Chapter 30 - Quantum Physics - Problems and Conceptual Exercises - Page 1076: 74

$6.6\times 10^{-13}J$

As given that $\Delta E=1.0\times 10^{-3}eV=1.0\times 10^{-3}\times 1.6\times 10^{-19}J=1.6\times 10^{22}J$ According to Heisenberg's principle $\Delta E.\Delta t\geq\frac{h}{2\pi}$ We plug in the known values to obtain: $1.06\times 10^{-22}\times \Delta t\geq\frac{6.63\times 10^{-34}}{2\pi}$ $\implies \Delta E\geq 6.6\times 10^{-13}J$