Question

An octahedral coordination complex with the electronic configuration $t_{2g}^4 e_g^0$ is expected to exhibit which of the following magnetic properties and d-d transition characteristics?

• A. Paramagnetic with 4 unpaired electrons; spin-allowed transitions
• B. Paramagnetic with 2 unpaired electrons; spin-allowed transitions
• C. Diamagnetic; spin-forbidden transitions
• D. Paramagnetic with 2 unpaired electrons; spin-forbidden transitions

Hint:

Don't mix up high-spin and low-spin systems! If this question had given a high-spin \(d^4\) system (\(t_{2g}^3 e_g^1\)), it would have 4 unpaired electrons. But because it specifies \(t_{2g}^4 e_g^0\), the pairing tells you instantly that \(n = 4 - 2 = 2\) unpaired electrons remain.

Answer 1

The Correct Option is B

Concept: In an octahedral crystal field environment, the five d-orbitals split into two sets separated by an energy gap (\(\Delta_o\)): the lower energy \(t_{2g}\) triplet (\(d_{xy}, d_{yz}, d_{xz}\)) and the higher energy \(e_g\) doublet (\(d_{z^2}, d_{x^2-y^2}\)). The given configuration is \(t_{2g}^4 e_g^0\), which represents a low-spin \(d^4\) system (occurring in the presence of a strong-field ligand where the crystal field splitting energy is greater than the electron pairing energy, \(\Delta_o > P\)).

Step 1: Analyzing unpaired electrons and magnetic behavior.
Let's distribute the 4 electrons in the three lower-energy \(t_{2g}\) orbitals following Hund's Rule of maximum multiplicity:
• The first three electrons enter separate orbitals with parallel spins: \(\uparrow, \uparrow, \uparrow\)
• The fourth electron is forced to pair up in the first available orbital due to the large \(\Delta_o\) gap: \(\uparrow\downarrow, \uparrow, \uparrow\) Counting the single, unpaired electrons: \[ \text{Number of unpaired electrons } (n) = 2 \] Since \(n = 2\), the complex is paramagnetic (and its spin-only magnetic moment would evaluate to \(\mu_s = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83\text{ B.M.}\)).

Step 2: Determining the selection rule status for d-d transitions.
According to the quantum mechanical spin selection rule, electronic transitions are strictly allowed only if the net spin multiplicity remains unchanged (\(\Delta S = 0\)). In this \(t_{2g}^4 e_g^0\) setup, moving one electron from the paired \(t_{2g}\) orbital up into an empty \(e_g\) orbital can happen *without* altering the intrinsic spin direction of that electron. Because a transition can occur where the number of unpaired electrons remains completely identical before and after excitation, the transition is spin-allowed, resulting in standard coordination color absorption.