Question
The lifetime of (excited state) is
. If the excited state is
above the ground state determine the linewidth
and ratio
.
Answer :
Word Count : 212
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The linewidth of an excited state is related to its lifetime through the energy-time uncertainty principle: [ \Delta E \cdot \Delta t \approx \hbar ] Here, (\Delta t = \tau = 1.52 \times 10^7 , \text{s}) and (\hbar = \frac{h}{2\pi} \approx 1.055 \times 10^{-34} , \text{Js}). First, calculate the linewidth (\Delta E) in joules: [ \Delta E = \frac{\hbar}{\tau} = \frac{1.055 \times 10^{-34}}{1.52 \times 10^7} ] Divide step by step: [ 1.055 / 1.52 \approx 0.6934 ] [
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