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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?

Problem

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

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

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

Zeff = Z - 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.

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