(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 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 Patom, which orbital will it come from?

Short Answer

Expert verified
In summary, for Phosphorus (P) with the electron configuration 1s² 2s² 2p⁶ 3s² 3p³, the effective nuclear charge (Z_eff) for both 3s and 3p valence electrons without valence electron screening would be +5. Using Slater's rules, Z_eff is +12.05 for 3s valence electrons and +12.9 for 3p valence electrons. The difference between these values and the detailed calculation result (5.6+ for 3s and 4.9+ for 3p electrons) is due to Slater's rules being an approximation and not accounting for certain electron interactions accurately. The 3s and 3p electrons experience different shielding levels due to their different spatial distributions. When a P atom loses an electron, the electron is removed from the 3s orbital since it has a lower energy and shielding effect than the 3p orbital.

Step by step solution

01

1. Calculate Core and Valence Electrons for Phosphorus

Phosphorus has an atomic number of 15, meaning it has 15 electrons. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p³. The 1s² 2s² 2p⁶ electrons (10 electrons) are the core electrons, while the 3s² 3p³ electrons (5 electrons) are the valence electrons.
02

2. Calculate Effective Nuclear Charge (a)

Assuming total core electron screening and no valence electron screening, we can calculate the effective nuclear charge (Z_eff) as follows: Z_eff = Z - core_electrons Z_eff = 15 - 10 (atomic number of P - number of core electrons) Z_eff = 5 Here, the effective nuclear charge for both 3s and 3p valence electrons would be +5.
03

3. Calculate Effective Nuclear Charge using Slater's Rules (b)

To find the Z_eff using Slater's rules, we first need to sum up the screening constants (S) for each of the orbitals: For 3s electron: S = (0.35 * 2) + (0.85 * 3) = 2.95 For 3p electron: S = (0.35 * 2) + (0.85 * 2) = 2.1 Now, we can calculate the Z_eff using Slater's rules: Z_eff(3s) = Z - S = 15 - 2.95 = 12.05 Z_eff(3p) = Z - S = 15 - 2.1 = 12.9 Using Slater's rules, the effective nuclear charge for 3s valence electrons is +12.05 and for 3p valence electrons, it's +12.9.
04

4. Discuss discrepancy between calculated values and actual values (c)

The calculated effective nuclear charges using Slater's rules are higher than the detailed calculation results (5.6+ for 3s and 4.9+ for 3p electrons). The discrepancy occurs because Slater's rules are an approximation and do not account for certain electron interactions accurately. The values obtained are different for 3s and 3p because they experience different levels of shielding due to their different spatial distributions around the nucleus.
05

5. Determine which orbital loses an electron (d)

To determine which orbital loses an electron, we should look at the ionization energy for each orbital. Electrons are removed from the orbital with the lowest ionization energy. In general, the ionization energy increases as we move from lower to higher energy orbitals. Since the 3s orbital has a lower energy and shielding effect than the 3p orbital, the 3s electron will be removed first.

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Most popular questions from this chapter

Elemental barium reacts more violently with water than does elemental calcium. Which of the following best explains this difference in reactivity? (i) Calcium has greater metallic character than does barium. (ii) The electron affinity of calcium is smaller than that of barium. (iii) The first and second ionization energies of barium are less than those of calcium. (iv) The atomic radius of barium is smaller than that of calcium. (v) The ionic radius of the barium ion is larger than that of the calcium ion.

Consider the \(\mathrm{A}_{2} \mathrm{X}_{4}\) molecule depicted here, where \(\mathrm{A}\) and \(\mathrm{X}\) are elements. The \(A-A\) bond length in this molecule is \(d_{1}\), and the four \(\mathrm{A}-\mathrm{X}\) bond lengths are each \(d_{2}\). (a) In terms of \(d_{1}\) and \(d_{2},\) how could you define the bonding atomic radii of atoms A and X? (b) In terms of \(d_{1}\) and \(d_{2}\), what would you predict for the \(X-X\) bond length of an \(X_{2}\) molecule? [Section \(\left.7.3\right]\)

Consider the isoelectronic ions \(\mathrm{F}^{-}\) and \(\mathrm{Na}^{+}\). (a) Which ion is smaller? (b) Using Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant, \(S,\) calculate \(Z_{\text {eff }}\) for the \(2 p\) electrons in both ions. (c) Repeat this calculation using Slater's rules to estimate the screening constant, \(S .(\mathbf{d})\) For isoelectronic ions, how are effective nuclear charge and ionic radius related?

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Ti}^{2+},(\mathbf{b})\) (d) \(\mathrm{PO}^{2-}\), (f) \(\mathrm{V}^{3+}\) \(\mathrm{Br}^{-}\) (c) \(\mathrm{Mg}^{2+}\) (e) \(\mathrm{Pt}^{2+}\)

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