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(A) The permanganate ion $(MnO_4^-)$ has a tetrahedral geometry where the central $Mn$ atom is in the $+7$ oxidation state.The electronic configuratio

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$(a) T, (b) T, (c) T, (d) F$

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(A) The permanganate ion $(MnO_4^-)$ has a tetrahedral geometry where the central $Mn$ atom is in the $+7$ oxidation state.The electronic configuration of $Mn$ is $[Ar] 3d^5 4s^2$,and for $Mn^{7+}$,it is $[Ar] 3d^0 4s^0$.$(a)$ There are $4$ $Mn-O$ $\sigma$ bonds formed by the overlap of $Mn$ $sd^3$ hybrid orbitals with $O$ $2p$ orbitals. Thus,$(a)$ is True $(T)$.$(b)$ There are $3$ $Mn-O$ $d\pi-p\pi$ bonds. Thus,$(b)$ is True $(T)$.$(c)$ Since it contains both $\sigma$ and $\pi$ bonds,$(c)$ is True $(T)$.$(d)$ Since $Mn^{7+}$ has a $d^0$ configuration,there are no unpaired electrons,making it diamagnetic. Thus,$(d)$ is False $(F)$.

Determine the correct $(T)$ and incorrect $(F)$ statements for the permanganate ion $(MnO_4^-)$:
$(a)$ $MnO_4^-$ contains $\sigma$ bonds.
$(b)$ $MnO_4^-$ contains $\pi$ bonds.
$(c)$ $MnO_4^-$ contains both $\sigma$ and $\pi$ bonds.
$(d)$ $MnO_4^-$ is paramagnetic.

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Determine the correct $(T)$ and incorrect $(F)$ statements for the permanganate ion $(MnO_4^-)$:$(a)$ $MnO_4^-$ contains $\sigma$ bonds.$(b)$ $MnO_4^-$ contains $\pi$ bonds.$(c)$ $MnO_4^-$ contains both $\sigma$ and $\pi$ bonds.$(d)$ $MnO_4^-$ is paramagnetic.