Question:

A compound formed by elements $A$ and $B$ crystallises in the cubic structure, where $A$ atoms are present at the corners of a cube and $B$ atoms are present at the face centres. The formula of the compound is

Updated On: May 17, 2024
  • $A_2B_2$
  • $AB_3$
  • $AB$
  • $A_3B$
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The Correct Option is B

Solution and Explanation

A-atoms are present at the corners of a cube. So, the number of A-atoms per unit cell $=8\times\frac{1}{8}=1$
Similarly, 5-atoms are present at face centres of a cube.
So, the number of B-atoms per unit cell
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =6\times\frac{1}{2}=3$
Hence, the formula of compound is $A B3.$
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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. 

Solid State

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.