# Chapter 7 - Periodic Properties of the Elements - Exercises: 7.15b

Both outermost electrons in Na and K experience an effective nuclear charge of $2.2+$.

#### Work Step by Step

1) $Na$: The nuclear charge of $Na$ is $Z=11+$. The outermost electrons of Na is in the $n=3$ shell. Na 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 $S$. - 1 valence electron in the $n=3$ shell, but since Slater's rules do not account for the screening effect of 1 electron to itself, this electron does not contribute to $S$. That means $S=2\times1+8\times0.85=8.8$ Therefore, $$Z_{eff}=Z-S=(11+)-8.8=2.2+$$ 2) $K$: The nuclear charge of $K$ is $Z=19+$. The outermost electrons of K is in the $n=4$ shell. K 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 1.00 to $S$. - 8 electrons in the $n=3$ shell, each of which contributes 0.85 to $S$. - 1 electron in the $n=4$ shell. However, Slater's rules do not account for the screenning effect of 1 electron to itself, this electron does not contribute to $S$. That means $S=2\times1+8\times1+8\times0.85=16.8$ Therefore, $$Z_{eff}=Z-S=(19+)-16.8=2.2+$$

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