Question

How many atoms can be assigned to its unit cell if an element forms?
(i) a body centred cubic cell, and?
(ii) a face centred cubic cell ?

Answer 1

Explanation:

) a face centred cubic cell? (ii) 1 body centre atom = 1X1= 1 atom .

Answer 2

Given: (i) a body-centred cubic cell.

(ii) a face-centred cubic cell.

To find: We have to find the number of atoms in each unit shell.

Solution:

• (i) A body-centred cubic cell.

A body-centred cubic shell has 8 atoms at eight corners of the cube which is equally shared by another 8 unit cells.

Thus the contribution of one unit shell is 8×1/8=1.

Again in body centred cubic shell, one atom is present in the centre.

So, the total number of toms is 1+1=2.

• (ii) A face-centred cubic cell.
• A face-centred cubic shell has 8 atoms at eight corners of the cube which is equally shared by another 8 unit cells.
• Thus the contribution of one unit shell is 8×1/8=1.
• Again in face centred cubic shell has six atoms in its faces.

So, the contribution of the atoms will be 6×1/2=3

So, the total number of toms is 1+3=4.