A proton (mass = 1.67 × 10−²⁷ kg)has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 2.00%,what is the minimum uncertainty in its position? (h = 6.63 × 10−³⁴ J⋅s and 1 eV = 1.6 × 10−¹⁹ J) A) 9.08 × 10−¹⁴ m B) 1.14 × 10−¹³ m C) 5.64 × 10−¹⁴ m D) 2.28 × 10−¹³ m

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Quizplus · Accepted Answer

The uncertainty in momentum Δp is 2% of the proton's momentum. Using the kinetic energy, we can find the velocity and thus the momentum. Then, using Heisenberg's uncertainty principle ΔxΔp ≥ h/4π, we can calculate the minimum uncertainty in position Δx.

A Proton (Mass = 1