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Ammonium chloride crystallises in a body...

Ammonium chloride crystallises in a body-centred cubic lattice with a unit distance of 387 pm. Calculate (a) the distance between oppositely charged ions in the lattice and (b) and radius of the `NH_(4)^(+)` ion of the radius of `Cl^(-)` ion is 181 pm.

Text Solution

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(a) In a body-centred cubic lattice, oppositely charged ions touch each other along the cross-diagonal of the cube.
So, `2r_(c) +2r_(a)=sqrt(3)a`
or `r_(c)+r_(a)=(sqrt(3))/(2)a`
`=(sqrt(3))/(2)xx387=335.15` pm. (b) Given that, `r_(a)=181` pm.
`r_(c)=335.15-181.0 =154.15` pm
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