How many number of atoms are there in a cube based unit cell, having one atom on each corner and two atoms on each body diagonal of cube?
How many number of atoms are there in a cube based unit cell, having one atom on each corner and two atoms on each body diagonal of cube?
- 4
- 8
- 9
- 6
The Correct Option is C
Solution and Explanation
In a cube-based unit cell, there is one atom located at each corner and two atoms located on each body diagonal.
The number of corners in a cube is 8, and each corner is shared by 8 unit cells. Therefore, the contribution of atoms at the corners is:
8 corners * 1/8 atom per corner = 1 atom
The number of body diagonals in a cube is 4, and each body diagonal is shared by 2 unit cells. Therefore, the contribution of atoms on the body diagonals is:
4 body diagonals * 2 atoms per diagonal = 8 atoms
Adding the contributions from the corners and body diagonals, we get:
1 atom (corners) + 8 atoms (body diagonals) = 9 atoms
So, the correct answer is (C) 9.
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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.