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Question

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) the radius of the NH+4 ion if the radius of Cl ions is 181 pm.

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Solution

(a) In a body-centred cubic lattice, oppositely charged ions touch each other along the cross-diagonal of the cube.

So, 2rc+2ra=3a

or rc+ra=32a

=32×387=335.15 pm.

(b) Given that, ra=181 pm

rc=335.15181.0=154.15 pm

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