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Chapter 23: Problem 51

If the lobes of a given \(d\) -orbital point directly at the ligands, will an electron in that orbital have a higher or lower energy than an electron in a \(d\) -orbital whose lobes do not point directly at the ligands?

Short Answer

Expert verified
An electron in a \(d\)-orbital whose lobes point directly at the ligands, such as the \(e_{g}\) set, will have a higher energy level due to stronger interactions with the ligands. On the other hand, an electron in a \(d\)-orbital whose lobes do not point directly at the ligands, like the \(t_{2g}\) set, will have a lower energy level due to weaker interactions with the ligands.

Step by step solution

01

Crystal Field Theory

To understand the effect of ligands on the energy levels of \(d\)-orbitals, we need to refer to the Crystal Field Theory (CFT). CFT explains the energy splitting of degenerate \(d\)-orbitals in transition metal complexes due to the interaction between the central metal ion and its surrounding ligands. When ligands approach the central metal ion, the electrostatic repulsion between the electrons in the \(d\)-orbitals and the negatively charged ligands causes a change in the energies of the \(d\)-orbitals.
02

Energy Splitting of \(d\)-Orbitals

In an octahedral complex, the five degenerate \(d\)-orbitals split into two energy levels: three orbitals (dxy, dyz, and dxz) at a lower energy level, called \(t_{2g}\) set, and two orbitals (dx2-y2 and dz2) at a higher energy level, called \(e_{g}\) set. The difference in energy between these sets is called the crystal field splitting energy, denoted as \(\Delta_{O}\). In the \(t_{2g}\) set, the orbital lobes lie between the ligands, resulting in less interaction with the ligands. On the other hand, in the \(e_{g}\) set, the lobes are pointing directly at the ligands, resulting in a stronger interaction leading to higher energy levels.
03

Comparing Energy Levels

Now, we can compare the energy levels of electrons in the two \(d\)-orbital types as asked in the exercise. An electron in a \(d\)-orbital that points directly at the ligands (such as the \(e_{g}\) set) will interact more strongly with the ligands and will thus have a higher energy. Conversely, an electron in a \(d\)-orbital whose lobes do not point directly at the ligands (such as the \(t_{2g}\) set) will have less interaction and therefore a lower energy level. In conclusion, an electron in a \(d\)-orbital whose lobes point directly at the ligands will have a higher energy than an electron in a \(d\)-orbital whose lobes do not point directly at the ligands.

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Most popular questions from this chapter

Generally speaking, for a given metal and ligand, the stability of a coordination compound is greater for the metal in the +3 rather than in the +2 oxidation state (for metals that form stable +3 ions in the first place). Suggest an explanation, keeping in mind the Lewis acid-base nature of the metal-ligand bond.

Determine if each of the following metal complexes is chiral and therefore has an optical isomer: (a) square planar \(\left[\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}\right],(\mathbf{b})\) octahedral $\left[\mathrm{Ni (\mathrm{en})\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+},$ (c) octahedral cis-[V(en) \(\left._{2} \mathrm{ClBr}\right]\).

Indicate the likely coordination number of the metal in each of the following complexes: (a) $\left[\mathrm{Ru}(\text { bipy })_{3}\right]\left(\mathrm{NO}_{3}\right)_{2}$ (b) $\operatorname{Re}(\text { o-phen })_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}$ (c) \(\mathrm{Pd}(\mathrm{PPh} 3)_{3} \mathrm{Cl}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Mn}(\mathrm{EDTA})\)

Explain why the transition metals in periods 5 and 6 have nearly identical radii in each group.

The lanthanide contraction explains which of the following periodic trends? (a) The atomic radii of the transition metals first decrease and then increase when moving horizontally across each period. (b) When forming ions the period 4 transition metals lose their \(4 s\) electrons before their \(3 d\) electrons. (c) The radii of the period 5 transition metals (Y-Cd) are very similar to the radii of the period 6 transition metals (Lu-Hg).
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