Atoms of element B form hcp lattice and those of the element A occupy 2/3 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?
Atoms of element B form hcp lattice and those of the element A occupy 2/3 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?
A3B4
A4B3
A2B3
A3B2
The Correct Option is D
Solution and Explanation
To determine the formula of the compound formed by elements A and B, we need to consider the ratio of the atoms in the compound based on their arrangement in the crystal lattice.
Given that the atoms of element B form a hexagonal close-packed (hcp) lattice, the closest packing ratio for this lattice is 2:1. This means that for every two atoms of element B, there is one atom of element A occupying the tetrahedral voids.
Since the atoms of element A occupy 2/3 of the tetrahedral voids, we can deduce that for every 2 atoms of element B, there will be 2/3 atoms of element A. Simplifying this ratio, we get:
2 atoms B : 2/3 atoms A
To simplify the ratio further, we can multiply it by 3 to eliminate the fraction:
(2 atoms B) x (3 atoms A / 2 atoms B) = 3 atoms A
Therefore, the formula of the compound formed by elements A and B is A3B2.
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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.