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CsCl has cubic structure of ions in whic...

CsCl has cubic structure of ions in which `Cs^(+)` ion is present in the body -centre of the cube. If density is 3.99 g `cm^(-3)` :
(a) Calculate the length of the edge of a unit cell.
(b) What is the distance between `Cs^(+)` and `Cl^(-)` ions ?
(c) What is the radius of `Cs^(+)` ion if the radius of `Cl^(-)` ion is 180 pm ?

Text Solution

Verified by Experts

We know that,
(a) `Z=(a^(3)xxrhoxxN)/(M)`
`Z=1, , 1 Cs^(+) + 1 Cl^(-)=1 CsCl`
`M=468.5`
`1=(a^(3)xx3.99xx6.023xx10^(23))/(168.5)`
`a=4.123xx10^(-8) cm =412` pm
(b) Distance between `Cs^(+) and Cl^(-)` ions
`=(asqrt(3))/(2)=(412xxsqrt(3))/(2)=356.8` pm
(c) `r_(Cs^(+))+r_(Cl^(-))=356.8`
`r_Cs^(+)+180=356.8`
`r_(Cs^(+))=176.8` pm
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