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Answer» `d_(xy), d_(xy)`
`d_(z^(2)), d_(yz)`
`d_(xy), d_(x^(2_(-)y^(2))`
`d_(x^(2_(-)y^(2))), d_(z^(2))` Solution :Lets us assume the six ligands are positioned symmertically along the Cartesian axes, with the central metal atom/ion at the origin. In an octahedral coordination entity with six ligands SURROUNDING the metal atom/ion, there will be repulsion between the electron inmetal d orbitals and the electrons (or negative charges) of the ligands. As the ligands approach form infinity toward the central metal atom/ion, first there is an increase in the energy of d orbitals relative to that of the free ion just as would be the CASE in a spherical field. As the distance of complex FORMATION approaches, such a repulsion is more when the metal d orbital is directed towards the LIGAND than when it is away form the ligand. Thus, the `d_(x^(2)-y^(2))` and `d_(z^(2))` orbitals lying along the axes and pointing towards the approaching ligands GET repelled more strongly than `d_(xy)` , `d_(yz)` , `d_(xz)` orbitals which have lobes directed between the axes and pointing a way form the approaching ligands. Consequently, the `d_(x^(2)-y^(2))` and `d_(z^(2))` orbitals get raised in energy while `d_(xy)` `d_(yz)` and `d_(xz)` orbitals are lowered in energy relative to the avarege energy in the spherical crystal field.
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