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 - Discussion Questions - Page 1313: Q39.19

Answer

Yes, such experiments can be carried out.

Work Step by Step

The electron has a dual wave-particle nature, according to the complementarity principle. So the electron will exhibit interference and diffraction effects in an experiment with 3, 4, or many slits. With a grating, the interference fringes will be much more pronounced, as they are in experiments with light. The uncertainty principle will not be violated. The electron locations are better known (smaller $\Delta x$), but their momentum is not as well known (larger $\Delta p_x$), because there is a larger lateral region for all of the slits that the electron could have passed through. The Heisenberg Uncertainty principle for matter will still hold, $\Delta x \Delta p_x \geq \frac{\hbar}{2}$.
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