Chemistry: Solid State: Number of Atoms in Cubic Unit Cells and Simple Cubic Unit Cell (For CBSE, ICSE, IAS, NET, NRA 2022)

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Number of Atoms in Cubic Unit Cells

  • In the cubic crystal system, the three distances are equal, and all the three angles are right angles.
  • The unit cells of three possible lattice types viz. , primitive or simple cubic, body centered cubic and the face centered cubic, belonging to cubic crystal system.

Number of Atoms Per Unit Cell

  • In unit cells the atoms are present in the corners, in body center and on face centers.
  • All the atoms do not belong to a single unit cell as they are shared between different unit cells.
  • It is important to know the number of atoms per unit cell.
Number of Atoms

Simple Cubic Unit Cell

  • The simple or primitive unit cell has the atoms at the corners of the cube.
  • A lattice point at the corner of the unit cell is shared by eight-unit cells, Therefore, the contribution of an atom at the corner to the unit cell will be 1/8.
  • The number of atoms per unit cell can be calculated as follows:

1. Number of corner atoms = 8

2. Contribution of each corner atom =

3. The number of atoms in a simple cubic unit cell =

Simple Cubic Unit Cell

Body Centered Cubic Unit Cell

  • A body centered cubic (bcc) unit cell has lattice points at the center of the cube.
  • The atom in the center of the cube belongs to the unit cell.
  • The corner atom in the simple cubic unit cell is shared by eight-unit cells.

The number of atoms per unit cell can be calculated as:

1. Number of corner atoms = 8

2. Contribution of each corner atom =

3. Contribution of all the corner atoms to the unit cell =

4. Number of atoms at the center of the cube = 1

5. Contribution to the unit cell = 1 (as it is not shared)

6. The number of atoms in a body centered cubic unit cell =

Faces Centered Cubic Unit Cell

  • A face centered cubic (FCC) unit cell has atoms at the corners and at the center of each face.
  • It has eight lattice points at the corners and six at the face centers.
  • A face centered lattice point is shared by two-unit cells

1. Number of corner atoms = 8

2. Contribution of each corner atom =

3. Contribution of all the corner atoms to the unit cell =

4. Number of atoms at the face center = 6

5. Contribution of each atom at the face center =

6. Contribution of all the face centered atoms to the unit cell =

7. The number of atoms points in a face centered cubic unit cell =

Faces Centered Cubic Unit Cell

The number of atoms per unit cell in different types of cubic unit cells is given in the following table:

Different Types of Unit Cells

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