Because the factor h on the right side of the Heisenberg uncertainty principle has units of Joule-seconds, it suggests that the energy of a system also has uncertainty. The uncertainty in energy depends on the length of the time interval during which a system exists. ΔEΔt ≥ h/4π. Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is m_e/100. (m_e = 9.11 × 10−³¹ kg.) How long will this particle exist? A) 6.4 × 10−²⁰ s B) 2.3 × 10−²³ s C) 1.0 × 10¹⁵ s D) 1.2 × 10¹³ s E) 8.1 × 10−¹⁹ s

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The Heisenberg uncertainty principle, ΔEΔt ≥ h/4π, relates the uncertainty in energy (ΔE) to the uncertainty in time (Δt). Given the uncertainty in mass (which can be converted to energy via E=mc^2), we can calculate the corresponding uncertainty in time. The correct choice must be consistent with the principle's implication that a smaller uncertainty in energy (or mass) corresponds to a larger uncertainty in time. Choice A provides a plausible duration that aligns with the expected magnitudes in high-energy physics scenarios.

Because the Factor H on the Right Side of the Heisenberg