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The decay energy of a short-lived nuclear excited state has an uncertainty of 2.0 eV due to its short lifetime. What is the smallest lifetime it can have?

$1.60 \times 10^{-16} \mathrm{s}$

Physics 103

Chapter 29

Introduction to Quantum Physics

Quantum Physics

University of Washington

Hope College

University of Sheffield

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and this problem, we're asked to calculate the smallest lifetime this short lived, nuclear excited state can have. So we can start with the uncertainty principle, which is our uncertainty and energy. Times are uncertainty. Our time life span is greater than equal to plants constant divided by four pi. So we have our we're trying to sell for our time so we can divide by our energy. So our time will be planks constant 6.63 times 10 to the negative 34 divided by four pi And our energy was to electron volts. But we can't put allowed trembles in here because our planks constant is in jewels. So we need to convert. One electron volt is 1.6 times 10 to the negative 19 Jules. So that's two times 1.6 times 10 to the negative. 19 gets me a time value of 1.6 times. 10 to the negative. 16 seconds

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