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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 number of atoms in this HCP unit cells is                                                      [JEE 2008]
  • a)
    4
  • b)
    6
  • c)
    12
  • d)
    17
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In hexagonal systems of crystals, a frequently encountered arrangement...
Calculation of the number of atoms in HCP unit cells:

Step 1: Identification of the unit cell

- The unit cell of HCP is a hexagonal prism.

Step 2: Determining the number of atoms in the unit cell

- There is one atom at each corner of the hexagonal prism, which gives 6 atoms.
- In addition, there are three atoms in the center of the prism, sandwiched between the top and bottom hexagons.
- Therefore, the total number of atoms in the unit cell is 6 + 3 = 9.

Step 3: Multiplying by the number of unit cells

- HCP has a stacking sequence of ABAB, i.e., every other layer is identical.
- Therefore, there are two unit cells per layer.
- Multiplying the number of atoms in the unit cell by the number of unit cells gives 9 x 2 = 18.
- However, half of the atoms on the edges of the unit cell belong to neighboring unit cells, so we have to divide by 2 to get the number of atoms in a single unit cell.
- Therefore, the final answer is 18/2 = 9 atoms in a single HCP unit cell.

Therefore, the correct option is (B) 6 atoms.
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Community Answer
In hexagonal systems of crystals, a frequently encountered arrangement...
1/6×12 + 1/2×2 + 3 =6 
12 corner atoms, 2 face center atoms, 3middle atoms.
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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 number of atoms in this HCP unit cells is [JEE 2008]a)4b)6c)12d)17Correct answer is option 'B'. Can you explain this answer?
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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 number of atoms in this HCP unit cells is [JEE 2008]a)4b)6c)12d)17Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 number of atoms in this HCP unit cells is [JEE 2008]a)4b)6c)12d)17Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 number of atoms in this HCP unit cells is [JEE 2008]a)4b)6c)12d)17Correct answer is option 'B'. Can you explain this answer?.
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