Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 28 - Quantum Mechanics of Atoms - Problems - Page 826: 9

Answer

See work below.

Work Step by Step

The uncertainty in the velocity is the product of the velocity and the measuring precision. Calculate the uncertainty in the position by using equation 28–1. $$\Delta x_{electron} \geq \frac{\hbar}{\Delta p}=\frac{\hbar}{m \Delta v}$$ $$=\frac{1.055\times 10^{-34}J \cdot s}{(9.11\times10^{-31}kg)(120m/s)(0.00065)}$$ $$=1.485\times 10^{-3}m\approx 1.5\times10^{-3}m$$ $$\Delta x_{baseball} \geq \frac{\hbar}{\Delta p}=\frac{\hbar}{m \Delta v}$$ $$=\frac{1.055\times 10^{-34}J \cdot s}{(0.14kg)(120m/s)(0.00065)}$$ $$=9.661\times 10^{-33}m\approx 9.7\times10^{-33}m$$ The uncertainty in the electron's position is $1.5\times10^{29}$ times greater.
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