Question

A solid made up of ions of A and B possesses an edge length of unit cell equal to $0.564$ nm has four formula units. Among the two ions, the smaller one occupies the interstitial void and the larger ions occupy the space lattice with ccp type of arrangement. One molecule of solid has mass as $9.712\times {10}^{-23}$ g. The density (in g cm${}^{-3}$) of solid is:

• A. $2.16$
• B. $0.54$
• C. $1.08$
• D. $1.562$

Answer 1

The correct option is A $2.16$

The expression for density of the unit cell is given below:

$a=0.564nm=564pm=564\times {10}^{-}10cm$
$d=\frac{ZM}{N_A\times a^3}$
where Z is effective no. of atoms, for CCP Z=4
Molar mass of $AB$:

1 molecule has a mass = $9.712\times {10}^{-23}$ g
1 mole has a mass, $M$ = $9.712\times {10}^{-23}\times N_A$ g
$d=\frac{4\times 9.712\times {10}^{-23}\times N_A}{N_A\times (564{)}^3\times {10}^{-30}}=2.16$ g cm${}^{-3}$

Hence, the correct option is A.