The magnetic moment of the complex [Mn(NCS)6]4– is 6.06 µB. Its electronic configuration is :
t2g3 eg2
In [Mn(NCS)6]4– the metal is Mn(II), a d5 ion, surrounded octahedrally by six N-bonded thiocyanate ligands. The magnetic moment tells how many electrons are unpaired and therefore whether the complex is high spin or low spin.
Step 1 — Spin-only values: one unpaired electron gives \(\sqrt{3} = 1.73\ \mu_B\) and five give \(\sqrt{5 \times 7} = 5.92\ \mu_B\). Step 2 — The observed 6.06 µB is close to 5.92 µB, so all five d electrons are unpaired. Step 3 — In an octahedral field this high-spin arrangement places three electrons in the lower t2g set and two in the upper eg set, because the pairing energy exceeds the splitting produced by NCS–.
The low-spin arrangement t2g5 eg0 leaves only one unpaired electron (about 1.7–2 µB). The labels t2 and e without the g subscript describe a tetrahedral field, not this six-coordinate octahedral complex. The arrangement t2g2 eg3 would require pairing in the upper set before the lower set is filled, which never happens for a ground state.
t2g3 eg2 option is correct.
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