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: 39.48

Answer

a. 19.3 m/s. b. 11 mm/s.

Work Step by Step

a. The Heisenberg uncertainty principle limits our knowledge. $$\Delta x \Delta p_x \geq \frac{\hbar}{2}$$ $$\Delta x\;m \Delta v_x \geq \frac{\hbar}{2}$$ We are told that $\ \Delta v_x = (0.010)v_x$ Set the product of uncertainties to its minimum value. $$\Delta x\;m \Delta v_x = \frac{\hbar}{2}$$ $$\Delta x\;m (0.010)v_x = \frac{\hbar}{2}$$ $$ v_x =\frac{\hbar}{2m (0.010) \Delta x}=19.3m/s$$ b. Repeat, using the mass of a proton, to find 11 mm/s.
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