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The CsCl has cubic structure of Cl^(-) i...

The `CsCl` has cubic structure of `Cl^(-)` ions in which `Cs^(+)` in which `Cs^(+)` ion is present in the body centre of the cube. It density is `3.99g cm^(-3)`.
The radius of `Cs^(+)` ion if the radius of `Cl^(-)` ion is `180 p m` is `:`

A

`180.6p m`

B

`276.8p m

C

`176.8p m`

D

`280.6 p m`

Text Solution

Verified by Experts

The correct Answer is:
c
The unit cell of `CsCl` has cubic arrangement of `Cl^(-)` ions and `Cs^(+)` ion is present in the body centre of the cube. Therefore, the unit cell contains one `Cs^(+)` and one `Cl^(-)` ion, `i.e.,z=1`
Molar mass of `CsCl=168.5g mol^(-1)`
Now Density`rho=(zxxm)/(a^(3)xxN_(0))`
or `a^(3)=(1xx168.5)/(3.99xx6.023xx10^(23))`
`=7.02xx10^(-23)cm^(3)`
`r_(Cs^(+))+r_(Cl^(-))=356.8p m`
`r_(Cs^(+))=356.8-180=176.8 p m`
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