To solve this problem, we need to understand the bonding and geometry of manganate and permanganate ions.$\newline$The manganate ion is $MnO_4^{2-}$ and the permanganate ion is $MnO_4^{-}.\newline$Both ions have a tetrahedral geometry. This geometry is due to the $\pi$-bonding between the manganese and oxygen atoms.$\newline$Let's analyze the bonding:$\newline$• Manganese in these ions is in a high oxidation state ($+6$ in manganate and $+7$ in permanganate).$\newline$• The $\pi$-bonding involves the overlap of $p$-orbitals of oxygen with $d$-orbitals of manganese.$\newline$• This $\pi$-bonding is responsible for the stabilization of the tetrahedral structure.$\newline$Analyzing the options:$\newline$• Option 1: The $\pi$-bonding involves overlap of $p$-orbitals of oxygen with $d$-orbitals of manganese. This is correct.$\newline$• Option 2: There is no $\pi$-bonding. This is incorrect as $\pi$-bonding is present.$\newline$• Option 3: The $\pi$-bonding involves overlap of $p$-orbitals of oxygen with $p$-orbitals of manganese. This is incorrect.$\newline$• Option 4: The $\pi$-bonding involves overlap of $d$-orbitals of oxygen with $d$-orbitals of manganese. his is incorrect.$\newline$Therefore, the correct option is Option 1.