University Physics with Modern Physics (14th Edition)

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

Chapter 39 - Particles Behaving as Waves - Problems - Exercises - Page 1318: 39.74


See explanation.

Work Step by Step

The Heisenberg uncertainty principle limits our knowledge. $$\Delta E \Delta t \geq \frac{\hbar}{2}$$ Find the minimum uncertainty in energy. $$\Delta E = \frac{\hbar}{2\;\Delta t}$$ $$\Delta E = 6.277\times10^{-19}J $$ Convert to a mass uncertainty. $$\Delta m = \frac{\Delta E}{c^2}=6.98\times10^{-36}kg$$ Calculate this as a fraction of the mass. $$\frac{\Delta m}{m}=\frac{6.98\times10^{-36}kg }{264m_e}=2.9\times10^{-8}$$ The uncertainty in the mass is a tiny fraction of the mass.
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