KCl crystallizes in the same type of lattice as does NaCl. Given that `r_(Na^+)//r_(Cl^(-))=0.55andr_(K^(+))//r_(Cl^(-))=0.74`.
Calculate the ratio of the side of the unit cell for KCl to that of NaCl

Options

A. 1.123
B. 0.891
C. 1.414
D. 0.141

Answer

A

Explanation

`(r_(Na^(+)))/(r_(Cl^(-)))=0.55,(r_(K^(+)))/(r_(Cl^(-)))=0.74 `
`(r_(Na^(+)))/(r_(Cl^(-)))+1=1.55` . . . (1)
`(r_(K^(+)))/(r_(Cl^(-)))+1=1.74` . . .. (2)
Dividing (2) by (1)
`(1.74)/(1.55)=(r_(K^(+))+r_(Cl^(-)))/(r_(Cl^(-)))xx(r_(Cl^(-)))/(r_(Na^(+))+r_(Cl^(-))) or (r_(K^(+))+r_(Cl^(-)))/(r_(Na^(+))+r_(Cl^(-)))=1.123`