Question

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

• A. $174\,pm$
• B. $158\,pm$
• C. $142\,pm$
• D. $126\,pm$

Answer 1

Answer: (B)

For bcc structure
Interionic distance $r^{+}+r^{-}=\frac{\sqrt{3}}{2}a$
(a = edge length)
$r^{+}_{NH^{+}_{4}}+r^{-}_{Cl^{-}}=\frac{\sqrt{3}}{2}a$
$r^{+}_{NH^{+}_{4}}+180=\frac{\sqrt{3}}{2}\times390$
$r^{+}_{NH^{+}_{4}} =338pm-180pm=158\,pm$