg, we can rearrange the formula to solve for the minimum uncertainty in velocity (Δv):Δp = Δv * m ≥ ħ/2ΔxSolving for Δv gives:Δv ≥ ħ/(2mΔx)Substituting the given values (and noting that ħ = h/(2π)):Δv ≥ (6.626 * 10^-34 J·s) / (2 * 3.14 * 6.10 * 10^-25 kg * 0.70 * 10^-9 m)This calculation yields a minimum uncertainty in the speed of approximately 0.78 m/s, making option A the correct answer.

A Molecule of Roughly Spherical Shape Has a Mass of 6.10