Question

The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively :

• A. 1:02:04
• B. 8:01:06
• C. 4:02:01
• D. 4:02:03

Answer 1

The Correct Option is A

To determine the ratio of the number of atoms in simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) structures, we need to understand the unit cell arrangement in each type of lattice:

1. Simple Cubic (SC):
   • A simple cubic unit cell has atoms only at the corners of the cube.
   • Each corner atom is shared by 8 adjacent unit cells, so each corner contributes \frac{1}{8} of an atom to the unit cell.
   • There are 8 corners, so the total contribution is 8 \times \frac{1}{8} = 1 atom per unit cell.
2. Body Centered Cubic (BCC):
   • In addition to the 8 corner atoms, BCC has one atom at the center of the cube.
   • The center atom contributes fully to the unit cell, so it counts as 1 whole atom.
   • The corner atoms contribute 1 atom, making a total of 1 + 1 = 2 atoms per unit cell.
3. Face Centered Cubic (FCC):
   • FCC has atoms at each corner, and one atom at the center of each face of the cube.
   • Each face atom is shared by 2 adjacent unit cells, contributing \frac{1}{2} of an atom per face.
   • There are 6 faces, resulting in a contribution of 6 \times \frac{1}{2} = 3 atoms from face-centered atoms.
   • Adding the 1 atom from the corners, the total is 1 + 3 = 4 atoms per unit cell.

Thus, the ratio of the number of atoms in SC: BCC: FCC is 1 : 2 : 4.

Therefore, the correct answer is 1:02:04.