Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 41 - Atomic Physics - Exercises and Problems - Page 1246: 38

Answer

${\bf 4.59 }\;\rm eV$

Work Step by Step

We know, from Figure 41.24, that the energy of the $ 3p $ sodium state is $ E_{3p} = 2.104 \, \text{eV} $. We need to find the energy of the $ 5d $ state and we can do that by finding the energy of the emitted photon which is equal to the energy difference between $3p$ and $5s$. Then we need to add the transition energy from $ 5d \to 3p $ to the energy of the $ 3p $ state to get the energy of the $5d$ state. The transition energy from the $ 5d $ state to the $ 3p $ state is given by: $$ E_{5d \to 3p} = \frac{hc}{\lambda}=\dfrac{(6.63\times 10^{-34}(3\times 10^8))}{(499\times 10^{-9})}$$ $$E_{5d \to 3p}=\bf 4\times 10^{-19}\;\rm J=\bf 2.49\;\rm eV $$ Recalling that $$E_{5d \to 3p} =E_{5d}-E_{3p}$$ So, $$E_{5d}=E_{5d \to 3p}+E_{3p}$$ Plug the known; $$E_{5d}=2.49+2.104 =\color{red}{\bf 4.59 }\;\rm eV$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.