Ammonium chloride crystallizes in a body centred cubic lattice with edge length of unit cell of $$390\,pm.$$  If the size of chloride ion is $$180\,pm,$$  the size of ammonium ion would be

Solution :
$$\eqalign{ & {\text{For }}bcc{\text{ structure}} \cr & {\text{Interionic distance}} \cr & = {r^ + } + {r^ - } = \frac{{\sqrt 3 }}{2}a\,\,\left( {a = {\text{edge length}}} \right) \cr & r_{NH_4^ + }^ + + r_{C{l^ - }}^ - = \frac{{\sqrt 3 }}{2}a \cr & r_{NH_4^ + }^ + + 180 = \frac{{\sqrt 3 }}{2} \times 390 \cr & r_{NH_4^ + }^ + = 338pm - 180pm = 158\,pm \cr} $$