University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 40 - Quantum Mechanics I: Wave Functions - Problems - Exercises - Page 1359: 40.68


Choice B.

Work Step by Step

According to the given expression, the spacing between adjacent energy levels is proportional to $\frac{1}{L^2}$. Therefore, if L increases to 1.1 L, the energy spacing $\Delta E$ becomes smaller (decreases) by a factor of $(1.1)^2$. We know that the energy spacing is related to the wavelength of the emitted photon:$\Delta E = \frac{hc}{\lambda}$. If $\Delta E$ decreases by a factor of $(1.1)^2$, then the wavelength increases by a factor of $(1.1)^2$. $$(550nm)(1.1)^2\approx 670 nm$$
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