question_answer

Nearest distance between two tetrahedral voids and between two octahedral voids are, respectively,

A) \[\frac{a}{\sqrt{2}},\frac{\sqrt{3}}{2}a\]                       

B) \[\frac{\sqrt{3}}{4}a,\frac{\sqrt{3}}{2}a\]

C) \[\frac{\sqrt{3}}{2}a,\frac{a}{\sqrt{2}}\]           

D) \[\frac{\sqrt{3}}{2}a,\frac{\sqrt{3}}{4}a\]

Correct Answer: C

Solution :

[c] Nearest distance between 2T.V's Nearest distance between 2 O.V. is: \[{{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}}={{\left( \frac{a}{2} \right)}^{2}}+{{\left( \frac{a}{2} \right)}^{2}}=\frac{{{a}^{2}}}{2}\]             \[AC=\frac{a}{\sqrt{2}}\]