1.

A face-centred cubic solid of an element A has a largest sized guest atom B at the body centre octahedral hole if insertion of B doesn't affect the original unit cell dimension, determine the packing fraction of the solid.

Answer»

Solution : In the given solid, there is one B and four A per unit cell.

Also, under the condition of largest possible size of B, it will be in contact of A present at the face CENTRES only and the FOLLOWING relatinship will exist :`4r_(A)sqrt(2)` and`2(r_(A)+r_(B))=a`
solving `(r_(B))/(r_(A))=0.414`
Now,packing fraction
`(phi)=(4pi)/(3)(4r_(A)^(3)+r_(B)^(3))xx(1)/(a^(3))=(4pi)/(3)(4r_(A)^(3)+r_(B)^(3))xx(1)/(1sqrt(2r_(A)^(3)))`
`(PI)/(12SQRT(2))[4+((r_(B))/(r_(A)))^(3)] =(pi)/(12(sqrt(2)))[4+(0.414)^(3)]=0.7536`


Discussion

No Comment Found

Related InterviewSolutions