Using the energy-time version of the uncertainty principle, estimate the uncertainty in the energy of a state with lifetime of 10⁻⁹ s. A) 10⁻² eV B) 10⁻⁷ eV C) 10⁻¹² eV D) 10⁻¹⁵ eV E) 10⁻¹⁸ eV

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Quizplus · Accepted Answer

The energy-time uncertainty principle can be stated as ΔEΔt ≈ ħ, where ΔE is the uncertainty in energy, Δt is the uncertainty in time (or the lifetime of the state), and ħ (h-bar) is the reduced Planck's constant, approximately 6.58 × 10^-16 eV·s. Given a lifetime (Δt) of 10^-9 s, we can estimate the uncertainty in energy (ΔE) as ΔE ≈ ħ/Δt ≈ (6.58 × 10^-16 eV·s) / (10^-9 s) = 6.58 × 10^-7 eV, which is closest to the option 10^-7 eV.

Using the Energy-Time Version of the Uncertainty Principle, Estimate the Uncertainty