Question:

A crystalline solid has $A^-$ ions at the corners and face centres whereas $B^+$ ions are at the body centre and edge centres of the unit cell. The simplest formula of the compound will be

Updated On: May 12, 2024
  • $A_2B$
  • $AB_2$
  • $AB_3$
  • $AB$
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The Correct Option is D

Solution and Explanation

Number of $A^-$ ions= $ { $\underset{\text{(at corners)}}{ {\frac{1}{8} \times 8 + }}$ $\underset{\text{(at face centres)}}{ {\frac{1}{2} \times 6 = 4 }}$ }$
Number of $B^+$ ions = $ { $\underset{\text{(atbody centre)}}{ {1 + }}$ $\underset{\text{(at edge centres)}}{ {12 \times \frac{1}{4} = 4 }}$ }$
$ { (A^-)_4 (B^+)_4 = A_4 B_4 = AB}$
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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.