A binary solid has a primitive cubical structure with $B^-$ ions constituting the lattice points and $A^+$ ions occupying $25\%$ of its tetrahedral holes. The molecular formula of the crystal is
- $AB$
- $A_2B$
- $AB_2$
- $AB_4$
The Correct Option is C
Solution and Explanation
$\therefore$ Number of tetrahedral holes in the lattice $=2 x$
$(\because$ Number of tetrahedral holes $=2 \times$ number of octahedral holes)
Now, $A^{+}$ ions occupy $25 \%$ of tetrahedral holes. Hence, number of tetrahedral holes occupied in the lattice $=2 x \times 25 \%=2 x \times \frac{25}{100}=\frac{x}{2}$
Since, number of octahedral holes $=$ Number of lattice points.
$\therefore$ Number of octahedral holes $=x$
$\therefore$ Molecular formula of the crystal is
$A_{x / 2} B_{x}$ or $A B_{2}$
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Concepts Used:
Solid State
Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions.
Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
- Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
- Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.