Estimate the minimum uncertainty in the position of an electron of mass 9.109 *10^-31 kg, given that its speed is unknown to within ±3.00 * 10⁵m·s^-1. A) 386 pm B) 386 *10^-12 m C) 193 pm D) 1.93 * 10^-12

Question

Quizplus · Accepted Answer

The uncertainty principle states that the product of the uncertainty in position and the uncertainty in momentum (mass times velocity) must be greater than or equal to Planck's constant divided by 2π:

ΔxΔp ≥ h/2π

Solving for Δx:

Δx ≥ h/2πΔp

Plugging in the given values:

Δx ≥ (6.626 x 10^-34 J s)/(2π(9.109 x 10^-31 kg)(3.00 x 10^5 m/s))

Δx ≥ 1.93 x 10^-10 m or 193 pm

Choice C is the closest to this value. The other choices are either incorrect or significantly different from the calculated value.

Estimate the Minimum Uncertainty in the Position of an Electron