Three elements A, B and C crystallise into a cubic solid lattice. Atoms A occupy the corners, B atoms, the cube centres and C atoms, the edge. The formula of the compound is

Question

Three elements A, B and C crystallise into a cubic solid lattice. Atoms A occupy the corners, B atoms, the cube centres and C atoms, the edge. The formula of the compound is (A) ABC (B)  ABC2  (C)  ABC3  (D)  ABC4

Tardigrade Admin · Accepted Answer

Number of atoms of A per unit cell =8 × (1/8) (at the corners) =1 Number of atoms of B per unit cell =1 (at the centre) =1 Number of atoms of C per unit cell =12 × (1/4) (at the edge centre) =3 So, the formula of the compound is A B C3.

Q. Three elements $A, B$ and $C$ crystallise into a cubic solid lattice. Atoms $A$ occupy the corners, $B$ atoms, the cube centres and $C$ atoms, the edge. The formula of the compound is

$A BC$

$A B C_{2}$

$A B C_{3}$

$A B C_{4}$

Number of atoms of $A$ per unit cell $= 8 \times \frac{1}{8}$ (at the corners) $= 1$
Number of atoms of $B$ per unit cell $= 1$ (at the centre) $= 1$
Number of atoms of $C$ per unit cell $= 12 \times \frac{1}{4}$
(at the edge centre) $= 3$
So, the formula of the compound is $A B C_{3}$ .

Q. Three elements A,B and C crystallise into a cubic solid lattice. Atoms A occupy the corners, B atoms, the cube centres and C atoms, the edge. The formula of the compound is

ABC

ABC2​

ABC3​

ABC4​