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Question

# The number of atoms in the hcp unit cell is

A

$4$

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B

$6$

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C

$12$

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D

$13$

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Solution

## The correct option is B $6$The explanation for the correct option(B)$6$Hexagonal close-packingThe second row can be stacked on top of the first in a staggered pattern such that its spheres fit in the depressions of the first row.If the first row's arrangement of spheres is referred to as 'A-type, the second row's arrangement may be referred to as 'B' type.Number of atoms in hcp unit cell In HCP, there are 6 corner atoms in the top layer and 6 corner atoms in the bottom layer, so 12 atoms in the unit cell. The contribution of each atom in the unit cell is one-sixth.Two atoms are present at two face centers. The contribution of each atom in the unit cell is one-half. Three atoms are placed within the volume of the unit cell and the contribution of each atom is 1.So, the number of atoms in the hcp unit cell is =$12×\frac{1}{6}+2×\frac{1}{2}+3=6$The explanation for the incorrect optionThe number of atoms in the hcp unit cell is $6$. So, options (A), (C), and (D) are incorrect.Hence, the number of atoms in the hcp unit cell is $6$. Hence, option (B) is correct.

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