All alkali metals crystallize into BCC strucutres. (a) Find an equation relating the metallic radius to the density of a BCC solid in terms of its molar mass. (b) Determine the relative size of Cs atom compared to a Li atom, if their densities are 1.87 g/cc and 0.53 g/cc, respectively.

All alkali metals crystallize into BCC strucutres. (a) Find an equatio

1.	All alkali metals crystallize into BCC strucutres. (a) Find an equation relating the metallic radius to the density of a BCC solid in terms of its molar mass. (b) Determine the relative size of Cs atom compared to a Li atom, if their densities are 1.87 g/cc and 0.53 g/cc, respectively.
Answer» Solution :(a) For a BCC solid of an element, there are two atoms per UNIT cell. `implies` Density (rho)=(2xxM)/(6.023xx10^(23)a^(3))` Also, in BCC of an atomic solid, `rho=(2Mxx3sqrt(3))/(6.023xx10^(23)xx64r^(3))=2.696xx10^(-23)(M)/(r^(3))` (B)`(rho_(Cs))/(rho_(LI))=(1.87)/(0.53)=(133)/(7)(r_(Li)/(r_(Cs)))^(3)` `(r_(Cs))/(r_(Li))=1.753 implies r_(Cs)=1.753 r_(Li)`