Question

The edge length of aunit cell of a metal having molecular mass 75 g/mol is 5 Å which crystallizes in a cubic lattice. If the density is 2 g/cc, the find the radius of the metal atom.

Answer 1

` p = ( Z xx M)/(a^(3) xx N_(0))/ (a^(3) xx N_(0)) or Z = ( p xx a^(3) xx N_(0))/M = ( 2g cm^(-3) xx ( 5 xx10^(-8) "cm")^(3) xx6.02 xx 10^(23) "mol"^(-1))/(75 "g mol" ^(-1))=2 `
This shows the t the metal has body -centred lattic. For BCC lattice,
` r = sqrt3/4 a= 1.732/4 xx 5 Å = 2.165 Å`