`CsCl` has cubic structure. Its density is `3.99 g cm^(-3)`. What is the distance between `Cs^(o+)` and `Cl^(Θ)` ions?
(Atomic mass of `Cs = 133`)

Explanation

CsCl has BCC structure. It has one formula unit in the unit cell. So Z=1
`rho=(ZxxM)/(a^3xxN_0)` or `a^3=(ZxxM)/(rhoxxN_0)=(1xx(133+35.5) "g mol"^(-1))/(3.99 g cm^(-3)xx6.02xx10^23 mol^(-1))=70.15xx10^(-24) cm^3`
`a=(70.15)^(1//3)xx10^(-8) cm^(3) =(70.15)^(1//3)xx10^2` pm (1pm=`10^(-10)` cm)
For BCC structure,
Interionic distance (d)`=(sqrt3a)2=1.732/2xx412.4=357` pm ltbr gt [To solve `(70.15)^(1//3)`, put `x=(70.15)^(1//3)`. Then log x=`1/3 log 70.15 =1/3xx1.8460=0.6153`
x=Antilog 0.6153=4.124]