KCl crystalizes in the same type of lattice as does NaCl and CsF in the CsCl type of structure. The molar mass of CsF is twice that of KCl and the a value of KCl is 1.5 times that of CsF.The ratio of the densities of CsF to that of KCl is

Options

A. 2.05
B. 1.69
C. 3.2
D. 4.51

Answer

B

Explanation

Since, there are 4 KCl per unit cell, the relation for `KCl` is, `(a_(1)^(3))/(4)xxN_(A)=(74.5)/(rho_(t))`
Since there is 1 CsF per unit cell, the relation for `CsF` is `(a_(2)^(3))/(1)xxN_(A)=(2xx74.5)/(rho_(2))`
Dividing the above two expressions, we get `(a_(1)^(3))/(4a_(2)^(3))=(1)/(2)xx(rho_(2))/(rho_(1))`
Now, `a_(1)=1.5a_(2),` so we have `((1.5)^(3)a_(2)^(3))/(4xxa_(2)^(3))=(1)/(2)xx(rho_(2))/(rho_(1)) implies (rho_(2))/(rho_(1))=((1.5)^(3))/(4)xx2=1.69`.