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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 empty space in this HCP unit cell is                                                                                         [JEE 2008]
  • a)
    74 %
  • b)
    47.6 % 
  • c)
    32 %
  • d)
    26 %
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In hexagonal systems of crystals, a frequently encountered arrangement...
Packing fraction = 74%
Empty space = 26%
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Most Upvoted Answer
In hexagonal systems of crystals, a frequently encountered arrangement...
As the packing efficiency of HCP is 74% , that means the remaining will be free space. so, 100-74= 26 that how it comes
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In hexagonal systems of crystals, a frequently encountered arrangement...
- **Calculation of Empty Space in HCP Unit Cell**
- **Total volume of the unit cell:**
- The total volume of the HCP unit cell can be calculated as the sum of the volumes occupied by the atoms and the empty space.
- The volume of the unit cell = 3 * Volume of one sphere (sphere at the corner) + 6 * Volume of one sphere (sphere at the face center)
- **Volume of spheres:**
- Volume of one sphere = (4/3) * π * r^3
- **Empty space in the unit cell:**
- The empty space in the unit cell is the difference between the total volume of the unit cell and the sum of the volumes of the spheres.
- Empty space = Total volume of the unit cell - (Number of spheres * Volume of one sphere)
- **Calculation:**
- Number of spheres in the unit cell = 3 (bottom layer) + 3 (top layer) = 6
- Total volume of the unit cell = 3 * (4/3) * π * r^3 + 6 * (4/3) * π * r^3
- Empty space = 3 * (4/3) * π * r^3 + 6 * (4/3) * π * r^3 - 6 * (4/3) * π * r^3
- **Final Calculation:**
- Empty space = 26% of the total volume of the unit cell
Therefore, the correct answer is option 'D', which is 26%.
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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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. 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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. 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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. 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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer?.
Solutions 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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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 [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of 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 [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer?, a detailed solution 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 empty space in this HCP unit cell is [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of 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 [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice 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 [JEE 2008]a)74 %b)47.6 %c)32 %d)26 %Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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