Which of the following best represents the effective nuclear charge (Z_ext{eff}) experienced by the valence electrons in a phosphorus (P) atom?

• A. Z_ext{eff} ext{ for P} ext{ is approximately } 7
• B. Z_ext{eff} ext{ for P} ext{ is approximately } 15
• C. Z_ext{eff} ext{ for P} ext{ is approximately } 3
• D. Z_ext{eff} ext{ for P} ext{ is approximately } 5.5

Answer: (D)

Verified step by step guidance

1. Understand that the effective nuclear charge (\(Z_{\text{eff}}\)) is the net positive charge experienced by an electron in a multi-electron atom, accounting for the shielding effect of other electrons.
2. Recall the formula for effective nuclear charge: \(Z_{\text{eff}} = Z - S\) where \(Z\) is the atomic number (number of protons) and \(S\) is the shielding constant representing the average number of electrons between the nucleus and the electron of interest.
3. Identify the atomic number of phosphorus (\(P\)), which is \(Z = 15\), meaning it has 15 protons in its nucleus.
4. Estimate the shielding constant \(S\) for the valence electrons of phosphorus. This involves considering the inner core electrons that shield the valence electrons from the full nuclear charge. For phosphorus, the inner electrons are those in the 1s, 2s, and 2p orbitals (total of 10 electrons).
5. Calculate \(Z_{\text{eff}}\) by subtracting the shielding constant \(S\) (approximately 9.5 to 10, depending on the method) from the atomic number \(Z = 15\), which gives an effective nuclear charge around 5.5 experienced by the valence electrons.