Question

What is the geometry of the manganate ion, $Mn{O_4}^{2-}?$

Answer 1

Hint: The three-dimensional arrangement of the atoms that make up a molecule is known as molecular geometry. It comprises the molecule's overall form, as well as bond lengths, bond angles, torsional angles, and any other geometrical factors that define each atom's location. The reactivity, polarity, phase of matter, colour, magnetism, and biological activity of a material are all influenced by molecular geometry.

Complete answer:
A central atom is placed in the middle of a tetrahedral molecular geometry, with four substituents located at the corners of the tetrahedron. When all four substituents are the same, as in methane and its heavier equivalents, the bond angles are $109.5{}^{\circ }$ . Point group Td includes methane and other fully symmetrical tetrahedral molecules, although most tetrahedral molecules have lesser symmetry. Chiral tetrahedral molecules are possible.
Now let us draw for $Mn{O_4}^{2-}$
We have Mn, therefore manganate is a sulphate ion counterpart for which VSEPR may be used directly.
Determine which atom in the structure is the centre atom. Normally, this is the least electronegative atom (Mn). Make a skeletal structure with the other atoms single-bonded to the central one. Make an octet for each atom by wrapping electron pairs around it. Count how many valence electrons there are in your test structure (32). Count how many valence electrons you have accessible now. Four electrons are absent from the trial structure. As a result, Create a new structure with one double bond for each missing pair of electrons and an octet for each O atom:
The octet of the Mn atom can be "extended." Determine the molecular geometry using VSEPR theory. Around the Mn atom, there are four bonding electron domains and no lone pairs.
 $A{X}_4$ is a kind of molecule.

Hence The molecular geometry is tetrahedral.

Note:
A manganate is any negatively charged molecular entity containing manganese as the centre atom in inorganic nomenclature. However, because it includes manganese in the +6 oxidation state, the term is typically used to the tetraoxidomanganate(2-) anion, $Mn{O_4}^{2-}$ , also known as manganate(VI). Manganates are the only manganese(VI) compounds that have been discovered.