Q26 / 200 · Manipal (MET) 2012 · Chemistry

In a face-centred cubic arrangement of $A$ and $B$ atoms whose $A$ atoms are at the corner of the unit cell and $B$ atoms at the face-centre, one of $A$ atom is missing from one corner in the unit cell. The simplest formula of the compound is

  • A
    $A_{24} B_7$
  • B
    $A_7 B_4$
  • Correct answer
    C
    $A_7 B_{24}$
  • D
    $A B_2$

Solution

No. of atoms of $A$ from corners of unit cell $=\frac{7}{8}$ No. of atoms of $B$ from faces of unit cell $=3$ $\therefore \qquad A: B=\frac{7}{8}: 3=7: 24$ Thus, formula of the compound is $A_7 B_{24}$.

Hence, the correct answer is option: 'C'.

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