In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is :

A crystal is made up of metal ions 'M₁' and 'M₂' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M₁' occupies 50% of octahedral voids and the cation 'M₂' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M₁' and 'M₂' are, respectively :

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge $$a$$. The distance between the centres of two nearest octahedral voids in the crystal lattice is :

A diatomic molecule X₂ has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm^–3. The number of molecules present in 200 g of X₂ is :
(Avogadro constant (N _A) = 6 $$ \times $$ 10²³ mol^–1 )