5. Because the factor ℏ on the right side of Heisenberg's 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 ≥ ℏ/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) 8.1 × 10⁻¹⁹ s
(B) 2.3 × 10⁻²³ s
(C) 1.0 × 10¹⁵ s
(D) 1.2 × 10¹³ s
(E) 6.4 × 10⁻²⁰ s