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Q.

How many atoms are there in a cube based unit cell having one atom on each corner and two atoms on each body diagonal?

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a

8

b

6

c

4

d

9

answer is D.

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Detailed Solution

detailed_solution_thumbnail

A cube has 8 corners, hence 8 atoms are positioned at each corner of the cube. However, these 8 atoms are distributed equally across 8 different units. Therefore, 
Atomic contribution at the corner = 8×18=1
In a cube, there are 4 body diagonals, and there are 2 atoms on each of them. These atoms are not shared by any other units because they are contained within the unit cell, Therefore,
Atomic contribution at the body diagonal = 2 ×4 = 8


So, the number of atoms in the cube-based unit cell is = 8 + 1 = 9

Therefore, the correct option is D 9

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