Shows ccp type of arrangement In \( Fe _{3} O _{4}\left[ Fe ^{ II } Fe

1.	Shows ccp type of arrangement In \( Fe _{3} O _{4}\left[ Fe ^{ II } Fe _{2}^{ III } O _{4}\right] O ^{2-} \) ions are arranged on \( \operatorname{ccp} \) arrangement. If \( Fe ^{2+} \) ions are arranged on tetrahedral voids and \( Fe ^{3+} \) ions are arranged on octahedral voids, then how much portion of tetrahedral and octahedral voids occupied respectively? (A) \( \frac{1}{4}, \frac{1}{8} \) (B) \( \frac{1}{4}, \frac{1}{2} \) (C) \( \frac{1}{8}, \frac{1}{2} \) (D) \( \frac{1}{2}, \frac{1}{4} \)
Answer» In the ccp arrangements, there is total 4 octahedral void and 8 tetrahedral voids. Then, on molecule of [Fe^II Fe₂^IIIO₄] occupied one unit cell. Fraction of tetrahedral void occupied by on molecule of Fe₃O₄ = \(\frac {No \,of\,Fe^{+2}ion\,per\,molecule}{No\,of\,tetrahedral\, void}\) = 1/8 Fraction of octahedral void occupied by one molecule of Fe₃O₄ = \(\frac {No \,of\,Fe^{+3}ion\,per\,molecule}{No\,of\,octahedral\, void}\) = 2/4 = 1/2 Therefore, the portion of tetrahedral and octahedral voids occupied 1/8, 1/2 respectively Hence, option (c) is right answer

Shows ccp type of arrangement In \( Fe _{3} O _{4}\left[ Fe ^{ II } Fe _{2}^{ III } O _{4}\right] O ^{2-} \) ions are arranged on \( \operatorname{ccp} \) arrangement. If \( Fe ^{2+} \) ions are arranged on tetrahedral voids and \( Fe ^{3+} \) ions are arranged on octahedral voids, then how much portion of tetrahedral and octahedral voids occupied respectively? (A) \( \frac{1}{4}, \frac{1}{8} \) (B) \( \frac{1}{4}, \frac{1}{2} \) (C) \( \frac{1}{8}, \frac{1}{2} \) (D) \( \frac{1}{2}, \frac{1}{4} \)

Answer»

In the ccp arrangements, there is total 4 octahedral void and 8 tetrahedral voids. Then, on molecule of [Fe^II Fe₂^IIIO₄] occupied one unit cell.

Fraction of tetrahedral void occupied by on molecule of

Fe₃O₄ = \(\frac {No \,of\,Fe^{+2}ion\,per\,molecule}{No\,of\,tetrahedral\, void}\)

= 1/8

Fraction of octahedral void occupied by one molecule of

Fe₃O₄ = \(\frac {No \,of\,Fe^{+3}ion\,per\,molecule}{No\,of\,octahedral\, void}\)

= 2/4

= 1/2

Therefore, the portion of tetrahedral and octahedral voids occupied 1/8, 1/2 respectively

Hence, option (c) is right answer