(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the \(3 s\) and \(3 p\) valence electrons in \(\mathrm{P}\) ? (b) Repeat these calculations using Slater's rules. (c) Detailed calculations indicate that the effective nuclear charge is \(5.6+\) for the \(3 s\) electrons and \(4.9+\) for the \(3 p\) electrons. Why are the values for the \(3 s\) and \(3 p\) electrons different? (d) If you remove a single electron from a \(\mathrm{P}\) atom, which orbital will it come from? Explain.

The phosphorus atom has an atomic number of 15, meaning it has 15 protons in the nucleus. The electron configuration is \[1s^2 2s^2 2p^6 3s^2 3p^3.\] If the core electrons (1s, 2s, and 2p) create perfect screening and valence electrons (3s and 3p) don't create any screening, then the effective nuclear charge acting on 3s and 3p valence electrons will be the total nuclear charge minus the core electrons charge: \[Z_\text{eff} = Z - \text{core electrons} = 15 - (2+2+6) = 15 - 10 = 5 .\] So, in this case, the effective nuclear charge acting on the 3s and 3p valence electrons would be 5+.

To calculate the effective nuclear charge using Slater's rules, we need to consider the electron shielding contributions from different orbital electrons. According to Slater's rules, the shielding constants are given for different orbitals: - For n=1, \(S = 0.30\) - For n=2, \(S = 0.85 \times \text{number of electrons}\) - For n=3, \(S = 1.00 \times \text{number of electrons}\) Let's first calculate the shielding for the 3s electrons: \[S(3s) = (2 \times 0.35) + (8 \times 0.85) + (1 \times 1.00) = 9.7\] Now, let's calculate the effective nuclear charge for the 3s electrons: \[Z_\text{eff}(3s) = Z - S(3s) = 15 - 9.7= 5.3+\] Now, let's calculate the shielding for the 3p electrons: \[S(3p) = (2 \times 0.35) + (8 \times 0.85) + (2 \times 1.00) = 9.0\] Now, let's calculate the effective nuclear charge for the 3p electrons: \[Z_\text{eff}(3p) = Z - S(3p) = 15 - 9.0 = 6.0+\] Using Slater's rules, we calculated that the effective nuclear charges are 5.3+ for the 3s electron and 6.0+ for the 3p electrons.

The 3s and 3p effective nuclear charges differ because the 3s electrons are closer to the nucleus than the 3p electrons, experiencing more attractive force from the nucleus. The given detailed calculation values are 5.6+ for the 3s electrons and 4.9+ for the 3p electrons. These values differ from our findings in part (b) due to Slater's rules being an approximation. However, the order is the same, with the 3s effective nuclear charge being higher than the 3p effective nuclear charge.

When you remove a single electron from a phosphorus atom, it will come from the orbital with the highest energy and least binding by the nucleus. In this case, the electron will come from the 3p orbital, as the effective nuclear charge for the 3p electrons is lower than that for the 3s electrons, meaning that they are less tightly bound to the nucleus.