A) \[\frac{1}{2},\frac{1}{8}\]
B) \[1,\frac{1}{4}\]
C) \[\frac{1}{2},\frac{1}{2}\]
D) \[\frac{1}{4},\frac{1}{8}\]
Correct Answer: A
Solution :
In \[ccp,{{O}^{2-}}\]ions are 4. |
Hence total negative charge =-8 |
Let \[{{\operatorname{Al}}^{3+}}\]ions be\[x\], and \[{{\operatorname{Mg}}^{2+}}\]ions be y. |
Total positive charge \[3x+2y\] |
\[\Rightarrow 3x+2y=8\] |
This relation is satisfied only by \[x=2\] |
And \[y=1.\] |
Hence number of \[{{\operatorname{Al}}^{3+}}=2\] |
And number of \[{{\operatorname{Mg}}^{2+}}=1\] |
\[\Rightarrow n=\]Fraction of octahedral holes occupied |
\[\operatorname{by}\,A{{l}^{3+}}=\frac{2}{4}=\frac{1}{2}\] |
And \[m=\]fraction of tetrahedral holes |
Occupied by\[{{\operatorname{Mg}}^{2+}}=\frac{1}{8}\] |
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