12th chemistry solid state -Number of Atoms in a Unit Cell

Number of Atoms in a Unit Cell

Calculation of number of atoms in a unit cell The number of atoms in a unit cell can be calculated, by using the following approximations. An atom at the corner is shared by 8 unit cells. Hence, an atom at the corner contributes 1/8 to the unit cell. An atom at the face is shared by 2 unit cells. Hence, an atom at the face contributes 1/2 to the unit cell. An atom within the body of a unit cell is shared by no other unit cell. Hence, an atom at the body contributes singly, i.e., 1 to the unit cell.

Primitive Cubic Unit Cell

Open structure for a primitive cubic unit cell is shown in the given figure.

Actual portions belonging to one unit cell are shown in the given figure.

Total number of atoms in one unit cell

Let us see the packing in a simple cubic unit cell through this video.

Body-Centred Cubic Unit Cell

Open structure for a body-centred cubic unit cell is shown in the given figure.

Actual portions belonging to one unit cell are shown in the given figure.

Total number of atoms in one unit cell

= 8 corners per corner atom + 1 body-centre atom

Face-Centred Cubic Unit Cell

Open structure for a face-centred cubic unit cell is shown in given figure.

Actual portions of atoms belonging to one unit cell are shown in the given figure.

Total number of atoms in one unit cell

= 8 corner atoms atom per unit cell + 6 face-centred atoms atom per unit cell

Now, let us visualise the packing in face-centred cubic lattice through this video.

Questions asked in previous years’ board examinations

Ques. What is the total number of atoms per unit cell in a face-centred cubic (fcc) structure? (1 mark) −2008 CBSE Delhi Sol: The total number of atoms per unit cell in a face-centred cubic (fcc) structure is 4 (8 corner atoms atom per unit cell + 6 face-centred atoms atom per unit cell) Ques. What is the number of atoms per unit cell in a body-centred cubic structure? (1 mark) −2007 CBSE Delhi Sol: The number of atoms per unit cell in a body-centred cubic structure is 2 (8 corner atoms × atom per unit cell + 1 body-centre atom).