The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

A solid having density of 9$$ \times $$10³ kg m^–3 forms face centred cubic crystals of edge length $$200\sqrt 2 $$ pm. What is the molar mass of the solid?
[Avogadro constant $$ \cong $$ 6 $$ \times $$ 10²³ mol^–1 , $$\pi $$ $$ \cong $$ 3]

A compound of formula A₂B₃ has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms :

Which premitive unit cell has unequal edge lengths (a $$ \ne $$ b $$ \ne $$ c) and all axial angles different from 90^o ?