Answer
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Step 1:: Determine the central atom and its number of electron groups.
The central atom in BF$_4^-$ is B (boron).
It has 4 electron groups around it, including the 4 bonding pairs it shares with the fluorine atoms.
Step 2:: Apply the electron group geometry formula.
The electron group geometry for an atom with 4 electron groups is tetrahedral.
Step 3:: Deduce the molecular geometry.
Since all 4 electron groups are bonding pairs (no lone pairs), the molecular geometry is also tetrahedral.
Step 4:: Verify the molecular geometry with a drawing or model.
This is the molecular geometry of BF$_4^-$.
Imagine a tetrahedron with the central boron atom at the center and the four fluorine atoms at the vertices.
Final Answer
The molecular geometry of BF$_4^-$ is tetrahedral.
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