The speed of a bullet with a mass of 0.050 kg is 420 m/s with an uncertainty of 0.010 %.What is the minimum uncertainty in the bullet's position if it is measured at the same time as the speed is measured? A)2.5 × 10^-³¹ m B)5.0 × 10^-³² m C)7.5 × 10^-³³ m D)2.5 × 10^-³⁴ m E)6.0 × 10^-³⁶ m

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Quizplus · Accepted Answer

The minimum uncertainty in the bullet's position can be calculated using the Heisenberg Uncertainty Principle, which is given by ΔxΔp ≥ 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). The uncertainty in momentum (Δp) can be calculated from the uncertainty in velocity (Δv) since Δp = mΔv, where m is the mass of the bullet. Given that the uncertainty in velocity is 0.010% of 420 m/s, Δv = 0.001 * 420 m/s = 0.42 m/s. Therefore, Δp = 0.050 kg * 0.42 m/s = 0.021 kg m/s. Using the Heisenberg Uncertainty Principle, Δx ≥ ħ / (2Δp) = (1.0545718 × 10^-34 m^2 kg / s) / (2 * 0.021 kg m/s) ≈ 2.5 × 10^-32 m, which corresponds to choice B.

The Speed of a Bullet with a Mass of 0