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In a high-spin d4 configuration, the electrons fill the t2g and eg orbitals as follows: \(t_{2_{g}}^{\uparrow\downarrow \uparrow\uparrow}\) \(e_{g}^{\uparrow\downarrow}\). There are two unpaired electrons.

In a low-spin d4 configuration, the electrons fill the t2g orbitals mostly due to the large splitting caused by strong-field ligands: \(t_{2_{g}}^{\uparrow\downarrow \uparrow\downarrow}\) \(e_{g}^{\downarrow}\). There is one unpaired electron. As there is only a one-electron difference between high-spin and low-spin d4 configurations, it doesn't satisfy the requirement. #Step 3: Examine d5 configuration#

In a high-spin d5 configuration, the electrons fill the t2g and eg orbitals as follows: \(t_{2_{g}}^{\uparrow\downarrow \uparrow\uparrow}\) \(e_{g}^{\uparrow\downarrow\uparrow}\). There are three unpaired electrons.

In a low-spin d5 configuration, the electrons fill the t2g and eg orbitals mostly due to the large splitting caused by strong-field ligands: \(t_{2_{g}}^{\uparrow\downarrow \uparrow\downarrow\uparrow}\) \(e_{g}^{\downarrow}\). There is one unpaired electron. As there is only a two-electron difference between high-spin and low-spin d5 configurations, this satisfies the requirement. #Step 4: Examine d6 and d7 configurations# We can deduce that the d6 and d7 configurations will also not satisfy the requirement as they will have fewer unpaired electrons in high-spin complexes compared to d5 high-spin complexes. Therefore, the d5 configuration is the only one that fulfills the condition. #Step 5: Identify possible metal ions# Now that we have identified the d5 electron configuration, we can name some possible metal ions for which this statement is true. These metal ions include: 1. Manganese (III) ion [Mn(III)] - has d4 configuration in its ground state, and d5 when it loses one more electron 2. Iron (II) ion [Fe(II)] - has d6 configuration in its ground state, and d5 when it loses one electron These metal ions, when part of an octahedral complex, would show a difference of two unpaired electrons between high-spin and low-spin configurations.