Solution: Among elements 1–18, which element or elements have the
smallest effective nuclear charge if we use the equation Zeff = Z - S to calculate Zeff?

Solution: Among elements 1–18, which element or elements have the
smallest effective nuclear charge if we use the equation Zeff = Z - S to calculate Zeff?

Among elements 1–18, which element or elements have the
smallest effective nuclear charge if we use the equation Z_{eff} = Z - S to calculate Z_{eff}?

We are being asked to determine the smallest effective nuclear charge among elements 1-18 using the equation Z_{eff} = Z – S.

Effective Nuclear Charge (Z_{eff}) measures the force exerted onto an electron by the nucleus and can be calculated using Slater’s Rules

$\overline{){{\mathbf{Z}}}_{{\mathbf{eff}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{Z}}{\mathbf{}}{\mathbf{-}}{\mathbf{}}{\mathbf{S}}}$

where:

Z is the nuclear charge or atomic number

S is the shielding constant.

**For this problem, we need to do the following steps.**

**Step 1: **Determine the atomic number.

**Step 2:** Determine the electron configuration and group them by n-values.

**Step 3:** Calculate for the shielding constant using Slater's Rules.

Recall: The shielding constant can be calculated using Slater’s Rules:

**For ns and np electrons:**

1. Each electron in the *same group* will contribute **0.35** to the S value. A 1s electron contributes **0.30** to the S value of another 1s electron.

2. Each electron in the *n–1 group* contributes **0.85** to the S value.

3. Each electron in the *n–2 or greater group* contributes **1.00** to the S value.

**Step 4: **Calculate for Zeff.