$A$ compound formed by $Mg$,$Al$,and $O$ is found to have a cubic close-packed $(CCP)$ array of oxide ions,in which $Mg^{2+}$ ions occupy $\frac{1}{8}^{th}$ of the tetrahedral voids and $Al^{3+}$ ions occupy $\frac{1}{2}$ of the octahedral voids. The formula for the compound is:

  • A
    $MgAl_4O_2$
  • B
    $Mg_2Al_3O_2$
  • C
    $MgAl_2O_4$
  • D
    $MgAlO$

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In a compound formed by atoms $A$ and $B$, atoms $A$ form a cubic close-packed $(CCP)$ structure, while atoms $B$ are located at the center of each edge. If the edge length of the cubic unit cell is $115 \ pm$, the distance of atom $A$ from the center of the cube is .......... $pm$.

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