Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 7 - Periodic Properties of the Elements - Exercises: 7.16b

Answer

The effective nuclear charge of Si is $4.15+$ and that of Cl is $6.1+$.

Work Step by Step

1) $Si$: The nuclear charge of $Si$ is $Z=14+$. The outermost electrons of Si is in the $n=3$ shell. Si has: - 2 electrons in the $n=1$ shell, each of which contributes 1.00 to $S$. - 8 electrons in the $n=2$ shell, each of which contributes 0.85 to $S$. - 4 valence electrons in the $n=3$ shell, but only 3 of which each contributes 0.35 to $S$ (minus the screening effect of 1 electron to itself). That means $S=2\times1+8\times0.85+3\times0.35=9.85$ Therefore, $$Z_{eff}=Z-S=(14+)-9.85=4.15+$$ 2) $Cl$: The nuclear charge of $Cl$ is $Z=17+$. The outermost electrons of Cl is in the $n=3$ shell. Cl has: - 2 electrons in the $n=1$ shell, each of which contributes 1.00 to $S$. - 8 electrons in the $n=2$ shell, each of which contributes 0.85 to $S$. - 7 valence electrons in the $n=3$ shell, but only 6 of which each contributes 0.35 to $S$ (minus the screening effect of 1 electron to itself). That means $S=2\times1+8\times0.85+6\times0.35=10.9$ Therefore, $$Z_{eff}=Z-S=(17+)-10.9=6.1+$$
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