The crystal field splitting energy for an octahedral complex can be calculated using the ligand field stabilization energy LFSE formula:LFSE = -0.4n_t + 0.6n_ewhere n_t is the number of electrons in the t2g orbitals and n_e is the number of electrons in the eg orbitals.In this case, we are given the LFSE as 4000 cm^-1. To determine the crystal field splitting energy , we need to know the number of d-electrons in the complex. However, this information is not provided. Assuming that the complex is a d6 octahedral complex which is a common scenario , we can proceed as follows:For a high-spin complex, the electron configuration would be t2g^4 eg^2, with 4 electrons in the t2g orbitals and 2 electrons in the eg orbitals. Plugging these values into the LFSE formula:4000 = -0.4 4 + 0.6 2 4000 = -1.6 + 1.24000 = -0.4 = -10000 cm^-1Since the crystal field splitting energy is negative, this indicates that the calculation is incorrect, and the complex is not high-spin.For a low-spin complex, the electron configuration would be t2g^6 eg^0, with 6 electrons in the t2g orbitals and 0 electrons in the eg orbitals. Plugging these values into the LFSE formula:4000 = -0.4 6 + 0.6 0 4000 = -2.4 = 4000 / -2.4 1667 cm^-1Since the crystal field splitting energy is positive, this indicates that the complex is low-spin.Therefore, for a d6 octahedral complex with a LFSE of 4000 cm^-1, the crystal field splitting energy is approximately 1667 cm^-1, and the complex is low-spin.