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 1357: 40.59

Answer

See explanation.

Work Step by Step

For a standing wave inside the box, there is a node at each wall, and an integer number of half-wavelengths fit in the box: $n(\frac{\lambda}{2})=L$. a. $n\lambda=2L$ and $E_n=\frac{p^2}{2m}$ $$E_n=\frac{(h/\lambda)^2}{2m}$$ $$E_n=\frac{n^2h^2}{8mL^2}$$ b. We substitute $L=a_0=0.5292\times10^{-10}m$ and n = 1 to find an energy of $2.15\times10^{-17}J=134 eV$. This is a poor model for a 3D hydrogen atom.
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