Question:
A solid is formed by two elements $P$ and $Q$. The element $Q$ forms cubic close packing and atoms of $P$ occupy one-third of tetrahedral voids. The formula of the compound is
A solid is formed by two elements $P$ and $Q$. The element $Q$ forms cubic close packing and atoms of $P$ occupy one-third of tetrahedral voids. The formula of the compound is
Updated On: Jun 14, 2022
- $ PQ_{3}$
- $P_{3}Q$
- $P_{2}Q_{3}$
- $P_{3}Q_{2}$
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The Correct Option is C
Solution and Explanation
Let the number of atoms in cubic close packing be $x$.
$\therefore$ Number of tetrahedral voids $=2 x$
Since, $Q$ forms cubic close packing, the number of $Q$ atoms $=x$
$P$ occupy one third of tetrahedral voids, the number of $p$ atoms $=\frac{2}{3} x$
$\frac{\text { Number of } P \text { atoms }}{\text { Number of } Q \text { atoms }}$
$=\frac{2 \cdot x}{3 x}=\frac{2}{3}$
Therefore, the formula of the compound is $P_{2} Q_{3}$.
$\therefore$ Number of tetrahedral voids $=2 x$
Since, $Q$ forms cubic close packing, the number of $Q$ atoms $=x$
$P$ occupy one third of tetrahedral voids, the number of $p$ atoms $=\frac{2}{3} x$
$\frac{\text { Number of } P \text { atoms }}{\text { Number of } Q \text { atoms }}$
$=\frac{2 \cdot x}{3 x}=\frac{2}{3}$
Therefore, the formula of the compound is $P_{2} Q_{3}$.
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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.