Q14 / 200 · Manipal (MET) 2014 · Chemistry

A body centre cubic lattice is made up of two different types of atoms $A$ and $B$. Atom $A$ occupies the body centre and $B$ occupying the corner positions. One of the corners is left unoccupied per unit cell. Empirical formula of such a solid is

  • A
    $A B$
  • B
    $A_2 B_3$
  • C
    $A_5 B_7$
  • Correct answer
    D
    $A_8 B_7$

Solution

There is one $A$ per unit cell $\begin{aligned} & \text { Number of } B \text { per unit cell }=\frac{1}{8} \times 7=\frac{7}{8} \\ & \begin{aligned} \text { Empirical formula } & =A_1 B_{7 / 8} \\ & =A_8 B_7 \end{aligned} \end{aligned}$

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

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