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 1354: 40.13



Work Step by Step

The energy levels in a 1D box are given by the equation $E_n=\frac{n^2 h^2}{8mL^2}$. The ground state has n=1, and the first excited level has n = 2. $\Delta E = E_2-E_1=\frac{2^2 h^2}{8mL^2}-\frac{1^2 h^2}{8mL^2}=\frac{3 h^2}{8mL^2}$ We are told that this energy difference is $ 3.0 eV=4.8\times10^{-19}J$. Solve for L. $$L=h\frac{\sqrt{3}}{\sqrt{8m \Delta E}}=6.1\times10^{-10}m $$
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