Question

How many of the following ions of 3d series have observed magnetic moment value greater than calculated from the spin-only magnetic moment formula

Ti³⁺, Ti²⁺, V²⁺, Cr²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺

• A. Ti³⁺
• B. Ti²⁺
• C. V²⁺
• D. Cr²⁺
• E. Mn²⁺
• F. Fe²⁺
• G. Co²⁺
• H. Ni²⁺
• I. Cu²⁺

Answer 1

Answer: (A), (F), (G), (H), (I)

5

Answer 2

The spin-only magnetic moment is calculated using the formula $\mu_s = \sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons. The observed magnetic moment can be greater than the spin-only value if there is a significant orbital contribution, which arises from the angular momentum of the electrons not fully quenched by crystal field effects or spin-orbit coupling.

Analyzing each ion:

• Ti³⁺ ([Ar] 3d¹): $n=1$. $\mu_s = 1.73$ BM. Ground state $^2T_{2g}$ (orbitally degenerate). Observed $\mu \approx 1.75$ BM. Greater.
• Ti²⁺ ([Ar] 3d²): $n=2$. $\mu_s = 2.83$ BM. Ground state $^3T_{1g}$ (orbitally degenerate). Observed $\mu \approx 2.7$ BM (often lower). Not greater.
• V²⁺ ([Ar] 3d³): $n=3$. $\mu_s = 3.87$ BM. Ground state $^4A_{2g}$ (non-degenerate). Orbital contribution negligible. Observed $\mu \approx 3.87$ BM. Not greater.
• Cr²⁺ ([Ar] 3d⁴): $n=4$. $\mu_s = 4.90$ BM. Ground state $^5E_g$ (orbitally degenerate), but Jahn-Teller effect usually quenches orbital contribution. Observed $\mu \approx 4.8$ BM. Not greater.
• Mn²⁺ ([Ar] 3d⁵): $n=5$. $\mu_s = 5.92$ BM. Ground state $^6A_{1g}$ (non-degenerate). Orbital contribution negligible. Observed $\mu \approx 5.92$ BM. Not greater.
• Fe²⁺ ([Ar] 3d⁶): $n=4$ (high spin). $\mu_s = 4.90$ BM. Ground state $^5E_g$ (orbitally degenerate). Significant orbital contribution enhances moment. Observed $\mu \approx 5.1-5.5$ BM. Greater.
• Co²⁺ ([Ar] 3d⁷): $n=3$ (high spin). $\mu_s = 3.87$ BM. Ground state $^4T_{1g}$ (orbitally degenerate). Significant orbital contribution enhances moment. Observed $\mu \approx 4.4-4.8$ BM. Greater.
• Ni²⁺ ([Ar] 3d⁸): $n=2$ (high spin). $\mu_s = 2.83$ BM. Ground state $^3A_{2g}$ (non-degenerate). Mixing with excited orbitally degenerate states ($^3T_{2g}$) via spin-orbit coupling leads to enhanced moment. Observed $\mu \approx 2.9-3.2$ BM. Greater.
• Cu²⁺ ([Ar] 3d⁹): $n=1$. $\mu_s = 1.73$ BM. Ground state $^2E_g$ (orbitally degenerate). Jahn-Teller distortion can lead to enhanced orbital contribution. Observed $\mu \approx 1.75-1.9$ BM. Greater.

The ions with observed magnetic moments greater than their spin-only values are Ti³⁺, Fe²⁺, Co²⁺, Ni²⁺, and Cu²⁺. Therefore, there are 5 such ions.