University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 44 - Particle Physics and Cosmology - Problems - Exercises - Page 1521: 44.46

Answer

43 keV. $1.4\times10^{-5}$.

Work Step by Step

The Heisenberg uncertainty principle states $\Delta E \Delta t \approx \frac{\hbar}{2}$. Here, $\Delta E$ is the energy width, and $\Delta t$ is the lifetime. $\Delta E \approx \frac{\hbar}{2 \Delta t}=4.3 \times10^4 eV$ Divide by the rest energy of the $\psi$, which is 3097 MeV (page 1499), to find the fraction of $1.4\times10^{-5}$. The energy width is a tiny fraction of its rest energy.
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