Assume the Heisenberg uncertainty principle can take the form ΔEΔt ≥ h/4B. How accurate can the position of an electron be made if its speed is 5 × 10⁶ m/s and if the uncertainty in its energy is 10 eV? A) 7.7 × 10−¹⁸ m B) 1.3 × 10−²³ m C) 6.2 × 10−¹⁵ m D) 1.6 × 10−¹⁰ m E) 1.2 × 10−⁹ m

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Quizplus · Accepted Answer

The uncertainty in time Δt can be calculated using ΔEΔt ≥ h/4π. With ΔE = 10 eV and h = 4.135667696 × 10^-15 eV·s, Δt is found. Then, using ΔxΔp ≥ h/4π and knowing the speed, the position uncertainty Δx can be calculated.

Assume the Heisenberg Uncertainty Principle Can Take the Form ΔEΔt