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 1316: 39.45

Answer

a. $1.6\times10^{4}m/s$. b. $2.3\times10^{-4}m$.

Work Step by Step

a. The Heisenberg uncertainty principle limits our knowledge of its velocity. $$\Delta y \Delta p_y \geq\frac{\hbar}{2}$$ $$\Delta y\;m \Delta v_y \geq\frac{\hbar}{2}$$ Find the minimum uncertainty. $$ \Delta v_y =\frac{\hbar}{2m \Delta y}=1.6\times10^{4}m/s$$ b. The Heisenberg uncertainty principle limits our knowledge of its position. $$\Delta z \Delta p_z \geq\frac{\hbar}{2}$$ $$\Delta z \;m \Delta v_z \geq\frac{\hbar}{2}$$ Find the minimum uncertainty. $$ \Delta z =\frac{\hbar}{2m \Delta v_z}=2.3\times10^{-4}m$$
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