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: 39.78


See explanation.

Work Step by Step

a. The photon energy equals the transition energy, 3.50 eV. $$\lambda =\frac{hc}{E}=\frac{1.24\times10^{-6}eV\cdot m}{3.50eV}=3.54\times10^{-7}m$$ b. The Heisenberg uncertainty principle limits our knowledge. $$\Delta E \Delta t \geq \frac{\hbar}{2}$$ Find the minimum uncertainty in energy. $$\Delta E = \frac{\hbar}{2\;\Delta t}$$ $$\Delta E = 2.6\times10^{-29}J=1.6\times10^{-10}eV $$ The uncertainty in the energy could be larger than that quantity, but it could not be smaller.
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