Question

An element having a bcc structure has $12.08\times {10}^{23}$ unit cells. The number of atoms in these cells is:

• A. $12.08\times {10}^{22}$
• B. $12.08\times {10}^{23}$
• C. $24.16\times {10}^{23}$
• D. $48.38\times {10}^{23}$

Answer 1

The correct option is C

$24.16\times {10}^{23}$

Explanation for correct option

(C)$24.16\times {10}^{23}$

Step1. BCC unit cell

• A body-centered cubic (BCC) unit cell contains one constituent particle (atom, molecule or ion) at its body center beside the ones that are at its corners.
• The number of atoms per unit cell in BCC is two.

Step2. Number of atoms in unit cell

$$\begin{gathered} \text{1unit cell of BCC=2 atoms} \\ 12.08\times {10}^{23}\text{unit cell of BCC has=2×}12.08\times {10}^{23} \\ =24.16\times {10}^{23} \end{gathered}$$

So, the number of atoms in this cell is $24.16\times {10}^{23}$.

Explanation for incorrect option

The number of atoms in this cell is $24.16\times {10}^{23}$. Hence options (A), (B), and (D) are incorrect.

Hence, option (C) is correct. The number of atoms in this cell is $24.16\times {10}^{23}$.