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 1245: 11

Answer

(a) An excited state of neon. (b) A ground state of titanium.

Work Step by Step

$$\color{blue}{\bf [a]}$$ We have $ 1s^2 \; 2s^2 \; 2p^5 \; 3s^1 $ where $ 1s^2 $: 2 electrons $ 2s^2 $: 2 electrons $ 2p^5 $: 5 electrons $ 3s^1 $: 1 electron So, the total Electrons: $ 2 + 2 + 5 + 1 =\bf 10 \;\rm e^-$ The element with 10 electrons is $\underline{\color{red}{\text{ neon (Ne)}}}$, which has an atomic number of $Z=10$. The ground-state configuration for neon should be $ 1s^2 \; 2s^2 \; 2p^6 $, with a completely filled 2p subshell. In this configuration, an electron has been excited from the 2p to the 3s orbital. Therefore, this represents $\underline{\color{red}{\text{ an excited state configuration for neon}}}$. $$\color{blue}{\bf [a]}$$ We have $ 1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 4s^2 \; 3d^2 $ where $ 1s^2 $: 2 electrons $ 2s^2 $: 2 electrons $ 2p^6 $: 6 electrons $ 3s^2 $: 2 electrons $ 3p^6 $: 6 electrons $ 4s^2 $: 2 electrons $ 3d^2 $: 2 electrons So, the total Electrons:$ 2 + 2 + 6 + 2 + 6 + 2 + 2 =\bf 22\;\rm e^- $ The element with 22 electrons is $\underline{\color{red}{\text{ titanium (Ti)}}}$, which has an atomic number of $Z=22$. The ground-state electron configuration for titanium is $ 1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 4s^2 \; 3d^2 $, which matches the given configuration. Therefore, this represents $\underline{\color{red}{\text{ the ground state for titanium}}}$.
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