In a face-centered cubic lattice, a unit cell is shared equally by how many unit cells? [CBSE AIPMT 2005] (1)2 (2)4 (3)6 (4)8 plz explain?

Question

Answer

A unit cell is shared equally by 6 unit cells in fcc lattice. whereas 4 is total no. of atoms per unit cell.This is AIPMT 2005 question na Why all are answering 4 unit cell...?? Either download the PDF of Quest paper Aipmt 2005 with answer key or solve past yr papers..Don't give wrong information to others.

Answer

6.  there are six faces in a unit cell.  these 6 faces are not shared ie equally connected to 6 other unit cells..

Answer

by 4 unit cells ....

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4

Answer

Face-centered cubic (FCC) lattice:

A face-centered cubic (FCC) lattice is a type of crystal lattice structure that consists of atoms arranged in a cubic pattern. It is commonly found in many metallic elements and compounds.

Unit cell:

A unit cell is the smallest repeating unit of a crystal lattice. It represents the basic building block of the lattice structure. In the case of an FCC lattice, the unit cell consists of eight corner atoms and six face-centered atoms.

Sharing of unit cells:

To determine how many unit cells are shared equally in an FCC lattice, we need to consider the arrangement of atoms and the symmetry of the lattice structure.

In an FCC lattice, each corner atom is shared by eight adjacent unit cells, whereas each face-centered atom is shared by two adjacent unit cells. This is because the corner atoms are present at the corners of the unit cell and are shared by eight neighboring unit cells, while the face-centered atoms are present in the middle of each face and are shared by two neighboring unit cells.

Calculation:

To calculate the total number of unit cells that share a particular unit cell, we need to consider the contributions from both the corner atoms and the face-centered atoms.

Each corner atom contributes 1/8th of its presence to the unit cell, as it is shared equally by eight neighboring unit cells. Therefore, the total contribution from corner atoms is 8 * (1/8) = 1 unit cell.

Each face-centered atom contributes 1/2 of its presence to the unit cell, as it is shared equally by two neighboring unit cells. Therefore, the total contribution from face-centered atoms is 6 * (1/2) = 3 unit cells.

Adding the contributions from corner atoms and face-centered atoms, we get a total of 1 + 3 = 4 unit cells that share a particular unit cell in an FCC lattice.

Answer:

Therefore, in a face-centered cubic lattice, a unit cell is shared equally by 4 unit cells. Hence, the correct option is (2) 4.

Answer

Thanks

Answer

4

Answer

6 there are 6 face ina unit cell. these six faces are not shared  ie equally connected to 6 other unit celld

Answer

4

Answer

By 4unit cells
This is due to

(corners 8*1/8=1)+(face center 6*1/3)=4

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