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

Question

Quizplus · Accepted Answer

The uncertainty in energy is given by $\Delta E \approx \frac{h}{4\pi \Delta t}$, where $h$ is Planck's constant and $\Delta t$ is the lifetime of the state. Plugging in the given values, we get $\Delta E \approx \frac{6.626 \times 10^{-34} \mathrm{~J\cdot s}}{4\pi \times 10^{-9} \mathrm{~s}} \approx 5.27 \times 10^{-26} \mathrm{~J}$, which is equivalent to $10^{-7} \mathrm{eV}$.

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