Potassium effective nuclear charge

Account for the fact that the ionization energy of potassium is less than that of sodium despite the latter having the smaller effective nuclear charge. 

It is relatively easy to pull one electron away from a potassium atom but very difficult to remove a second one. Use the shell model and the idea of effective nuclear charge to explain why. 

The correct answer is (E). For the same reasons that it has the lowest electronegativity, potassium has the lowest ionization energy. The outermost electron has the most shielding between it and the nucleus with the smallest effective nuclear charge. 

Thus, an electron in the As (rather than the 3d) atomic orbital is under the influence of a greater effective nuclear charge and in the ground state of potassium, it is the As atomic orbital that is occupied. 

The first ionization energies of sodium, potassium and rubidium atoms are 5.14, 4.34 and 4.17 eV, respectively. Use equation (7.37) to calculate the effective nuclear charge experienced by the outermost s electron in each of these atoms. 

A An electron attaching itself to a potassium atom would occupy the 4s orbital, pairing up with the valency electron already present. There would be interelectronic repulsion between the two 4s electrons, but this is overcome by the effective nuclear charge of the K ion. In the calcium case the 4s orbital is already full, and the extra electron must find space in a 3d orbital, which is the next level of lowest energy. 

Vertically, removing the 4s electron from a potassium atom should take less energy than removing the 3s electron of sodium because the electron being removed is farther from the effective nuclear charge. 

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