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In a face-centered cubic lattice, a unit cell is shared equally by how many unit cells ?

  1. A
    8
  2. B
    4
  3. C
    2
  4. D
    6

Solution & Step-by-step Explanation

In a face-centered cubic (FCC) lattice, each unit cell has 8 corner atoms and 6 face-centered atoms. The corner atoms are shared by 8 adjacent unit cells, while the face-centered atoms are shared by 2 adjacent unit cells. To determine how many unit cells share a single unit cell, we need to consider the sharing of the corner and face-centered atoms. Since each corner atom is shared by 8 unit cells and each face-centered atom is shared by 2 unit cells, the total number of unit cells that share a single unit cell is equal to the sum of the number of unit cells that share the corner atoms and the number of unit cells that share the face-centered atoms. However, this question is asking about the sharing of the unit cell itself, not the atoms within it. A unit cell in an FCC lattice is shared by 8 adjacent unit cells, but in the context of this question, it seems to be asking how many unit cells a single unit cell is shared with, in terms of being at the corner or face of adjacent cells. In that case, a unit cell is at the corner of 8 adjacent cells and at the face of 6 adjacent cells, but when considering how many cells it is shared with, it's more about how it's part of a larger structure. The correct interpretation in the context of crystal lattices and how unit cells are shared or contribute to the structure is that a unit cell in an FCC lattice contributes to or is part of 8 adjacent unit cells when considering the corners, but this doesn't directly answer the question as it's phrased. The question seems to imply a different kind of sharing or contribution, possibly referring to how many cells a single cell is directly adjacent to or part of in a lattice structure, which could be interpreted in a few ways. However, considering standard descriptions of lattice structures, a face-centered cubic unit cell is directly involved with or shared among its immediate neighbors in a way that's not fully captured by simply counting corner or face shares. For clarity and sticking to common descriptions in crystallography, the question's intent might be misunderstood without a visual aid or further context. Given the usual way these structures are described, a unit cell in an FCC lattice is part of a larger structure where it's directly connected to or shares space with adjacent cells, but the question's phrasing doesn't align perfectly with standard crystallographic terminology. Thus, the question might be seen as somewhat ambiguous without further clarification on what "shared equally" means in this context. However, considering the typical way of describing lattice structures and the connections between unit cells, the question seems to aim towards understanding the relationship between adjacent cells in a lattice.

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In a face-centered cubic lattice, a unit cell is shared equally by how many unit cells ?
A
8
B
4
C
2
D
6

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