Question

The number of atoms present in a unit cell of a monoatomic element of a simple cubic lattice, body-centered cubic and face-centered cubic respectively is:

• A. 2, 2, and 4
• B. 1, 2, and 4
• C. 1, 2, and 6
• D. 1, 4, and 6

Answer 1

Answer: (B)

1, 2, and 4

$1.$ For simple cubic

Atoms presents at body corners which contributes $\frac{1}{8}$ to the cell.

$Z_{effective}=\frac{1}{8}\times 8=1$

$2.$ For body centered cubic

One atom at body centre and $8$ at body corners.

$Z_{effective}=\frac{1}{8}\times 8+1=2$

$3.$ For face centered cubic:

$6$ atoms at face centres and $8$ at body corners

$Z_{effective}=8\times \frac{1}{8}+\frac{1}{2}\times 6=4$