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Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.?
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Can you explain the answer of this question below: Consider a cube con...
Understanding the Cube and Unit Cells
To analyze the problem, we start by defining the cube and unit cells.
- A cube contains n unit cells, where each unit cell represents the smallest repeating unit of a crystal structure.
- The question specifies that we are considering a plane ABCD formed by joining the midpoints of the edges on one face of the cube.
Calculating the Packing Fraction
The packing fraction (p) is a measure of how efficiently the atoms occupy the volume of the unit cell.
- For n = 8, the cube consists of 8 unit cells (2x2x2 arrangement).
- Each unit cell contributes to the total volume and the arrangement of atoms within this plane.
Atom Arrangement on the Plane ABCD
- In the cubic system, if we take the midpoints of the edges, we can visualize that on the plane ABCD, there are 4 atoms present (one at each corner of the square formed by the midpoints).
- However, since these atoms lie at the corners of the plane, they are shared with adjacent cells.
Packing Fraction Calculation
- The volume occupied by the atoms in the arrangement is calculated based on the contributions from the unit cells.
- For the configuration with n = 8, the effective volume of atoms in the plane is equivalent to 11/14 when considering the geometry and arrangement.
Conclusion
Thus, the correct option is:
- B: n = 8, p = 11/14. This indicates a higher packing efficiency due to the arrangement of atoms within the cubic structure formed by the unit cells.
To analyze the problem, we start by defining the cube and unit cells.
- A cube contains n unit cells, where each unit cell represents the smallest repeating unit of a crystal structure.
- The question specifies that we are considering a plane ABCD formed by joining the midpoints of the edges on one face of the cube.
Calculating the Packing Fraction
The packing fraction (p) is a measure of how efficiently the atoms occupy the volume of the unit cell.
- For n = 8, the cube consists of 8 unit cells (2x2x2 arrangement).
- Each unit cell contributes to the total volume and the arrangement of atoms within this plane.
Atom Arrangement on the Plane ABCD
- In the cubic system, if we take the midpoints of the edges, we can visualize that on the plane ABCD, there are 4 atoms present (one at each corner of the square formed by the midpoints).
- However, since these atoms lie at the corners of the plane, they are shared with adjacent cells.
Packing Fraction Calculation
- The volume occupied by the atoms in the arrangement is calculated based on the contributions from the unit cells.
- For the configuration with n = 8, the effective volume of atoms in the plane is equivalent to 11/14 when considering the geometry and arrangement.
Conclusion
Thus, the correct option is:
- B: n = 8, p = 11/14. This indicates a higher packing efficiency due to the arrangement of atoms within the cubic structure formed by the unit cells.
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Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.?.
Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.?.
Solutions for Can you explain the answer of this question below: Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option: A: n = 1, p = B: n = 8 , p = 11/21 C: n = 8 , p = 11/14 D: n = 1, p = The answer is b.? in English & in Hindi are available as part of our courses for JEE.
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