Question

The number of atoms per unit cell in a simple cubic, face-centered cubic and body-centred cubic are ...... respectively.

• A. $1,4,2$
• B. $4,1,2$
• C. $2,4,1$
• D. $4,8,2$

Answer 1

The correct option is A $1,4,2$

The number of atoms per unit cell in a simple cubic, face-centered cubic and body-centred cubic are 1,4,2 respectively.
(1)
The number of atoms contained in one simple cubic unit cell of monoatomic substance is 1.
8 atoms are present at 8 corners of a simple cubic unit cell. Each atom contributes one eigth to the unit cell. Total contribution $=8\times \frac{1}{8}=1$
(2)
The number of atoms contained in one face-centred cubic unit cell of monoatomic substance is 4.
8 atoms are present at 8 corners of a fcc unit cell. Each atom contributes one eigth to the unit cell. Total contribution $=8\times \frac{1}{8}=1$
6 atoms are present at 6 corners of a fcc unit cell. Each atom contributes one half to the unit cell. Total contribution $=6\times \frac{1}{2}=3$
Total number of atoms in one fcc unit cell $=1+3=4$.
(3)
The number of atoms contained in one body-centred cubic unit cell of monoatomic substance is 2.
8 atoms are present at 8 corners of a bcc unit cell. Each atom contributes one eigth to the unit cell. Total contribution $=8\times \frac{1}{8}=1$
1 atom is present at body centre of a bcc unit cell. The atom contributes fully to the unit cell. Total contribution $=1\times \frac{1}{1}=1$
Total number of atoms in one fcc unit cell $=1+1=2$.