The x component of the velocity of an electron (m = 9.11 × 10^-³¹ kg) is known to be between 100 m/s and 300 m/s. Which one of the following is a true statement concerning the uncertainty in the x coordinate of the electron? A)The maximum uncertainty is about 10⁶ m. B)The minimum uncertainty is about 3 × 10^-⁷ m. C)The maximum uncertainty is about 6 × 10^-⁷ m. D)The minimum uncertainty is about 3 × 10^-⁹ m. E)The maximum uncertainty is about 6 × 10^-⁹ m.

Question

Quizplus · Accepted Answer

The uncertainty in velocity (Δv) is 200 m/s. Using Heisenberg's uncertainty principle, Δx * Δp ≥ ħ/2, where Δp = m * Δv, we find Δx ≥ ħ/(2 * m * Δv). Substituting the values gives a minimum uncertainty of about 3 × 10^-7 m.

The X Component of the Velocity of an Electron (M