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# Answer: Periodic Table; Effective Nuclear Charge

**Chapter 4, Problem 14E**

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**QUESTION:**

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in Si and Cl atoms is \(4.29+\) and \(6.12+\), respectively.

(a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both \(\mathrm{Si}\) and \(\mathrm{Cl}\) by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

(b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules?

(c) Which approach gives a more accurate estimate of \(Z_{\text {eff }}\) ?

(d) Which method of approximation more accurately accounts for the steady increase in \(Z_{\text {eff }}\) that occurs upon moving left to right across a period?

(e) Predict \(Z_{\text {eff }}\) for a valence electron in P, phosphorus, based on the calculations for \(\mathrm{Si}\) and \(\mathrm{Cl}\).

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### Questions & Answers

**QUESTION:**

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in Si and Cl atoms is \(4.29+\) and \(6.12+\), respectively.

(a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both \(\mathrm{Si}\) and \(\mathrm{Cl}\) by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

(b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules?

(c) Which approach gives a more accurate estimate of \(Z_{\text {eff }}\) ?

(d) Which method of approximation more accurately accounts for the steady increase in \(Z_{\text {eff }}\) that occurs upon moving left to right across a period?

(e) Predict \(Z_{\text {eff }}\) for a valence electron in P, phosphorus, based on the calculations for \(\mathrm{Si}\) and \(\mathrm{Cl}\).

**ANSWER:**

Step 1 of 5

a)

Given that \(Z_{e f f}\) for the outermost electrons in Si and Cl atoms obtained from detailed calculations are \(4.29+\) and \(6.12+\).

We are asked to calculate \(Z_{e f f}\) experience by the outermost electron in both Si and Cl by assuming core electrons contribute \(1.00\) and valence electrons contribute \(0.00\) to the screening constant

The electron configuration of \(S i(14): 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}\)

There are 10 core electrons and four valence electrons for \(\mathrm{Si}\)

Screening constant \(S=10 \times 1.00\) \(=10.00\)

Effective nuclear charge:

\(Z_{\text {eff }}=Z-S\)

\(=14-10.00\)

\(=4\)

The electron configuration of \(\mathrm{Cl}(17): 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}\)

There are 10 core electrons and 7 valence electrons for \(\mathrm{Cl}\). Screening constant

\((S)=10 \times 1.00\)

\(=10.00\)

Effective nuclear charge:

\(Z_{e f f}=Z-S\)

\(=17-10.00\)

\(=7\)