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(A) In a tetrahedral crystal field,the $d$-orbitals split into two sets: $e$ (lower energy) and $t_2$ (higher energy).The orbitals in the $t_2$ set ar

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$A$,$B$ and $D$ only

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(A) In a tetrahedral crystal field,the $d$-orbitals split into two sets: $e$ (lower energy) and $t_2$ (higher energy).The orbitals in the $t_2$ set are $d_{xy}, d_{yz}, d_{xz}$,which have higher energy than the $e$ set $(d_{x^2-y^2}, d_{z^2})$.Therefore,the energy ordering is $d_{xy} = d_{yz} = d_{xz} > d_{x^2-y^2} = d_{z^2}$.Evaluating the statements:Statement $A$: $d_{xy} = d_{xz} > d_{x^2-y^2}$ is true because $t_2$ orbitals have higher energy than $e$ orbitals.Statement $B$: $d_{xy} = d_{yz} > d_{z^2}$ is true because $t_2$ orbitals have higher energy than $e$ orbitals.Statement $C$: $d_{x^2-y^2} > d_{z^2} > d_{xz}$ is false because $d_{x^2-y^2}$ and $d_{z^2}$ are degenerate ($e$ set) and have lower energy than $d_{xz}$ ($t_2$ set).Statement $D$: $d_{x^2-y^2} = d_{z^2}$ is true as they belong to the same degenerate $e$ set.Thus,statements $A, B$,and $D$ are true.

Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex?
$A$. $d_{xy} = d_{xz} > d_{x^2-y^2}$
$B$. $d_{xy} = d_{yz} > d_{z^2}$
$C$. $d_{x^2-y^2} > d_{z^2} > d_{xz}$
$D$. $d_{x^2-y^2} = d_{z^2}$
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Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex?$A$. $d_{xy} = d_{xz} > d_{x^2-y^2}$$B$. $d_{xy} = d_{yz} > d_{z^2}$$C$. $d_{x^2-y^2} > d_{z^2} > d_{xz}$$D$. $d_{x^2-y^2} = d_{z^2}$Choose the correct answer from the given below: