Consider following statements regarding the magnetic moment of the 3d transition metal complexes:

A. Octahedral complexes of $$Mn^{II}$$​  (high spin) and $$Fe^{III}$$ (high spin) have $$\mu_{eff}$$ approximately equal to their $$\mu_{spin}$$ values.​

B. Tetrahedral complexes of $$Ni^{II}$$ and octahedral complexes of $$Co^{II}$$​ have orbital contribution added to their magnetic moments.

C. Orbital contribution is quenched for metal ions having A or E ground state.

D. Octahedral complexes of $$Cu^{II}$$ have $$\mu_{eff} > \mu_{spin}$$ value at 300 K due to orbital contribution added to their magnetic moments​

Choose the correct answer from the options given below:

Correct option is C

Paramagnetism arises from unpaired electrons. Each electron has a magnetic moment with one component associated with the spin angular momentum of the electron and (except when the quantum number l=0) a second component associated with the orbital angular momentum. For many complexes of first row d-block metal ions we can ignore the second component and the magnetic moment, can be regarded as being determined by the number of unpaired electrons, n. The two equations are related because the total spin quantum number S=n/2.

$$\mu_{\text{spin-only}} = 2 \sqrt{S(S + 1)}$$

$$\mu_{\text{spin-only}} = \sqrt{n(n + 2)}$$

​​By no means do all paramagnetic complexes obey the spin only formula and caution must be exercised in its use. It is often the case that moments arising from both the spin and orbital angular momenta contribute to the observed magnetic moment. The energy difference between adjacent states with J values of J^' and (J^'+1) is given by the expression (J^'+1)λ where λ is called the spin–orbit coupling constant. The value of λ varies from a fraction of a cm^-1 for the very lightest atoms to a few thousand cm^-1 for the heaviest ones. The extent to which states of different J values are populated at ambient temperature depends on how large their separation is compared with the thermal energy available, kT; at 300 K, kT~200 cm^-1 or 2.6 kJ mol^-1. It can be shown theoretically that if the separation of energy levels is large, the magnetic moment is given by the following equation. 

$$\mu_{\text{eff}} = g_J \sqrt{J(J + 1)} \\\text{where} \quad g_J = 1 + \left( \frac{S(S + 1) - L(L + 1) + J(J + 1)}{2J(J + 1)} \right)$$

For many (but not all) first row metal ions, λ is very small and the spin and orbital angular momenta of the electrons operate independently. For this case, the van Vleck formula has been derived. Strictly, the equation given below applies to free ions but, in a complex ion, the crystal field partly or fully quenches the orbital angular momentum. 

$$\mu_{eff} = \sqrt{4S(S + 1) + L(L + 1)}$$  (effective magnetic moment)

If there is no contribution from orbital motion, then the above equation reduces to the equation given below which is the spin-only formula. Any ion for which L=0 (e.g. high-spin d⁵ Mn²⁺ or Fe³⁺ in which each orbital with m_l= +2, +1, 0, -1, -2 is singly occupied, giving L= 0) 

$$\mu_{eff} = \sqrt{4S(S + 1)} = 2 \sqrt{S(S + 1)}$$​

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