Given: A molecule with formula AX2Y2 is described using periodic trends. X has the highest electronegativity, Y has the second highest electronegativity, and A is the rarest monatomic non-radioactive element of its group with the lowest ionization energy among A, X, and Y.
Find: The shape of the molecule.
From the solution working, the most electronegative element is identified as fluorine, so X=F. The second most electronegative element is identified as oxygen, so Y=O. The rarest monatomic non-radioactive p-block element of its group with lower ionization energy than F and O is identified as xenon, so A=Xe.
Thus, the molecule considered in the solution is XeOF4. This indicates a discrepancy with the printed formula AX2Y2 in the question text; the solution clearly works with XeOF4 and concludes the geometry from that identified molecule.
Apply VSEPR theory to XeOF4:
Steric number=5+1=6
There are 5 bonded atoms around xenon and 1 lone pair on xenon.
A steric number of 6 gives an octahedral electron-pair geometry. With one lone pair, the molecular shape becomes square pyramidal.
Therefore, the correct option is A.