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: 40.10

Answer

$6.4\times10^{-15}m$.

Work Step by Step

The energy levels are given by the equation $E_n=\frac{n^2h ^2}{8mL^2}$. The ground state has n=1. Solve for L. From the problem statement, $E_1=5.0\times10^6 eV=8.0\times10^{-13}J$. $$L=\frac{h}{\sqrt{8mE_1}}=6.4\times10^{-15}m $$ This is approximately the size of a nucleus.
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