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In a hexaonal system system of cycstals,...

In a hexaonal system system of cycstals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are refular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-paked is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spherres are then placed overt the first layer so that they toych each other and represent the second layer so that they toych each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is convered with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be `r`.
The empty space in this hcp unit cell is

A

4

B

6

C

12

D

17

Text Solution

Verified by Experts

The correct Answer is:
B

Number of atoms in one unit cell
`=12xx(1)/(6)+3+2xx(1)/(2)=6`
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In hexagonal system of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagon and three atoms are sandwiched in between them. A space filling 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 sphere as closely as possible. Three spheres are then placed over the first layer so that they touch other and represent the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be same The volume of this HCP unit cell is

In hexagonal systems of crystals, a frequently ecounted arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are reqular hexagons and three atoms are sandwiched in between them. A space-filling 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 sphere 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 volume of this HCP unit cell is

Knowledge Check

  • In a hexaonal system system of cycstals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are refular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-paked is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spherres are then placed overt the first layer so that they toych each other and represent the second layer so that they toych each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is convered with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be r . The number of atom in this hcp unit cell is

    A
    `4`
    B
    `6`
    C
    `12`
    D
    `17`

  • In a hexaonal system system of cycstals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are refular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-paked is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spherres are then placed overt the first layer so that they toych each other and represent the second layer so that they toych each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is convered with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be r . The voume of this hcp unit cell is

    A
    `24sqrt2r^(3)`
    B
    `16sqrt2r^(3)`
    C
    `12sqrt2r^(3)`
    D
    `(64)/(3sqrt3r^(3))`

  • 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 are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (hcp), is constitued of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three 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 touched three spheres of the bottom layer. Finally, the second layer is convered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'. The volume of this hcp unit cell is

    A
    `24 sqrt(2)r^(3)`
    B
    `16 sqrt(2)r^(3)`
    C
    `12 sqrt(2)r^(3)`
    D
    `(64r^(3))/(3sqrt(3))`

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