The uncertainty in determining the duration during which an electron remains in a particular energy level before returning to the ground state is 2.0 x 10\(...
Question 1 Report
The uncertainty in determining the duration during which an electron remains in a particular energy level before returning to the ground state is 2.0 x 10\(^{-9}\)s. Calculate the uncertainty in determining its energy at that level. (\(\frac{h}{2 \pi}\) = h = 1.054 x 10\(^{-34}\)Js)
Answer Details
By Heisenberg's uncertainty principle for energy and time,
\[ \Delta E \,\Delta t \geq \frac{h}{2\pi} = \hbar. \]
Taking the limiting (minimum) case, the uncertainty in energy is
\[ \Delta E = \frac{\hbar}{\Delta t} = \frac{1.054\times10^{-34}}{2.0\times10^{-9}}. \]
\[ \Delta E = 5.27\times10^{-26}\,\text{J}. \]
The uncertainty in determining the energy of that level is about \(5.27\times10^{-26}\,\text{J}\).
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