question_answer

           

DIRECTION: Read the passage given below and answer the questions that follows:

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms sandwiched in between them. A space-of this model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. There spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'.

The number of atoms in the HCP unit cell is

A) 4

B) 6

C) 12

D) 17

Correct Answer: B

Solution :

[b] In 1 unit cell of hcp, the number of atoms can be calculated as follows

Number of atoms in a unit cell of hcp

\[=12\times \frac{1}{6}+2\times \frac{1}{2}+3=6\]

i.e. the correct answer is option [b]

[: in a hexagonal close packing (hcp) the spheres in the first and third layers are vertically aligned. (See figure below]