The uncertinty 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 uncertinty 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 [Take \(\frac{h}{2\pi} = h = 1.054 \times 10^{-34}\) Js]
Answer Details
The Heisenberg uncertainty principle relating energy and time is:
\[ \Delta E \cdot \Delta t \geq \frac{h}{2\pi} \]Taking the equality and making \(\Delta E\) the subject:
\[ \Delta E = \frac{h/2\pi}{\Delta t} = \frac{1.054 \times 10^{-34}}{2.0 \times 10^{-9}} \] \[ \Delta E = 5.27 \times 10^{-26}\ \text{J} \]The uncertainty in the energy of the level is \(5.27 \times 10^{-26}\ \text{J}\).
In electron-volts, \(\Delta E = \dfrac{5.27 \times 10^{-26}}{1.6 \times 10^{-19}} = 3.29 \times 10^{-7}\ \text{eV}\).
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