Compare the $x$ and $y$ bond lengths in the following molecules:
Structure $1$: $HO-S(=O)-S(=O)-OH$ (where $x$ is the $S-S$ bond length)
Structure $2$: $HO-S(=O)_2-S(=O)-OH$ (where $y$ is the $S-S$ bond length)

Fill in the blanks given below:
$(i)$ The two theories based on the principles of quantum mechanics are ........ and ......... .
$(ii)$ The electronic configuration of carbon in the excited state is ........... .
$(iii)$ Through the combination of atomic orbitals,....... are formed.
$(iv)$ The ${\rm{CH}}_4$ molecule has a .......... shape.

The number of electrons in the valence shell of the central atom of a molecule is $8$. The molecule is

Among the following,the correct statement$(s)$ is(are):
$A$. $Al(CH_3)_3$ has the three-centre two-electron $(3c-2e)$ bonds in its dimeric structure.
$B$. $BH_3$ has the three-centre two-electron $(3c-2e)$ bonds in its dimeric structure $(B_2H_6)$.
$C$. $AlCl_3$ has the three-centre two-electron bonds in its dimeric structure.
$D$. The Lewis acidity of $BCl_3$ is greater than that of $AlCl_3$.

Which of the following species does not exist?

The lattice energy of $NaCl$ is $-780 \, kJ \, mol^{-1}$. The enthalpies of hydration of $Na^{+}_{(g)}$ and $Cl^{-}_{(g)}$ ions are $-406 \, kJ \, mol^{-1}$ and $-364 \, kJ \, mol^{-1}$ respectively. The enthalpy of solution of $NaCl_{(s)}$ is $..... \, kJ \, mol^{-1}$.