Question

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? 

• A. 4
• B. 8
• C. 9
• D. 6

Answer 1

The Correct Option is C

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.

Answer 2

Atoms in a Cube-Based Unit Cell 

Let's analyze the unit cell:

• 1 atom on each corner of the cube → Total corners = 8
• Each corner atom is shared by 8 unit cells → Contribution = \( \frac{1}{8} \times 8 = 1 \) atom

 

2 atoms on each body diagonal of the cube:

• Total number of body diagonals in a cube = 4
• 2 atoms per diagonal × 4 diagonals = 8 atoms
• Each of these atoms lies completely within the unit cell → Contribution = 8 atoms

 

Total atoms = 1 (from corners) + 8 (from body diagonals) = 9 atoms

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Correct Answer: 9