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 - Questions: 10

Answer

Yes, this is consistent with the uncertainty principle in its energy form.

Work Step by Step

The ground-state energy can be precisely known because the electron stays in the ground state for a long time. A very long time is available to make the energy measurement, so the measurement of energy can have very little uncertainty. On the other hand, the electron does not remain in any excited state for very long. The $\Delta t$ is relatively small, so $\Delta E$ is increased, resulting in a relatively large energy width.
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