Home
Class 12
CHEMISTRY
In hexagonal systems of crystals, a freq...

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 constituted 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 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 ‘r’.
The volume of this HCP unit cell is

A

`12sqrt2 r^3`

B

`24sqrt2 r^3`

C

`16sqrt2 r^3`

D

`64/(3sqrt3)r^3`

Text Solution

Verified by Experts

The correct Answer is:
B
`C=sqrt2/3` 4r=Height of the unit cell
Base area`=6xxsqrt3/4(2r)^2`
Volume of the hexagon=Area of base x Height `=6.sqrt2/3 a^2xxc=24sqrt2.r`
Promotional Banner

Topper's Solved these Questions

  • QUALITATIVE ANALYSIS PART 1

    RESONANCE ENGLISH|Exercise A.L.P|39 Videos

  • SOLID STATE

    RESONANCE ENGLISH|Exercise PHYSICAL CHEMITRY (SOLID STATE)|45 Videos

Similar Questions

Explore conceptually related problems

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 constituted 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 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 ‘r’. The empty space in this HCP unit cell is :

In a hexagonal system 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 hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-packed is constituted 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 overt the first layer so that they touch each other and represent the second layer so that they touch 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 converted 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 number of atom in this hcp unit cell is

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) 74% (b) 48.6% (c) 32% (d) 26%

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 hexagons and three atoms are sandwiched in between them. A space -filling model of this structure, called hexagonal close-packed (HCP), is consituted of a sphere on a flat surface surrouneded in the same plane by six identical spheres as closely possible. Three sphere are then palces over the first layer so that they touch each other and represent second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of enery sphere to be r. The number of atoms in the HPC unit cell is :

In a hexagonal crystal:

Draw a regular hexagon of side 5 cm.

The number of atoms present in a hexagonal close-packed unit cell is:

The number of atoms present in a hexagonal close-packed unit cell is:

In a regular hexagon ABCDEF, vec(AE)

RESONANCE ENGLISH-RANK BOOSTER-All Questions
  1. Statement-1 : The ratio of Zn^2+ and F^(-) per unit cell of ZnS and Ca...

    Text Solution

    |

  2. Assertion :In NaCIcrystal each Na^(+) ion is tourching 6 CI^(-) ion bu...

    Text Solution

    |

  3. In hexagonal systems of crystals, a frequently encountered arrangement...

    Text Solution

    |

  4. In a Carius determination, 0.25g of an organic substance gave 0.24g of...

    Text Solution

    |

  5. The type of seciconductor shown by crystal capable of showing Schotlky...

    Text Solution

    |

  6. When an atom or an ion is missing from its nomal lattice site a lattic...

    Text Solution

    |

  7. When an atom or an ion is missing from its normal lattice site, a latt...

    Text Solution

    |

  8. Only those atoms which four covalent bonds produce a repetitive three ...

    Text Solution

    |

  9. Only those atoms which four covalent bonds produce a repetitive three ...

    Text Solution

    |

  10. Only those atoms which four covalent bonds produce a repetitive three ...

    Text Solution

    |

  11. Column-I and Column-II contains four entries each.Entries of Column-I ...

    Text Solution

    |

  12. {:("Column-I","Column-II"),((A)"74% occupancy of space",(p)"cubic clos...

    Text Solution

    |

  13. A(2)B molecules(" molar mass " = 259.8 g//"ml") crystallises in a hex...

    Text Solution

    |

  14. NA spheres of radius 'R' are melted in x xxNA smaller spheres, so that...

    Text Solution

    |

  15. Total number of faces in a truncated octahedron=x Total number of fa...

    Text Solution

    |

  16. An ionic compound MCl is simultaneously doped with 10^(-6) mole % NCl2...

    Text Solution

    |

  17. Explain the term transuranic elements?

    Text Solution

    |

  18. Ionic solid B^+A^(-) crystallizes in rock salt type of structure.1.296...

    Text Solution

    |

  19. The arrangement of elements in a group of three was done by Döbereiner...

    Text Solution

    |

  20. In F.C.C. arrangement of identical spheres, distance between two neare...

    Text Solution

    |