What is the effective nuclear charge (Zeff) for a valence electron in an aluminum (Al) atom?
(core electrons contribute 0.85 and valence electrons contribute 0.35 to the shielding value, S)

Question

What is the effective nuclear charge (Zeff) for a valence electron in an aluminum (Al) atom? 
(core electrons contribute 0.85 and valence electrons contribute 0.35 to the shielding value, S)

BlackTom AI · Accepted Answer

We start by identifying the numbers involved for aluminum (Z = 13) and its electron configuration. Aluminum has 10 core electrons and 3 valence electrons (3s2 3p1).

Option analysis:

- If we used S = 10 core electrons × 0.85 per core electron = 8.5, and we treated all 3 valence electrons as contributing 0.35 each (3 × 0.35 = 1.05), we would get S = 9.55 and Zeff = 13 − 9.55 = 3.45. This value (3.45) is not listed, so this straightforward “all valence electrons fully shield” approach is inconsistent with the given choices and Slater-type reasoning that treats shielding by same-group electrons differently.

- Option 2.5: This would imply Zeff is lower, suggesting a larger shielding value. If Zeff were 2.5, then S would be 13 − 2.5 = 10.5. That would require total shielding well above the core shielding alone (8.5) by about 2.0 more, which would imply more shielding than allowed by the standard counts (and even counting all valence electrons at 0.35 each would give only 1.05 extra). Therefore 2.5 is inconsistent with the given shielding scheme.

- Option 3.15: This would correspond to S = 13 − 3.15 = 9.85. That implies only a small additional shielding beyond the core contribution of 8.5 from valence electrons (0.35 per electron). But with 3 valence electrons, the maximum additional shielding from all valence electrons would be 1.05, giving S = 9.55, not 9.85. So 3.15 is not consistent with counting the valence electrons correctly.

- Option 3.80: This aligns with a standard Slater-like calculation for an ns/np valence electron where core electrons contribute 0.85 each (10 core electrons give 8.5), and only the other valence electrons shield the considered electron at 0.35 each. Since there are 2 other valence electrons besides the one in question, the valence shielding is 2 × 0.35 = 0.70. Total shielding S = 8.5 + 0.70 = 9.20, yielding Zeff = 13 − 9.20 = 3.80. This matches the option and follows the typical rule for shielding within the same period.

- Option 4.15: Achieving Zeff = 4.15 would require S = 8.85. That would mean far less shielding from valence electrons than allowed by the 0.35 per other valence electron and would underestimate the contribution from core electrons if we follow the given scheme. It contradicts the core-electron shielding and the 0.35 per other valence electron relationship.

- Option 4.50: This would imply S = 8.50, i.e., only core electrons contribute shielding and none from valence electrons, or an unrealistically small valence shielding. Given there are two other valence electrons that should contribute 0.35 each, this option ignores a component of shielding and is therefore inconsistent.

In summary, the only consistent calculation under the stated contributions (core electrons 0.85 each; other valence electrons 0.35 each) yields S = 8.5 + 0.70 = 9.20, giving Zeff = 3.80, which matches option 3.80.

What is the effective nuclear charge (Zeff) for a valence electron in an aluminum (Al) atom? (core electrons contribute 0.85 and valence electrons contribute 0.35 to the shielding value, S)

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