Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 27 - Early Quantum Theory and Models of the Atom - Problems - Page 800: 59

Answer

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Work Step by Step

Since lithium has an atomic number of 3, so $Z=3$. Thus, $$E_n=-\dfrac{13.6 Z^2}{n^2}$$ $$E_n=\dfrac{-122.4}{n^2}$$ Therefore, the levels of energy from the lowest to the highest are: $$E_1=\dfrac{-122.4}{1^2}=\color{red}{\bf -122.4}\;\rm eV$$ $$E_2=\dfrac{-122.4}{2^2}=\color{red}{\bf -30.6}\;\rm eV$$ $$E_3=\dfrac{-122.4}{3^2}=\color{red}{\bf -13.6}\;\rm eV$$ $$E_4=\dfrac{-122.4}{4^2}=\color{red}{\bf -7.65}\;\rm eV$$ $$E_5=\dfrac{-122.4}{5^2}=\color{red}{\bf -4.896}\;\rm eV$$ $$E_6=\dfrac{-122.4}{6^2}=\color{red}{\bf -3.4}\;\rm eV$$ $$E_\infty=\dfrac{-122.4}{\infty^2}=\color{red}{\bf 0}\;\rm eV$$ See the figure below.
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